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Lecture Materials
TOPIC 3
YIELD CURVES AND INTEREST FORECASTS
ECONOMICS MONEY MARKETS AND BANKING
James M Johannes Interim Associate Dean for Executive and Evening MBA Programs
Aschenbrener Chair of Banking amp Finance Graduate School of Banking-Prochnow Professor of Banking
Director Puelicher Center for Banking Education Director Officer Education Program
University of Wisconsin-Madison Madison Wisconsin
jjohannesbuswiscedu 608-265-2323
August 2-5 2016
Topic 3
Yield Curves and Interest Forecasts
I Yield Curve (Term Structure of Interest Rates) Basics1 What is the Yield Curve
bull Interest rates on financial instruments vary because of default risk liquidity risk call provisions etc
bull Holding all the above constant it also appears rates vary because of maturity The relationship between interest rates and maturity all else fixed is called the term structure of interest rates or the yield curve
bull Where do we find the yield curve
bull Typical yield curve
2
Yield Curves are Important so Found Everywhere
3
Note downward sloping when rates high
Flatter when rates moderate
Upward sloping when rates low
4
II Determinants of the Yield Curve ShapeA Segmented Markets View independent markets
i S i S
10
D D
Short-term funds Long-term funds
Players Fed Banks Insurancepension companies
Instruments T-bills commercial paper Mortgages bonds note
5
bull Implied Yield Curve
i
10 bull bull
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
6
bull Implied Yield Curve
i
10
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
08bull bull
bull
bull
Fed sold T-bills from its portfolio This should lower T-bill prices and raise short term rates
Fed then purchased long term Treasury Securities trying to drive long term debt prices up and long rates down
7
Observation 1 Twist does not change ldquomoneyrdquo in circulation-if the Fed sells one thing and buys another the ldquomoneyrdquo stays the same
technically the monetary base more on this friday 8
Government Yield Curve
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8
Maturity (years)
Inte
rest
Rat
ePoint 2 Operation Twist no help for bankers
Original spread 4
New spread 1
9
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
1 | 2 | ||
2 | 3 | ||
3 | 4 | ||
4 | 5 | ||
5 | 6 | ||
6 | 7 | ||
7 | 8 | ||
8 | 9 |
1 | |
2 | |
3 | |
4 | |
5 | |
6 | |
7 | |
8 |
Topic 3
Yield Curves and Interest Forecasts
I Yield Curve (Term Structure of Interest Rates) Basics1 What is the Yield Curve
bull Interest rates on financial instruments vary because of default risk liquidity risk call provisions etc
bull Holding all the above constant it also appears rates vary because of maturity The relationship between interest rates and maturity all else fixed is called the term structure of interest rates or the yield curve
bull Where do we find the yield curve
bull Typical yield curve
2
Yield Curves are Important so Found Everywhere
3
Note downward sloping when rates high
Flatter when rates moderate
Upward sloping when rates low
4
II Determinants of the Yield Curve ShapeA Segmented Markets View independent markets
i S i S
10
D D
Short-term funds Long-term funds
Players Fed Banks Insurancepension companies
Instruments T-bills commercial paper Mortgages bonds note
5
bull Implied Yield Curve
i
10 bull bull
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
6
bull Implied Yield Curve
i
10
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
08bull bull
bull
bull
Fed sold T-bills from its portfolio This should lower T-bill prices and raise short term rates
Fed then purchased long term Treasury Securities trying to drive long term debt prices up and long rates down
7
Observation 1 Twist does not change ldquomoneyrdquo in circulation-if the Fed sells one thing and buys another the ldquomoneyrdquo stays the same
technically the monetary base more on this friday 8
Government Yield Curve
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8
Maturity (years)
Inte
rest
Rat
ePoint 2 Operation Twist no help for bankers
Original spread 4
New spread 1
9
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
1 | 2 | ||
2 | 3 | ||
3 | 4 | ||
4 | 5 | ||
5 | 6 | ||
6 | 7 | ||
7 | 8 | ||
8 | 9 |
1 | |
2 | |
3 | |
4 | |
5 | |
6 | |
7 | |
8 |
I Yield Curve (Term Structure of Interest Rates) Basics1 What is the Yield Curve
bull Interest rates on financial instruments vary because of default risk liquidity risk call provisions etc
bull Holding all the above constant it also appears rates vary because of maturity The relationship between interest rates and maturity all else fixed is called the term structure of interest rates or the yield curve
bull Where do we find the yield curve
bull Typical yield curve
2
Yield Curves are Important so Found Everywhere
3
Note downward sloping when rates high
Flatter when rates moderate
Upward sloping when rates low
4
II Determinants of the Yield Curve ShapeA Segmented Markets View independent markets
i S i S
10
D D
Short-term funds Long-term funds
Players Fed Banks Insurancepension companies
Instruments T-bills commercial paper Mortgages bonds note
5
bull Implied Yield Curve
i
10 bull bull
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
6
bull Implied Yield Curve
i
10
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
08bull bull
bull
bull
Fed sold T-bills from its portfolio This should lower T-bill prices and raise short term rates
Fed then purchased long term Treasury Securities trying to drive long term debt prices up and long rates down
7
Observation 1 Twist does not change ldquomoneyrdquo in circulation-if the Fed sells one thing and buys another the ldquomoneyrdquo stays the same
technically the monetary base more on this friday 8
Government Yield Curve
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8
Maturity (years)
Inte
rest
Rat
ePoint 2 Operation Twist no help for bankers
Original spread 4
New spread 1
9
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
1 | 2 | ||
2 | 3 | ||
3 | 4 | ||
4 | 5 | ||
5 | 6 | ||
6 | 7 | ||
7 | 8 | ||
8 | 9 |
1 | |
2 | |
3 | |
4 | |
5 | |
6 | |
7 | |
8 |
Yield Curves are Important so Found Everywhere
3
Note downward sloping when rates high
Flatter when rates moderate
Upward sloping when rates low
4
II Determinants of the Yield Curve ShapeA Segmented Markets View independent markets
i S i S
10
D D
Short-term funds Long-term funds
Players Fed Banks Insurancepension companies
Instruments T-bills commercial paper Mortgages bonds note
5
bull Implied Yield Curve
i
10 bull bull
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
6
bull Implied Yield Curve
i
10
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
08bull bull
bull
bull
Fed sold T-bills from its portfolio This should lower T-bill prices and raise short term rates
Fed then purchased long term Treasury Securities trying to drive long term debt prices up and long rates down
7
Observation 1 Twist does not change ldquomoneyrdquo in circulation-if the Fed sells one thing and buys another the ldquomoneyrdquo stays the same
technically the monetary base more on this friday 8
Government Yield Curve
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8
Maturity (years)
Inte
rest
Rat
ePoint 2 Operation Twist no help for bankers
Original spread 4
New spread 1
9
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
1 | 2 | ||
2 | 3 | ||
3 | 4 | ||
4 | 5 | ||
5 | 6 | ||
6 | 7 | ||
7 | 8 | ||
8 | 9 |
1 | |
2 | |
3 | |
4 | |
5 | |
6 | |
7 | |
8 |
Note downward sloping when rates high
Flatter when rates moderate
Upward sloping when rates low
4
II Determinants of the Yield Curve ShapeA Segmented Markets View independent markets
i S i S
10
D D
Short-term funds Long-term funds
Players Fed Banks Insurancepension companies
Instruments T-bills commercial paper Mortgages bonds note
5
bull Implied Yield Curve
i
10 bull bull
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
6
bull Implied Yield Curve
i
10
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
08bull bull
bull
bull
Fed sold T-bills from its portfolio This should lower T-bill prices and raise short term rates
Fed then purchased long term Treasury Securities trying to drive long term debt prices up and long rates down
7
Observation 1 Twist does not change ldquomoneyrdquo in circulation-if the Fed sells one thing and buys another the ldquomoneyrdquo stays the same
technically the monetary base more on this friday 8
Government Yield Curve
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8
Maturity (years)
Inte
rest
Rat
ePoint 2 Operation Twist no help for bankers
Original spread 4
New spread 1
9
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
1 | 2 | ||
2 | 3 | ||
3 | 4 | ||
4 | 5 | ||
5 | 6 | ||
6 | 7 | ||
7 | 8 | ||
8 | 9 |
1 | |
2 | |
3 | |
4 | |
5 | |
6 | |
7 | |
8 |
II Determinants of the Yield Curve ShapeA Segmented Markets View independent markets
i S i S
10
D D
Short-term funds Long-term funds
Players Fed Banks Insurancepension companies
Instruments T-bills commercial paper Mortgages bonds note
5
bull Implied Yield Curve
i
10 bull bull
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
6
bull Implied Yield Curve
i
10
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
08bull bull
bull
bull
Fed sold T-bills from its portfolio This should lower T-bill prices and raise short term rates
Fed then purchased long term Treasury Securities trying to drive long term debt prices up and long rates down
7
Observation 1 Twist does not change ldquomoneyrdquo in circulation-if the Fed sells one thing and buys another the ldquomoneyrdquo stays the same
technically the monetary base more on this friday 8
Government Yield Curve
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8
Maturity (years)
Inte
rest
Rat
ePoint 2 Operation Twist no help for bankers
Original spread 4
New spread 1
9
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
1 | 2 | ||
2 | 3 | ||
3 | 4 | ||
4 | 5 | ||
5 | 6 | ||
6 | 7 | ||
7 | 8 | ||
8 | 9 |
1 | |
2 | |
3 | |
4 | |
5 | |
6 | |
7 | |
8 |
bull Implied Yield Curve
i
10 bull bull
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
6
bull Implied Yield Curve
i
10
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
08bull bull
bull
bull
Fed sold T-bills from its portfolio This should lower T-bill prices and raise short term rates
Fed then purchased long term Treasury Securities trying to drive long term debt prices up and long rates down
7
Observation 1 Twist does not change ldquomoneyrdquo in circulation-if the Fed sells one thing and buys another the ldquomoneyrdquo stays the same
technically the monetary base more on this friday 8
Government Yield Curve
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8
Maturity (years)
Inte
rest
Rat
ePoint 2 Operation Twist no help for bankers
Original spread 4
New spread 1
9
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
1 | 2 | ||
2 | 3 | ||
3 | 4 | ||
4 | 5 | ||
5 | 6 | ||
6 | 7 | ||
7 | 8 | ||
8 | 9 |
1 | |
2 | |
3 | |
4 | |
5 | |
6 | |
7 | |
8 |
bull Implied Yield Curve
i
10
1 30 maturity
bull Operation Twist (early 1960rsquos) To raise short rates and lower long rates Fed was to sell bills and buy bonds
12
08bull bull
bull
bull
Fed sold T-bills from its portfolio This should lower T-bill prices and raise short term rates
Fed then purchased long term Treasury Securities trying to drive long term debt prices up and long rates down
7
Observation 1 Twist does not change ldquomoneyrdquo in circulation-if the Fed sells one thing and buys another the ldquomoneyrdquo stays the same
technically the monetary base more on this friday 8
Government Yield Curve
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8
Maturity (years)
Inte
rest
Rat
ePoint 2 Operation Twist no help for bankers
Original spread 4
New spread 1
9
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
1 | 2 | ||
2 | 3 | ||
3 | 4 | ||
4 | 5 | ||
5 | 6 | ||
6 | 7 | ||
7 | 8 | ||
8 | 9 |
1 | |
2 | |
3 | |
4 | |
5 | |
6 | |
7 | |
8 |
Observation 1 Twist does not change ldquomoneyrdquo in circulation-if the Fed sells one thing and buys another the ldquomoneyrdquo stays the same
technically the monetary base more on this friday 8
Government Yield Curve
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8
Maturity (years)
Inte
rest
Rat
ePoint 2 Operation Twist no help for bankers
Original spread 4
New spread 1
9
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
1 | 2 | ||
2 | 3 | ||
3 | 4 | ||
4 | 5 | ||
5 | 6 | ||
6 | 7 | ||
7 | 8 | ||
8 | 9 |
1 | |
2 | |
3 | |
4 | |
5 | |
6 | |
7 | |
8 |
Government Yield Curve
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8
Maturity (years)
Inte
rest
Rat
ePoint 2 Operation Twist no help for bankers
Original spread 4
New spread 1
9
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
1 | 2 | ||
2 | 3 | ||
3 | 4 | ||
4 | 5 | ||
5 | 6 | ||
6 | 7 | ||
7 | 8 | ||
8 | 9 |
1 | |
2 | |
3 | |
4 | |
5 | |
6 | |
7 | |
8 |
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
1 | 2 | ||
2 | 3 | ||
3 | 4 | ||
4 | 5 | ||
5 | 6 | ||
6 | 7 | ||
7 | 8 | ||
8 | 9 |
1 | |
2 | |
3 | |
4 | |
5 | |
6 | |
7 | |
8 |
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
1 | 2 | ||
2 | 3 | ||
3 | 4 | ||
4 | 5 | ||
5 | 6 | ||
6 | 7 | ||
7 | 8 | ||
8 | 9 |
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
Credit Policy (like a pure twist operation) can be neutral as far as the money supply goes but can also be a credit policy that is not neutral in outcome For example suppose the Fed ldquotwistsrdquo by selling Treasury securities and buying Mortgage backed securities Money supply stays the same but the Fed provides ldquocreditrdquo directlyand specifically to the housing sector Credit policy is not ldquomonetaryrdquo policy because it does not increase bank reserves or the monetary base
Fiscal policy (ldquogovernment spendingrdquo) Fed lending $ it earned off investing bank reserves in treasury securities ($ it could have given back to the Treasury)to JPMorgan to purchase Bear Stearns or the $50 billion dollars the Fed loaned its ldquosubsidiariesrdquo Maiden Lane II and III to purchase residential mortgage-backed securities from AIG and multi-sector collateralized debt obligations on which AIG has written credit default swap contracts to keep AIG afloat
Good point to bring up the many different dimensions of ldquomonetary policyrdquo
Pure Monetary policy is usually viewed as something that affects the money supply monetary base or bank reserves or maybe basic interest rate levels
10
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
BPure Expectations View (sometimes called the Rational Expectations View)1 Example Suppose an investor has a two-year time
horizon (holding period) Suppose further that 1-year and 2-year deposits exist Suppose further that the current 1-year rates is 4 and the depositor thinks the 1-year rate one year from now will be 10 What rate would you have to offer to get this depositor to put money in a 2-year deposit
bull What does the depositor expect to make on two 1-year deposits (Letrsquos ignore compounding)
First year return + expected second year return
04 + 10 = 14 = 1411
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
bull What would seller of 2-year deposithave to offer to attract a buyer
R2 + R2 = 14
2 R2 = 14
R2 = 07 = 7
12
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
2 Implications for Yield Curve
bull Example shows that the 2-year rate will end up being roughly the average of the current 1-year rate and the expected 1-year rate ie
bull This implies that the yield curve is drawn for some market expectation of short-term rates in the future
i
Yield curve given the
07 bull Market thinks the 1-year
rate next year is going to be
04 bull 10
1 2 maturity
2100407 +
=
What if This Doesnrsquot Hold
a) If R2 lt 7 nobody will buy 2yr Bonds Price will fall rate will increase
b) If R2 gt 7 everybody will buy 2yr Bonds Price will Rise rate will fall
13
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
bull This implies that the ldquoexpectedrdquo future direction of rates is embedded in the yield curve To see this what if the market thinks the 1-year rate next year will be 4 or 20
I
12 bull If 1-year rate next year expected to be 20
07 bull If 1-year rate next year expected to be 10
04 bull bull If 1-year rate next year expected to be 4
03 bull If 1-year rate next year expected to be 2
1 2 maturity
22004R2
+=
21004R2
+=
20404R2
+=
20204R2
+=
14
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
15
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
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061978 | |
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00064762908 | |
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061980 | |
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061982 | |
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061984 | |
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061988 | |
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061992 | |
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061994 | |
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00072107502 | |
00063107566 |
bull Conclusion (compare to picture of typical yield curve)
Yield Curve Slope
Marketsrsquo Guess of Where Rates are Headed
Flat No change in rates
Upward Rates will rise
Downward Rates will fall16
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
bull Formal yield curve forecasts
Let Ri = current known rate from the WSJ on i period
Investments
tFi = forward rates = marketsrsquo guess of rate on i
period investments t periods from now
Then
2R2 = R1 + 1F1 (invest in a 2 yr or two 1 yrs)
3R3 = R1 + 21F2 (invest in a 3 yr or a one and a two)
3R3 = 2R2 + 2F1 (invest in a 3 yr or a two and a one)
Solutions
3F2RR
3F2RR
2FRR
12
2
11
11
3
1
2
+=
+=
+=
2
317
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
Example Yield Curve on June 2 2016
R1 = 0068 R2 = 0089R3 = 0103
What does the market think the 1-year rate will be in 2017
2 R2 = R1 + 1F1
1F1 = 2 R2 - R1 = 2(0089) - 0068 = 011Last year 1F1 = 011 so it overestimated
What does the market think the 1-year rate will be in Aug 20183R3 = 2R2 + 2F1
2F1 = 3(0103) - 2(0089) = 0131 18
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
One year Implied Forward
Graph found in Monetary trends Forward rates- numbers differ a little from pure forward because they interpolate and smooth 19
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
Four Applications of this Theory
1 Riding the yield curve
2 Loan interest swaps
3 QErsquos and ldquoTwistrdquo
4 Forecasting rates
20
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
21
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
III Yield Curve Games
A Riding the Yield Curve for Fun and Profit
bull Basic idea Assuming a positively sloped yield curve purchase a security with a maturity longer than your expected holding period
bull Rationale You will make money because 1) longer maturities pay higher rates 2) when you sell it in the security will have a shorter maturity hence lower rates hence a capital gain
Yield
07
04
1 2 maturity (years) 22
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
bull Example You want to invest for 1 year Current 1-year rate is 4 2-year rate is 7
-- If you buy 1-year security make 4
-- If ldquoriderdquo price per dollar of face of 2-year security is 8734 If sell in one year when 1-year rate is 4 get 9615
10110098734
87349615Profit ==minus
=
87342(107)
100Price
100 2
(107) Price
==
=
9615(104)100Price
100 (104) Price
==
=
23
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
bull Will this work in an ldquoefficient marketrdquo
-- What will you be able to sell the security at next year The market expects the rate on 1-year securities to be 10 This implies the price will be 9090
bull NOTE You will make money riding the yield curve as long as the 1-year rate next year turns out to be less than the market forecast If the rate turns out to be more than the market forecast you will lose money The market forecast is a ldquobreakevenrdquo rate
40408734
87349090Profit ==minus
=minus
24
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
What if 1 year rate next year ends up 14
08734
87348772Profit asympminus
=minus
25
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
Forward Rate - Actual Rate
-40
-30
-20
-10
00
10
20
30
40
061976
061978
061980
061982
061984
061986
061988
061990
061992
061994
061996
061998
062000
062002
Rates went up more than the market thought ie got burned is you rode
(markets underestimated inflation)
Article recom -mands riding
If positive market overestimated what rates would be ie rate ended up less than the market expected
Forwards over estimate in part because the risk premium is not netted out of the long rate before the calculation is done 26
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
061976 | |
00150397834 | |
00142374434 | |
00150317838 | |
00117218389 | |
00144256815 | |
00058228906 | |
00104353405 | |
00121364464 | |
00124329953 | |
00064256449 | |
00086158825 | |
0005210293 | |
00023102794 | |
00032054151 | |
-00007969586 | |
00030018323 | |
00037033754 | |
00012045251 | |
00036041107 | |
00049049283 | |
00040067934 | |
00021078269 | |
00011033482 | |
061978 | |
00028009226 | |
-00020996676 | |
-0006399549 | |
-00144922943 | |
-00146683574 | |
-00126695014 | |
-00092726021 | |
-00104754717 | |
-00078808073 | |
-00067895024 | |
-00012895024 | |
-00076888199 | |
-00133771981 | |
-00189754137 | |
-00315451101 | |
-0018419735 | |
-00074700685 | |
-00125689141 | |
-0029772015 | |
-00289780548 | |
00064762908 | |
00231564872 | |
00135003291 | |
061980 | |
-00082867096 | |
-00069923712 | |
-00086997758 | |
-00245857765 | |
-00200641174 | |
-00079442897 | |
-00212410589 | |
-0004363123 | |
-00088982763 | |
-0022197472 | |
-00013528744 | |
-00155893348 | |
-00173881697 | |
-00067834133 | |
0010200309 | |
00329022188 | |
00050196513 | |
-00058828445 | |
00009054671 | |
0009600706 | |
00045050548 | |
00108042464 | |
00015170813 | |
061982 | |
00293276934 | |
0023671085 | |
00339780244 | |
00190692371 | |
00153375229 | |
00179516481 | |
00112464095 | |
00132475946 | |
00130352531 | |
00126319416 | |
00042319651 | |
0005024658 | |
00065217877 | |
0014526382 | |
00161360294 | |
00139525999 | |
0012747153 | |
00167483971 | |
00134498271 | |
00095511178 | |
00113468758 | |
00082562759 | |
00120587587 | |
061984 | |
00191644917 | |
00146332767 | |
00192344506 | |
00248441839 | |
00215627299 | |
00201660843 | |
00155759585 | |
00119708574 | |
00242657655 | |
0025882692 | |
00252797437 | |
00172734787 | |
00163767754 | |
00176733087 | |
00188766263 | |
0018366892 | |
00161454208 | |
00090213987 | |
00094156038 | |
00130120435 | |
00095030272 | |
0003106351 | |
00076165401 | |
061986 | |
0011415056 | |
00096151043 | |
00121318049 | |
00104296633 | |
00089217769 | |
00089151129 | |
00072191435 | |
0008118271 | |
0003114345 | |
00054253897 | |
00172539813 | |
0016655515 | |
00117541432 | |
0008048435 | |
00142416922 | |
00225609815 | |
00125498224 | |
00156444247 | |
0016338284 | |
00101273443 | |
00082293881 | |
00077314363 | |
00111335196 | |
061988 | |
00064260696 | |
00100195618 | |
00072126654 | |
00011053279 | |
-00012966722 | |
00014009175 | |
00006015497 | |
-00007986819 | |
00043011043 | |
00056007407 | |
00062001468 | |
0004900083 | |
-00042995458 | |
-00011998521 | |
00035003327 | |
00020000093 | |
00011000835 | |
-00007996658 | |
00015026779 | |
00028062529 | |
00051072358 | |
00072094465 | |
00086094535 | |
061990 | |
0006004484 | |
00058072741 | |
00085095026 | |
00090101255 | |
00084078371 | |
00093063148 | |
0013522515 | |
0010733876 | |
00156460526 | |
00153474492 | |
00107398097 | |
00125338473 | |
00175350014 | |
00151399414 | |
00146352468 | |
00160319377 | |
00185427972 | |
00153404771 | |
00148629957 | |
00150811583 | |
00246073879 | |
00220037009 | |
00211038103 | |
061992 | |
00165557529 | |
00173501015 | |
00130488564 | |
00118588964 | |
0017778125 | |
00213888632 | |
00189765314 | |
00148487571 | |
00133372012 | |
00108348702 | |
00106371904 | |
00131371257 | |
00123347927 | |
00120303171 | |
00095232295 | |
00077222846 | |
00113324773 | |
00127347457 | |
00087347692 | |
00075346587 | |
00086443252 | |
00097508395 | |
00136413636 | |
061994 | |
0012240055 | |
00104364153 | |
00091375284 | |
00081362266 | |
00062349258 | |
00099189005 | |
00127197665 | |
00109157545 | |
00086115099 | |
0008708469 | |
00070027264 | |
00021006058 | |
00022034189 | |
00059050024 | |
00041034179 | |
00038011459 | |
00022002371 | |
00024000095 | |
00019000381 | |
-00021992281 | |
00044097209 | |
0007416714 | |
00075200303 | |
061996 | |
00102166651 | |
00056122646 | |
00108151186 | |
00085122785 | |
00051074369 | |
00048091116 | |
00088151501 | |
00047129726 | |
0006516673 | |
00104199641 | |
0010015878 | |
00095151386 | |
0006811607 | |
00080136794 | |
0007812282 | |
00062091125 | |
00043059264 | |
00067034208 | |
00017013683 | |
0001401149 | |
00035027422 | |
00030030746 | |
00033021339 | |
061998 | |
00035009491 | |
00062003422 | |
00051001528 | |
-00046999136 | |
00003000096 | |
-00000999904 | |
00003011578 | |
00028030946 | |
00063069574 | |
00042080332 | |
00055152599 | |
00111257279 | |
0008725745 | |
00091219011 | |
00064159715 | |
00074175377 | |
00033091047 | |
0002406387 | |
00054096495 | |
00078143193 | |
00069090473 | |
00032058879 | |
00112216684 | |
062000 | |
00042063725 | |
00015002354 | |
00002002356 | |
-00027990567 | |
00007041568 | |
00029059186 | |
00003002385 | |
00034000382 | |
00040001534 | |
00070060108 | |
00116222008 | |
00096241359 | |
00099170237 | |
0012308128 | |
00109087532 | |
00095156357 | |
00116352319 | |
00184774897 | |
00167740897 | |
00124610486 | |
00207955543 | |
00201862217 | |
00197809086 | |
062002 | |
0014035308 | |
00078134532 | |
00063077074 | |
00068066503 | |
00090182185 | |
00087149926 | |
00082142463 | |
00072107502 | |
00063107566 |
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
1 yr T- notes - mat constants | 2yr T- notes - mat constants | Source | httpwwwfederalreservegovreleasesh15datamtcm2ytxt | ||||||||||
Date | Rate | Date | Rate | Implied one year forward rate | Forecast error | ||||||||
061976 | 652 | 061976 | 706 | 1076 | |||||||||
62 | 071976 | 685 | 1075 | 14 | |||||||||
6 | 081976 | 663 | 1073 | 15 | |||||||||
584 | 091976 | 642 | 1070 | 14 | |||||||||
55 | 101976 | 598 | 1065 | 15 | |||||||||
529 | 111976 | 581 | 1063 | 12 | |||||||||
489 | 121976 | 538 | 1059 | 14 | |||||||||
529 | 011977 | 59 | 1065 | 06 | |||||||||
547 | 021977 | 609 | 1067 | 10 | |||||||||
55 | 031977 | 609 | 1067 | 12 | |||||||||
544 | 041977 | 596 | 1065 | 12 | |||||||||
584 | 051977 | 625 | 1067 | 06 | |||||||||
58 | 061977 | 613 | 1065 | 09 | |||||||||
594 | 071977 | 627 | 1066 | 05 | |||||||||
637 | 081977 | 661 | 1069 | 02 | |||||||||
653 | 091977 | 671 | 1069 | 03 | |||||||||
697 | 101977 | 711 | 1073 | -01 | |||||||||
695 | 111977 | 714 | 1073 | 03 | |||||||||
696 | 121977 | 718 | 1074 | 04 | |||||||||
728 | 011978 | 749 | 1077 | 01 | |||||||||
734 | 021978 | 757 | 1078 | 04 | |||||||||
731 | 031978 | 758 | 1079 | 05 | |||||||||
745 | 041978 | 774 | 1080 | 04 | |||||||||
782 | 051978 | 801 | 1082 | 02 | |||||||||
061978 | 809 | 061978 | 824 | 1084 | 01 | ||||||||
839 | 071978 | 849 | 1086 | 00 | |||||||||
831 | 081978 | 837 | 1084 | 03 | |||||||||
864 | 091978 | 857 | 1085 | -02 | |||||||||
914 | 101978 | 885 | 1086 | -06 | |||||||||
1001 | 111978 | 942 | 1088 | -14 | |||||||||
103 | 121978 | 972 | 1091 | -15 | |||||||||
1041 | 011979 | 986 | 1093 | -13 | |||||||||
1024 | 021979 | 972 | 1092 | -09 | |||||||||
1025 | 031979 | 979 | 1093 | -10 | |||||||||
1012 | 041979 | 978 | 1094 | -08 | |||||||||
1012 | 051979 | 978 | 1094 | -07 | |||||||||
957 | 061979 | 922 | 1089 | -01 | |||||||||
964 | 071979 | 914 | 1086 | -08 | |||||||||
998 | 081979 | 946 | 1089 | -13 | |||||||||
1084 | 091979 | 1006 | 1093 | -19 | |||||||||
1244 | 101979 | 1149 | 1105 | -32 | |||||||||
1239 | 111979 | 1181 | 1112 | -18 | |||||||||
1198 | 121979 | 1139 | 1108 | -07 | |||||||||
1206 | 011980 | 115 | 1109 | -13 | |||||||||
1392 | 021980 | 1342 | 1129 | -30 | |||||||||
1582 | 031980 | 1488 | 1139 | -29 | |||||||||
133 | 041980 | 125 | 1117 | 06 | |||||||||
939 | 051980 | 945 | 1095 | 23 | |||||||||
061980 | 816 | 061980 | 873 | 1093 | 14 | ||||||||
865 | 071980 | 903 | 1094 | 07 | |||||||||
1024 | 081980 | 1053 | 1108 | -08 | |||||||||
1152 | 091980 | 1157 | 1116 | -07 | |||||||||
1249 | 101980 | 1209 | 1117 | -09 | |||||||||
1415 | 111980 | 1351 | 1129 | -25 | |||||||||
1488 | 121980 | 1408 | 1133 | -20 | |||||||||
1408 | 011981 | 1326 | 1124 | -08 | |||||||||
1457 | 021981 | 1392 | 1133 | -21 | |||||||||
1371 | 031981 | 1357 | 1134 | -04 | |||||||||
1432 | 041981 | 1415 | 1140 | -09 | |||||||||
162 | 051981 | 1546 | 1147 | -22 | |||||||||
1486 | 061981 | 1451 | 1142 | -01 | |||||||||
1572 | 071981 | 1535 | 1150 | -16 | |||||||||
1672 | 081981 | 1628 | 1158 | -17 | |||||||||
1652 | 091981 | 1646 | 1164 | -07 | |||||||||
1538 | 101981 | 1554 | 1157 | 10 | |||||||||
1241 | 111981 | 1288 | 1134 | 33 | |||||||||
1285 | 121981 | 1329 | 1137 | 05 | |||||||||
1432 | 011982 | 1457 | 1148 | -06 | |||||||||
1473 | 021982 | 1482 | 1149 | 01 | |||||||||
1395 | 031982 | 1419 | 1144 | 10 | |||||||||
1398 | 041982 | 142 | 1144 | 05 | |||||||||
1334 | 051982 | 1378 | 1142 | 11 | |||||||||
061982 | 1407 | 061982 | 1447 | 1149 | 02 | ||||||||
1324 | 071982 | 138 | 1144 | 16 | |||||||||
1143 | 081982 | 1232 | 1132 | 29 | |||||||||
1085 | 091982 | 1178 | 1127 | 24 | |||||||||
932 | 101982 | 1019 | 1111 | 34 | |||||||||
916 | 111982 | 98 | 1104 | 19 | |||||||||
891 | 121982 | 966 | 1104 | 15 | |||||||||
862 | 011983 | 933 | 1100 | 18 | |||||||||
892 | 021983 | 964 | 1104 | 11 | |||||||||
904 | 031983 | 966 | 1103 | 13 | |||||||||
898 | 041983 | 957 | 1102 | 13 | |||||||||
89 | 051983 | 949 | 1101 | 13 | |||||||||
966 | 061983 | 1018 | 1107 | 04 | |||||||||
102 | 071983 | 1069 | 1112 | 05 | |||||||||
1053 | 081983 | 1107 | 1116 | 07 | |||||||||
1016 | 091983 | 1079 | 1114 | 15 | |||||||||
981 | 101983 | 1057 | 1113 | 16 | |||||||||
994 | 111983 | 1066 | 1114 | 14 | |||||||||
1011 | 121983 | 1084 | 1116 | 13 | |||||||||
99 | 011984 | 1064 | 1114 | 17 | |||||||||
1004 | 021984 | 1079 | 1115 | 13 | |||||||||
1059 | 031984 | 1131 | 1120 | 10 | |||||||||
109 | 041984 | 1169 | 1125 | 11 | |||||||||
1166 | 051984 | 1247 | 1133 | 08 | |||||||||
061984 | 1208 | 061984 | 1291 | 1137 | 12 | ||||||||
1203 | 071984 | 1288 | 1137 | 17 | |||||||||
1182 | 081984 | 1243 | 1130 | 19 | |||||||||
1158 | 091984 | 122 | 1128 | 15 | |||||||||
109 | 101984 | 116 | 1123 | 19 | |||||||||
982 | 111984 | 1065 | 1115 | 25 | |||||||||
933 | 121984 | 1018 | 1110 | 22 | |||||||||
902 | 011985 | 993 | 1108 | 20 | |||||||||
929 | 021985 | 1017 | 1111 | 16 | |||||||||
986 | 031985 | 1071 | 1116 | 12 | |||||||||
914 | 041985 | 1009 | 1110 | 24 | |||||||||
846 | 051985 | 939 | 1103 | 26 | |||||||||
78 | 061985 | 869 | 1096 | 25 | |||||||||
786 | 071985 | 877 | 1097 | 17 | |||||||||
805 | 081985 | 894 | 1098 | 16 | |||||||||
807 | 091985 | 898 | 1099 | 18 | |||||||||
801 | 101985 | 886 | 1097 | 19 | |||||||||
788 | 111985 | 858 | 1093 | 18 | |||||||||
767 | 121985 | 815 | 1086 | 16 | |||||||||
773 | 011986 | 814 | 1086 | 09 | |||||||||
761 | 021986 | 797 | 1083 | 09 | |||||||||
703 | 031986 | 721 | 1074 | 13 | |||||||||
644 | 041986 | 67 | 1070 | 10 | |||||||||
665 | 051986 | 707 | 1075 | 03 | |||||||||
061986 | 673 | 061986 | 718 | 1076 | 08 | ||||||||
627 | 071986 | 667 | 1071 | 14 | |||||||||
593 | 081986 | 633 | 1067 | 11 | |||||||||
577 | 091986 | 635 | 1069 | 10 | |||||||||
572 | 101986 | 628 | 1068 | 12 | |||||||||
58 | 111986 | 628 | 1068 | 10 | |||||||||
587 | 121986 | 627 | 1067 | 09 | |||||||||
578 | 011987 | 623 | 1067 | 09 | |||||||||
596 | 021987 | 64 | 1068 | 07 | |||||||||
603 | 031987 | 642 | 1068 | 08 | |||||||||
65 | 041987 | 702 | 1075 | 03 | |||||||||
7 | 051987 | 776 | 1085 | 05 | |||||||||
68 | 061987 | 757 | 1083 | 17 | |||||||||
668 | 071987 | 744 | 1082 | 17 | |||||||||
703 | 081987 | 775 | 1085 | 12 | |||||||||
767 | 091987 | 834 | 1090 | 08 | |||||||||
759 | 101987 | 84 | 1092 | 14 | |||||||||
696 | 111987 | 769 | 1084 | 23 | |||||||||
717 | 121987 | 786 | 1086 | 13 | |||||||||
699 | 011988 | 763 | 1083 | 16 | |||||||||
664 | 021988 | 718 | 1077 | 16 | |||||||||
671 | 031988 | 727 | 1078 | 10 | |||||||||
701 | 041988 | 759 | 1082 | 08 | |||||||||
74 | 051988 | 8 | 1086 | 08 | |||||||||
061988 | 749 | 061988 | 803 | 1086 | 11 | ||||||||
775 | 071988 | 828 | 1088 | 08 | |||||||||
817 | 081988 | 863 | 1091 | 06 | |||||||||
809 | 091988 | 846 | 1088 | 10 | |||||||||
811 | 101988 | 835 | 1086 | 07 | |||||||||
848 | 111988 | 867 | 1089 | 01 | |||||||||
899 | 121988 | 909 | 1092 | -01 | |||||||||
905 | 011989 | 918 | 1093 | 01 | |||||||||
925 | 021989 | 937 | 1095 | 01 | |||||||||
957 | 031989 | 968 | 1098 | -01 | |||||||||
936 | 041989 | 945 | 1095 | 04 | |||||||||
898 | 051989 | 902 | 1091 | 06 | |||||||||
844 | 061989 | 841 | 1084 | 06 | |||||||||
789 | 071989 | 782 | 1078 | 05 | |||||||||
818 | 081989 | 814 | 1081 | -04 | |||||||||
822 | 091989 | 828 | 1083 | -01 | |||||||||
799 | 101989 | 798 | 1080 | 04 | |||||||||
777 | 111989 | 78 | 1078 | 02 | |||||||||
772 | 121989 | 778 | 1078 | 01 | |||||||||
792 | 011990 | 809 | 1083 | -01 | |||||||||
811 | 021990 | 837 | 1086 | 02 | |||||||||
835 | 031990 | 863 | 1089 | 03 | |||||||||
84 | 041990 | 872 | 1090 | 05 | |||||||||
832 | 051990 | 864 | 1090 | 07 | |||||||||
061990 | 81 | 061990 | 835 | 1086 | 09 | ||||||||
794 | 071990 | 816 | 1084 | 07 | |||||||||
778 | 081990 | 806 | 1083 | 06 | |||||||||
776 | 091990 | 808 | 1084 | 06 | |||||||||
755 | 101990 | 788 | 1082 | 09 | |||||||||
731 | 111990 | 76 | 1079 | 09 | |||||||||
705 | 121990 | 731 | 1076 | 08 | |||||||||
664 | 011991 | 713 | 1076 | 09 | |||||||||
627 | 021991 | 687 | 1075 | 14 | |||||||||
64 | 031991 | 71 | 1078 | 11 | |||||||||
624 | 041991 | 695 | 1077 | 16 | |||||||||
613 | 051991 | 678 | 1074 | 15 | |||||||||
636 | 061991 | 696 | 1076 | 11 | |||||||||
631 | 071991 | 692 | 1075 | 13 | |||||||||
578 | 081991 | 643 | 1071 | 18 | |||||||||
557 | 091991 | 618 | 1068 | 15 | |||||||||
533 | 101991 | 591 | 1065 | 15 | |||||||||
489 | 111991 | 556 | 1062 | 16 | |||||||||
438 | 121991 | 503 | 1057 | 19 | |||||||||
415 | 011992 | 496 | 1058 | 15 | |||||||||
429 | 021992 | 521 | 1061 | 15 | |||||||||
463 | 031992 | 569 | 1068 | 15 | |||||||||
43 | 041992 | 534 | 1064 | 25 | |||||||||
419 | 051992 | 523 | 1063 | 22 | |||||||||
061992 | 417 | 061992 | 505 | 1059 | 21 | ||||||||
36 | 071992 | 436 | 1051 | 23 | |||||||||
347 | 081992 | 419 | 1049 | 17 | |||||||||
318 | 091992 | 389 | 1046 | 17 | |||||||||
33 | 101992 | 408 | 1049 | 13 | |||||||||
368 | 111992 | 458 | 1055 | 12 | |||||||||
371 | 121992 | 467 | 1056 | 18 | |||||||||
35 | 011993 | 439 | 1053 | 21 | |||||||||
339 | 021993 | 41 | 1048 | 19 | |||||||||
333 | 031993 | 395 | 1046 | 15 | |||||||||
324 | 041993 | 384 | 1044 | 13 | |||||||||
336 | 051993 | 398 | 1046 | 11 | |||||||||
354 | 061993 | 416 | 1048 | 11 | |||||||||
347 | 071993 | 407 | 1047 | 13 | |||||||||
344 | 081993 | 4 | 1046 | 12 | |||||||||
336 | 091993 | 385 | 1043 | 12 | |||||||||
339 | 101993 | 387 | 1044 | 10 | |||||||||
358 | 111993 | 416 | 1047 | 08 | |||||||||
361 | 121993 | 421 | 1048 | 11 | |||||||||
354 | 011994 | 414 | 1047 | 13 | |||||||||
387 | 021994 | 447 | 1051 | 09 | |||||||||
432 | 031994 | 5 | 1057 | 08 | |||||||||
482 | 041994 | 555 | 1063 | 09 | |||||||||
531 | 051994 | 597 | 1066 | 10 | |||||||||
061994 | 527 | 061994 | 593 | 1066 | 14 | ||||||||
548 | 071994 | 613 | 1068 | 11 | |||||||||
556 | 081994 | 618 | 1068 | 12 | |||||||||
576 | 091994 | 639 | 1070 | 10 | |||||||||
611 | 101994 | 673 | 1074 | 09 | |||||||||
654 | 111994 | 715 | 1078 | 08 | |||||||||
714 | 121994 | 759 | 1080 | 06 | |||||||||
705 | 011995 | 751 | 1080 | 10 | |||||||||
67 | 021995 | 711 | 1075 | 13 | |||||||||
643 | 031995 | 678 | 1071 | 11 | |||||||||
627 | 041995 | 657 | 1069 | 09 | |||||||||
6 | 051995 | 617 | 1063 | 09 | |||||||||
564 | 061995 | 572 | 1058 | 07 | |||||||||
559 | 071995 | 578 | 1060 | 02 | |||||||||
575 | 081995 | 598 | 1062 | 02 | |||||||||
562 | 091995 | 581 | 1060 | 06 | |||||||||
559 | 101995 | 57 | 1058 | 04 | |||||||||
543 | 111995 | 548 | 1055 | 04 | |||||||||
531 | 121995 | 532 | 1053 | 02 | |||||||||
509 | 011996 | 511 | 1051 | 02 | |||||||||
494 | 021996 | 503 | 1051 | 02 | |||||||||
534 | 031996 | 566 | 1060 | -02 | |||||||||
554 | 041996 | 596 | 1064 | 04 | |||||||||
564 | 051996 | 61 | 1066 | 07 | |||||||||
061996 | 581 | 061996 | 63 | 1068 | 08 | ||||||||
585 | 071996 | 627 | 1067 | 09 | |||||||||
567 | 081996 | 603 | 1064 | 10 | |||||||||
583 | 091996 | 623 | 1066 | 06 | |||||||||
555 | 101996 | 591 | 1063 | 11 | |||||||||
542 | 111996 | 57 | 1060 | 09 | |||||||||
547 | 121996 | 578 | 1061 | 05 | |||||||||
561 | 011997 | 601 | 1064 | 05 | |||||||||
553 | 021997 | 59 | 1063 | 09 | |||||||||
58 | 031997 | 622 | 1066 | 05 | |||||||||
599 | 041997 | 645 | 1069 | 07 | |||||||||
587 | 051997 | 628 | 1067 | 10 | |||||||||
569 | 061997 | 609 | 1065 | 10 | |||||||||
554 | 071997 | 589 | 1062 | 10 | |||||||||
556 | 081997 | 594 | 1063 | 07 | |||||||||
552 | 091997 | 588 | 1062 | 08 | |||||||||
546 | 101997 | 577 | 1061 | 08 | |||||||||
546 | 111997 | 571 | 1060 | 06 | |||||||||
553 | 121997 | 572 | 1059 | 04 | |||||||||
524 | 011998 | 536 | 1055 | 07 | |||||||||
531 | 021998 | 542 | 1055 | 02 | |||||||||
539 | 031998 | 556 | 1057 | 01 | |||||||||
538 | 041998 | 556 | 1057 | 04 | |||||||||
544 | 051998 | 559 | 1057 | 03 | |||||||||
061998 | 541 | 061998 | 552 | 1056 | 03 | ||||||||
536 | 071998 | 546 | 1056 | 03 | |||||||||
521 | 081998 | 527 | 1053 | 04 | |||||||||
471 | 091998 | 467 | 1046 | 06 | |||||||||
412 | 101998 | 409 | 1041 | 05 | |||||||||
453 | 111998 | 454 | 1046 | -05 | |||||||||
452 | 121998 | 451 | 1045 | 00 | |||||||||
451 | 011999 | 462 | 1047 | -00 | |||||||||
47 | 021999 | 488 | 1051 | 00 | |||||||||
478 | 031999 | 505 | 1053 | 03 | |||||||||
469 | 041999 | 498 | 1053 | 06 | |||||||||
485 | 051999 | 525 | 1057 | 04 | |||||||||
51 | 061999 | 562 | 1061 | 06 | |||||||||
503 | 071999 | 555 | 1061 | 11 | |||||||||
52 | 081999 | 568 | 1062 | 09 | |||||||||
525 | 091999 | 566 | 1061 | 09 | |||||||||
543 | 101999 | 586 | 1063 | 06 | |||||||||
555 | 111999 | 586 | 1062 | 07 | |||||||||
584 | 121999 | 61 | 1064 | 03 | |||||||||
612 | 012000 | 644 | 1068 | 02 | |||||||||
622 | 022000 | 661 | 1070 | 05 | |||||||||
622 | 032000 | 653 | 1068 | 08 | |||||||||
615 | 042000 | 64 | 1067 | 07 | |||||||||
633 | 052000 | 681 | 1073 | 03 | |||||||||
062000 | 617 | 062000 | 648 | 1068 | 11 | ||||||||
608 | 072000 | 634 | 1066 | 07 | |||||||||
618 | 082000 | 623 | 1063 | 04 | |||||||||
613 | 092000 | 608 | 1060 | 02 | |||||||||
601 | 102000 | 591 | 1058 | 00 | |||||||||
609 | 112000 | 588 | 1057 | -03 | |||||||||
56 | 122000 | 535 | 1051 | 01 | |||||||||
481 | 012001 | 476 | 1047 | 03 | |||||||||
468 | 022001 | 466 | 1046 | 00 | |||||||||
43 | 032001 | 434 | 1044 | 03 | |||||||||
398 | 042001 | 423 | 1045 | 04 | |||||||||
378 | 052001 | 426 | 1047 | 07 | |||||||||
358 | 062001 | 408 | 1046 | 12 | |||||||||
362 | 072001 | 404 | 1045 | 10 | |||||||||
347 | 082001 | 376 | 1041 | 10 | |||||||||
282 | 092001 | 312 | 1034 | 12 | |||||||||
233 | 102001 | 273 | 1031 | 11 | |||||||||
218 | 112001 | 278 | 1034 | 10 | |||||||||
222 | 122001 | 311 | 1040 | 12 | |||||||||
216 | 012002 | 303 | 1039 | 18 | |||||||||
223 | 022002 | 302 | 1038 | 17 | |||||||||
257 | 032002 | 356 | 1046 | 12 | |||||||||
248 | 042002 | 342 | 1044 | 21 | |||||||||
235 | 052002 | 326 | 1042 | 20 | |||||||||
062002 | 22 | 062002 | 299 | 1038 | 20 | ||||||||
196 | 072002 | 256 | 1032 | 18 | |||||||||
176 | 082002 | 213 | 1025 | 14 | |||||||||
172 | 092002 | 2 | 1023 | 08 | |||||||||
165 | 102002 | 191 | 1022 | 06 | |||||||||
149 | 112002 | 192 | 1024 | 07 | |||||||||
145 | 122002 | 184 | 1022 | 09 | |||||||||
136 | 012003 | 174 | 1021 | 09 | |||||||||
13 | 022003 | 163 | 1020 | 08 | |||||||||
124 | 032003 | 157 | 1019 | 07 | |||||||||
042003 | 127 | 042003 | 162 | 1020 | 06 |
27
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
LIBOR SWAPS
Suppose the banker wants to receive variable rate interest but the customer wants to pay fixed
Impasse No Deal
Solution Let the customer pay fixed then swap the fixed for Libor (variable) in the interest swap market
The curve on the next page says the market will trade about 413 fixed each year for two years in exchange for 3 month Libor each quarter for two years
28
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
So letrsquos use a somewhat far fetched example to show the principle The customer pays fixed 7 and our bank SWAPs it out by paying 413 to get whatever Libor turns out to be 29
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
CURRENT RATES DOWN RATES UPRATES UP1 2 4
LOAN RATE 7 7 7 7CD RATE (LIBOR) -4 - 3 - 6 - 8
Internal Spread 3 4 1 -1(LOAN RATE-CD RATE)
SWAP SIDEPay Fixed 413 413 413 413Get Libor 4 3 6 8
Net on SWAP -13 -113 +187 +387
$ INLoan Rate 7 7 7 7Get Libor in SWAP Mkt 4 3 6 8
$OUTCD Rate to Customer 4 3 6 8Fixed to SWAP Mkt 413 413 413 413
Interest to Bank 287 287 287 28730
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
How does the market come up with this tradeoff (Letrsquos use annual Libor for simplicity)
)7(2104yearstwoforyearnextnow
ratefixedTheLiborLiborR2FR 2111
=+
=+
Then market will add a risk premium in case customer defaults
31
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Real World
Suppose a customer knows that the market typically overestimates short-term rates
In our example suppose customer thinks rate next year on 1 year stuff is going to be 8 not 10
Then they will prefer the variable to the fixed because 4 + 8 lt 7 + 7
32
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Quantitative Easing How Did the Fed Get Away with Lowering Long-term rates
Huge shift in fed portfolio away from Treasury Securities33
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Total Assets held by the Federal Reserve $ tillions
$4
$3
$2
$1
$0
QE1 QE2 QE3
2006 2007 2008 2009 2010 2011 2012 2013 2014
34
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
QE1 Bailout PhaseQE1 is a nickname developed to refer to the first round of quantitative easing in November 2008 Purchase GSE debt of $100 billion and MBS of $500 billion (then increased to $200 billion and $125 trillion in 2009 plus $300 billion in long ndashterm treasuries)
QE2 KICK START ECONOMY PHASE 1
Basically $600 billion in longer term treasuries
QE3 We Need MoreThe Fed buys $85 billion a month in both MBS and Treasuries from banks
Then promised rates would stay low Called ldquoforward guidancerdquo
Why did they do this Go back to our example Suppose R1=4 1f1 =10 then R2=7 Only way Fed can drive R2=5 for example is to promise that 1f1 =6 In other words ldquopromiserdquo that short rates would stay low If not nobody would hold the 5 security they would sell P down rate up defeating the Fedrsquos intention
35
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Income Expense ProfitsPos GAP 06 + 06 05 + 05 020 06 + 06 02 + 02 08Neg 09 + 09 02 + 02 14
bull R1 = 04 R2 = 07 1r1 = 05
Pos 06 + 07 05 + 05 030 06 + 07 02 + 03 08Neg 09 + 09 02 + 03 13
Note the following when rates rose1) Pos GAP would cause NII to increase Neg GAP would cause NII to fall2) But had you had a Neg GAP you could have made more $
GAP Managementbull Suppose assets marked up 2 liabilities down 2 rArr spread 4 a yearbull R1 = 04 R2 = 07 1r1 = 04
So standard GAP games are all about making more $ not maximizing earnings
36
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37
Interest ForecastingThere are three ways to forecast interest rates
1 Roll your own
Nominal rate = real rate + expected inflation
Forecast Real GDP Forecast inflation
2 Use implied forward rates
3 Look at the futures market
Suppose you (I) think a bushel of corn will sell for $100 a year from now Would you agree now to sell it to me then for less than $100 Would I agree to pay more than $100
So the price will end up being close to our ldquobestrdquo guess of the price
Same is true for the t-bills fed funds bonds
37