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Interest Rate Futures. July 2011. Introduction. Interest rate Futures Short term interest rate futures (STIR) Long term interest rate futures (LTIR). World interest rate contracts. 2010 Break down of interest rate contract volume by product group. Source: FIA Magazine March/April 2011. - PowerPoint PPT Presentation
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Interest Rate Futures
July 2011
1
Introduction Interest rate Futures
Short term interest rate futures (STIR) Long term interest rate futures (LTIR)
2
World interest rate contracts
3
2010 Break down of interest rate contract volume by product group
4
Source: FIA Magazine March/April 20115
6
7
Volume by geographical zone
8
• Principle value of 1 Mil with a three-month maturity• Quote : 100 - yield
• yield = (discount/price)(360/day to maturity)
• price = 1 mil – discount yield(%)*1 Mil*DTM 360
9
Short term interest rate futures Eurodollar Assume discount yield is 8.32 % with 90 days
to maturity what is the price?• price = 1 mil – discount yield(%)*1 Mil*DTM
360• Price = 1,000,000 -
[(.0832*1,000,000*90 )/360]• = 979,200
Quotation = 100-.0832 = 91.68
10
Pricing futures
)1(0, CSF to
CS
F t1
0
,0
Cost of carry model in perfect market• market is perfect• financing cost is the only carrying charge• ignore the different between forward and futures prices • ignore the options the seller may possess
11
Interest rate futures and arbitrage
DTM discount yield Face value discount Price A B C D [B*(A/360)]*C C-D
77 6% 100,
0000, 128,
3333. 987
167
167 10% 100,
0000, 463,
8889
953 611
90 125. % 100,
0000, 312,
5000. 968
750
167 days
90 days
77 days6%
10%
12.5%
Jan 5
Mar 22
12
Interest rate futures and arbitrage
167 days
90 days
77 days8%
10%
12.5%
Jan 5
Mar 22
DTMdiscount
yield Face value discount Price A B C D [B*(A/360)]*C C-D
77 8
10000,
00
17,111
11 982889,
16
7 10%
10000,
00
46,388.
89 953611,
90
125.%
10000,
00
31,250.
00 968750,
13
Interest rate futures and arbitrage
For no arbitrage to happen: Holding 167 days t-bill(10%) must give equal
yield to hold 77 days t-bill followed by 90days t-bill (12.5%) from futures delivery
Only yield that prevent arbitrage is 953611 = 968750-(96850*(x)*(77/360)) 953611/968750 = 1-(.213889x) X = .73063
DTM discount yield Face value discount Price A B C D [B*(A/360)]*C C-D
77 6% 100,
0000, 128,
3333. 987
167
167 10% 100,
0000, 463,
8889
953 611
90 125. % 100,
0000, 312,
5000. 968
750
14
Financing cost and implied repo rate
CS
F t1
0
,0
1+C = 968,750/953611 = 1.015875
DTM discount yield Face value discount Price A B C D [B*(A/360)]*C C-D
77 6%
100,000,
0 128,
3333. 98
7167,
167 10%
100,000,
0 463,
8889
95 3611,
90125. %
100,000,
0 312,
5000. 96
8750
implied repo rate >financing costcash n carry
borrow fund buy cash bond , sell futures, hold bond n deliver against futures
implied repo rate <financing cost
reverse cash n carry
Buy futures, sell bond short, invest proceed until futures expires take delivery and repay short sales
15
Interest rate futures and arbitrage
instrument Lending rate Borrowing rate77 day T-bill 73063. 75563
167day t-bill 10 1025
Unequal borrowing and lending rate
DTM discount yield Face value discount Price A B C D [B*(A/360)]*C C-D
77 6
100000 0 12833
9871, 67
167 10% 100000
0 46389, 9536,
11
90 12.29% 100000
0 30725, 9692,
75
16
Interest rate futures and arbitrage
instrument Lending rate Borrowing rate77 day T-bill 73063. 75563
167day t-bill 10 1025
Unequal borrowing and lending rate
DTMdiscount
yield Face value discount Price A B C D
[B*(A/
360)]*C C-D
77 8% 1000,
000
1711, 111.
982, 889
167 10% 1000,
000
4638, 889.
953, 611
90
1297.%
1000, 000
3242, 500.
967, 575
17
The futures yield and forward rate of interest
1.048646 = x * 1.015875 X = 1.032259 ; forward rate =3.2559%
167 days
90 days
77 days
7.3063%
10%
12.5%
953,611 968,750
953,611 1,000,000
1.015875
1.048646
18
Longer maturity interest rate futures Treasury bond Futures Treasury Note futures
19
US Treasury Note & Bond Futures
20
US Treasury Note Futures
21
Delivery of Bond futures
Majority of position will be liquidated or rolled forward and only tiny amount resulted in delivery
22
Deliverable grade
Deliverable grade is defined in contract specification and is varied by contract. Several bonds could be delivered against the contract. Seller will choose the cheapest to
deliver bond to deliver. Conversion factors will adjust for the differences in coupons and maturity among the
deliverable bonds. (approximate from assume face value of bond is 1$ and discounted the CF from bond at 6% using bond pricing equation)
When delivery , invoice piece will equal converted futures price + accrued interest converted futures price = contract scale factor (1000)* settlement price *conversion factors
23
Invoice price
If accrued interest is 519.71
24
Delivery process
25
Conversion factor
26
The cost of carry model for T-bond futuresCash and carry arbitrage for a T-bond T-bond that is deliverable on a futures contract has an 8% coupon and cost 100$. Financing rate 7.3063% on a discount basis for 77 days until futures contract is
deliverable.
Jan-05
Sell one T-bond Futures for 10169
2
Borrow 100103 for 77 days @7.3063%Buy 8% t-bond for 100103
Mar-22
Deliver T-bond against futures get10169
2
Paid debt 10169
2
profit 0
invoice amount = accrued interest + cost
interest =(7 7 /1 8 2 )* 4 %*100000,
1 ,69
2
invoice amount in next 77 days
101
,692
cost of buy T-BondPV of invoice amount
- 101692 73063 *(( . %
77360*101692
100
,103
Assume perfect market no seller options27
Speculating with interest rate futures Outright position
Long trader: betting interest rate will fall and futures prices will rise Short trader: betting interest rate will rise and futures prices will fall
Example : Trader Expect short term interest rate will rise.
Date Futures Market
September 20 Sell 1 Dec Eurodollar futures at 90.30
September 25 Buy 1 Dec Eurodollar futures at 90.12
Profit : 90.30-90.12
Total gain 18 basis points *25 = 450$
28
Speculating with interest rate futures Spread position
Intra-commodity : speculate on the term structures of interest Example : Trader expects that the current very steep upward sloping yield curve
would flatten within six month. (not sure whether rates were going to rise or fall.
.
Date Futures Market
Mar 20 Buy the DEC Eurodollar futures at 86.50Sell the SEP Eurodollar futures at 87.50
September 25 Sell the DEC Eurodollar futures at 88.14Buy the SEP Eurodollar futures at 89.02
Profit : (88.14-86.50)+(87.50-89.02)=1.64-1.52=12
Total gain 12 basis points *25 = 300$
TTM Futures contract Futures Yield (%)
Futures quotation
3 month JUN 12.00 88.00
6 month SEP 12.50 87.50
9 month DEC 13.50 86.50
29
Speculating with interest rate futures Spread position
Inter-commodity : speculate on shifting risk level between instrument Example : International debt crisis, bank involved in international lending has more risk.
May expect to find a widening of yield spread between T-bill and Eurodollar deposit.
.Date Futures Market
Feb 17 Sell 1 DEC Eurodollar futures at 90.29Buy 1 DEC T-bill Futures at 91.18
Oct 14 Buy 1 DEC Eurodollar futures at 89.91Sell 1 DEC T-bill futures at 91.02
Profit : (90.29-89.91)+(91.07-91.18)= 0.38-0.11 =0.27
Total gain 27 basis points *25 = 675$
30
Hedging with interest rate futures
Date Cash Market Futures Market
Dec 15 Fund manager learns he will receive 970,000 in six month to invest in T-billMarket yield 12% is attractive and want to lock in yieldFace value of bill to purchase is 1 million
Buy T-bill futures to mature in six monthFutures prices = 1 Mil – (1 mil*(.12*(90/360))) = 970,000
June 15 Receive 970,000 to investMarket yield drop to 10%1 million face value of T0bill now cost 975,000
Loss = -5000
Offset position by selling T-bill at futures yield 10% or futures prices 975,000(1,000,000- (1,000,000*(.1*90/360)))
Profit =5,000
Net wealth change = 0
Long hedge
31
Hedging with interest rate futures
Date Cash Market Futures Market
March • A bank makes a 9 month fixed rate loan to a client.• Financed by a six month CD at 3% but need to rolled over for 3 month at the expected rate of 3.5%• bank is vulnerable to the rate rising over the expected rate.
• Short SEP Eurodollar at 96.5 • futures prices reflecting 3.5% futures yield
September
• 3 month LIBOR is now 4.5%• Bank’s cost of fund is 1% over the expected rate of 3.5%• Additional coats equal (90/360)*.01*1,000,000 =2,500
•Offset position by long Eurodollar at futures yield 4.5% or futures prices 95.5
•Profit 100 basis points *25 =2,500
Net after hedge = 0
Short hedge
32
Hedging with interest rate futures
Date Cash Market Futures Market
T=0 • A company decides to sell 90day commercial paper in 3 months in the amount of 1,000 million, at the expected yield of 18%, which should net the firm 955 million.
• Short 1000 T-bill futures contracts to mature in 3 months with a yield of 16% • futures prices per contract is 960,000
T= 3 months
• market view changes and perceived CD has more risk ; yield widen to 2.25%• CD rate is now 18.5% instead of 18%• sale of CD thus get the firm of 953.750 million
•Opportunity loss 955-953.75 = -1.25 million
• T-bill futures about to matures•T-bill futures rate = spot rate =16.25% (raised as expected more inflation)• futures prices is 959,375 per contract•Gain 625 per contract or total gain 625,000 $
Net after hedge = -625,000$
Cross hedge
DTM discount yield Face value discount Price A B C D [B*(A/360)]*C C-D
90 18%
10,000,
00
45,000.
00
9550,
00
90 16%
10,000,
00
40,000.
00
9600,
00
90
185.0%
10,000,
00
46,250.
00
9537,
50
90
162.5%
10,000,
01
40,625.
04
9593,
76
33
Thank you
34