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Principles of Performance |
The Use and Abuse of
Conventional Analytics
Nigel Johnson
Director of Performance Trust University®
Module 2
Chicago, IL | June 27, 2016
Purpose
To critique the cornerstones of conventional analytics.
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 3
In This Module
Current Practice in Fixed-Income Investing
Conventional Analysis: Risk and Reward
Yield – A Good Measure of Reward?
Yield – What is it Really?
Duration – A Good Measure of Risk?
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 4
In This Module
Current Practice in Fixed-Income Investing
Conventional Analysis: Risk and Reward
Yield – A Good Measure of Reward?
Yield – What is it Really?
Duration – A Good Measure of Risk?
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 5
The Status Quo
I, like my peers, came from the loan or accounting side
of the institution. Most of us inherited oversight of the
investment function and have never had any real formal
training in fixed-income analytics.
A Portfolio Manager
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 6
The Status Quo
I, like my peers, was taught how to sell a bond.
We figured that portfolio managers knew what they
needed. As long as we stuck to high credit quality all
we needed to figure out was, “What will he/she buy?”
A Broker
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 7
The Status Quo: Wall Street vs. Main Street
I, like my peers, was taught how to…
Economist
An Investigation of Top-Down Investing…
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 8
Definition
Top-Down Investing
An investment approach that involves first looking
at the “Big Picture” in the economy, then choosing
to invest or not to invest in securities that will
out-perform given the “Big Picture.”
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 9
Every six months, over 50 economists predict interest rates
a year from now for a column in The Wall Street Journal.
How many even come close?
Economic Predictions
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 10
Economist Predictions 1 Year in Advance
What percentage of the economists came within 30 bps?
1
2
3
4
5
6
Dec 2007 Dec 2008 Dec 2009 Dec 2010 Dec 2011 Dec 2012 Dec 2013 Dec 2014 Dec 2015
WITHIN 30 BPS 2%8%6%0%10% 0% 24% 0%8%
Source: Wall Street Journal
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 11
1
2
3
4
5
6
Dec 2007 Dec 2008 Dec 2009 Dec 2010 Dec 2011 Dec 2012 Dec 2013 Dec 2014 Dec 2015
WITHIN 50 BPS
Economist Predictions 1 Year in Advance
What about 50 bps?
13%17%15%0%33% 0% 35% 0%22%
Source: Wall Street Journal
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 12
Economists’ Predictions
An economic forecaster is like a cross-eyed javelin
thrower; they do not win many accuracy contests,
but they keep the crowd’s attention.
ANONYMOUS
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 13
In a recent survey, Jim Bianco studied 20 years of
The Wall Street Journal interest rate surveys and
found that as a group, they successfully predicted the
future direction of interest rates only 30% of the time.
The problem with “top-down investing”
If the forecast is wrong, the investment will be wrong.
And would you know which security to buy even if your
forecast was correct?
Top-Down Investing
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 14
Peter Lynch’s Stock Market Wisdom Applies
to All Investments
Nobody can predict interest rates, the future
direction of the economy, or the stock market.
Dismiss all such forecasts and concentrate on
what’s actually happening to your investments.
If you don’t study your investments you have
the same chance of success as you do in a poker
game if you bet without looking at your cards.
PETER LYNCHPARAPHRASED FROM
BEATING THE STREET
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 15
Key Takeaway
Seeking fixed-income outperformance
is not about guessing future interest rates.
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 16
In This Module
Current Practice in Fixed-Income Investing
Conventional Analysis: Risk and Reward
Yield – A Good Measure of Reward?
Yield – What is it Really?
Duration – A Good Measure of Risk?
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 17
Back to the Sandlot/Lobby
Fundamentals of CDs
Rate Yield
2 Numbers:
What are they?
&
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 18
Coupons reinvested at
_____%
For Bonds, Yield is Not What You Get
CD RateInterest Payments
Compounded at the Rate
CD Yield
??????
I Don’t Know!
Yield on a CD
Yield on a Bond
Bond Yield
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 19
Note: Bond yields are reported on a semi-annual compounding basis
Cash Flow DescriptionCash
Flow
Accumulated
Cash Flow
Initial Investment -100 ???
1st Coupon (6 Months) 3.50 3.500 The first coupon
2nd Coupon (6 Months) 3.50 ??? Interest on interest? At what reinvestment rate?
3rd Coupon (6 Months) 3.50 ???
4th Coupon (6 Months) 3.50 ???
Return of Principal 100 ???
An Illustration
2-Yr Treasury: 7% Coupon, 7% Yield (Price = 100, or “Par”)
Dollars Today
Present Value
Coupon Interest
plus
Interest on Interest
Dollars Tomorrow
Future Value
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 20
Let’s assume a 7% reinvestment rate for all cash flows
Cash Flow DescriptionCash
Flow
Accumulated
Cash Flow
Initial Investment -100
1st Coupon (6 Months) 3.50 3.500 Coupon is only cash flow
2nd Coupon (6 Months) 3.50 7.123 New coupon plus 3.50 x (1 + reinvestment rate)
3rd Coupon (6 Months) 3.50 10.872 New coupon plus 7.123 x (1 + reinvestment rate)
4th Coupon (6 Months) 3.50 14.752 New coupon plus 10.872 x (1 + reinvestment rate)
Return of Principal 100 114.752 Total Ending Dollars
An Illustration
2-Yr Treasury: 7% Coupon, 7% Yield (Price = 100, or “Par”)
Dollars Today
Present Value
Coupon Interest
plus
Interest on Interest
Dollars Tomorrow
Future Value
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 21
When different reinvestment rates are used, we arrive at different
effective compounded yields.
In fact, this result is also known as Total Rate of Return (Total Return).
Yield on a bond is not like yield on a CD because the compounding rate
is unknown. Yield is NOT “what you get” on a bond.
What if a Different Reinvestment Rate is Used?
Beginning
Dollars
Reinvestment
Rate
Ending
Dollars
Effective,
Compounded Yield
$1,000,000.00 7.00% $1,147,523 7.00%
$1,000,000.00 3.00% $1,143,182 6.80%
$1,000,000.00 10.00% $1,150,854 7.15%
As we will see, Total Return is the true measure
of “what you get” on a bond.
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 22
Implication
5-Yr Treasury and 5-Yr Corp with a +100 Spread ($1 Million Face)
Compare Two Similar Bonds
UST Corporate Bond
Year 1 6.50 7.50
Year 2 6.50 7.50
Year 3 6.50 7.50
Year 4 6.50 7.50
Year 5 6.50 7.50
Compounded
Income (Implied)$376,894 $445,044
If yield is not “what you get” on a bond then spread, or additional yield
of one bond over another, is not what you additionally get on a bond.
The implied spread differential in income between these two bonds
is $68,150. But are we treating these bonds consistently?
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 23
Are We Being Consistent?
In the real world, portfolio managers reinvest their cash flows at
consistent reinvestment rates, regardless of their sources.
We are not, because we are using inconsistent reinvestment rates
to arrive at those results (not a level playing field).
6.5% US Treasury 7.50% Corporate Bond
Reinvestment
Rate$$ Return $$ Return
Difference
in Dollars
Difference
in Returns
6.50% $376,894 6.50%
7.50% $445,044 7.50%
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 24
Where is the 100 bps Spread?
Holding reinvestment rate constant results in less than 100 bps
difference in return, and less than the $68,150.
6.5% US Treasury 7.50% Corporate Bond
Reinvestment
Rate$$ Return $$ Return
Difference
in Dollars
Difference
in Returns
6.50% $376,894 6.50% $434,614 7.35%
7.50% $385,440 6.63% $445,044 7.50%
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 25
Not only is yield not “what you get,”
but spread is not the difference in what you get.
Where is the 100 bps Spread?
In fact, no matter where we set the consistent reinvestment rate,
the 100 bps actual realized spread is elusive.
6.5% US Treasury 7.50% Corporate Bond
Reinvestment
Rate$$ Return $$ Return
Difference
in Dollars
Difference
in Returns
3.50% $351,602 6.12% $405,723 6.93% $54,121 0.81%
4.50% $359,727 6.24% $415,098 7.07% $55,371 0.83%
5.50% $368,071 6.37% $424,726 7.21% $56,655 0.84%
6.50% $376,894 6.50% $434,614 7.35% $57,974 0.85%
7.50% $385,440 6.63% $445,044 7.50% $59,327 0.87%
8.50% $394,476 6.77% $455,193 7.65% $60,717 0.88%
9.50% $403,754 6.90% $465,899 7.80% $62,145 0.90%
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 26
The Truth About Mortgage-Backed “Yields”
We have been on the record for a very long time of the same phenomenon in
the mortgage-backed security world for 20 years. In fact, our CEO, Rich Berg,
co-authored the article on below in 1994.
How come I have all these high yields in my portfolio,
but I’m not making the money?
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 27
Reinvestment
Rate
Realized
Yieldvs Quoted
Realized
Yieldvs Quoted
Realized
Spread
“Realized Yield and Spread”
Benchmark
5-Yr Treasury
5.27% Purchase Yield
6.31% 5.38% +0.11 6.31% 0 0.93
5.27% 5.27% 0 5.93% -0.38 0.66
4.50% 5.19% -0.08 5.66% -0.65 0.47
3.00% 5.03% -0.24 5.13% -1.18 0.10
MBS Alternative
15-Yr MBS
6.31% Purchase Yield
MBS Spread
104 bps
Not only is yield not “what you get,”
but spread is not the difference in what you get.
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 28
Impact of Reinvestment Rate Over a Longer Horizon
Assuming an average reinvestment rate of 7% from 1981 – 1991
the 10-yr return was 10.88% and total net dollars was
$1,884,840.79 or $749,610 less than “expected.”
2-Yr 3-Yr 5-Yr 10-Yr
Yield (%) 13.97 13.67 13.46 13.33
Duration 1.69 2.40 3.56 5.41
Feb 15
1981
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 29
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 30
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 31
The disconnect between yields and “what you get” is even more obvious
when you consider negative yield cases. Consider this CMO:
A Note on Negative Yields and Reinvestment Rates
In order for the negative yield to be “what you get” you would
have to reinvest the cash flows at negative rates.
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 32
Here is a “What You Get” (Total Return) Calculator
It is asking for a reinvestment rate. We know we would not reinvest cash flows
at -3.799%, the only way that could be the Total Return.
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 33
“Worst Case” Reinvestment
Assuming we didn’t reinvest at all, the Total Return would be 214 bps higher
than the reported yield. In Module 6, we will see other shortfalls of the yield
table approach to analyzing mortgages.
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 34
In the bond world,
yield is not what
you actually get.
Reprinted from the ABA Banking Journal
We have been educating
investors on this
topic for decades!
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 35
In This Module
Current Practice in Fixed-Income Investing
Conventional Analysis: Risk and Reward
Yield – A Good Measure of Reward?
Yield – What is it Really?
Duration – A Good Measure of Risk?
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 36
Definition
What is a bond?
A certificate of debt issued by a government, agency
or corporation guaranteeing payment of the original
principal plus interest by a specified future date.
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 37
A Bond is a Series of Cash Flows
3-Yr Bond, 2.00% Coupon
Period 16-Mo
Period 212-Mo
Period 318-Mo
Period 424-Mo
Period 530-Mo
Period 6*36-Mo
*Chart is illustrative. It is not to scale.
1%
$10,000
1%
$10,000
1%
$10,000
1%
$10,000
1%
$10,000
100 + 1%
$1,010,000
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 38
FV = PV (1 + i)n
The Time Value of Money
Where:
PV = Present Value
i = Discount Rate Per Period
n = Number of Periods
FV = Future Value
EXAMPLE
1 Period 2 Periods
FV = 100 (1 + 7%)1 FV = 100 (1 + 7%)2
107 = 100 (1 + 0.07)1 114.5 = 100 (1 + 0.07)2
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 39
Future Value
In 1626, Peter Minuit
bought Manhattan Island
from the Canarsee tribe
for an alleged fee of $24
in goods.
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 40
22.96 Square Miles
Population of 1.6 Million
Population Density of 70,595 per square mile
Per Capita Income of over $100,000
Only 12% of Voters registered Republican
Last time the island voted Republican…
Manhattan Island Interesting Facts
1920
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 41
New York was originally called New Amsterdam
The Vaults 80 feet beneath the Federal Reserve Bank
on Wall Street store 25% of the World’s bullion
The Dutch traded New Amsterdam (New York) to the British
in exchange for the tiny Indonesian island of Pulau Run
Manhattan Island Interesting Facts
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 42
New York was originally called New Amsterdam
The Vaults 80 feet beneath the Federal Reserve Bank
on Wall Street store 25% of the World’s bullion
The Dutch traded New Amsterdam (New York) to the British
in exchange for the tiny Indonesian island of Pulau Run
Manhattan Island Interesting Facts
Estimated Value:
$8 Trillion
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 43
Manhattan Island Interesting Facts
Did the Canarsee Tribe
make a good or bad deal?
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 44
3 Billion Dollars
FV = $24 x (1 + i)n
FV = $24 x (1.05)383
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 45
$24 Compounded for 383 Years
@ 5% would be $3 Billion
@ 6% would be $118 Billion
@ 7% would be $18 Trillion
@ 8% would be $152 Trillion
Compound interest is the most
powerful force in the Universe.
ALBERT EINSTEIN(MAYBE)
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 46
According to many historians, the Indians who sold the island did not
even live on the island.
The Canarsee tribe lived on Long Island, the Weckquaesgeek tribe
lived on Manhattan and were never consulted on the trade.
The Indians did not believe that anyone could own the land.
It Gets Better…
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 47
Where:
PV = Present Value
i = Discount Rate per period
n = Number of periods
FV = Future Value
The Time Value of Money
Price is the present value of the future cash flows
NOTE:
Since bond calculations conventionally use 2 periods per year,
i = yield / 2
PV = FV / (1 + i)n
FV = PV × (1 + i)n
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 48
Definitions
Price
The sum of the present value of future cash flows,
given a yield (discount rate).
Yield
The discount rate which, when used to present value
the future cash flows, results in the sum of those
present valued cash flows being equal to the price.
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 49
Price and Yield
For bonds whose cash flows don’t change when
interest rates change (bullets), once the yield is
given, the price can be solved for.
Conversely, if the price is given, the yield can
be solved for.
In a real sense, yield is price and price is yield.
PRICE = CF1
+CF2
+…+CFn
( 1 + y/2)1 (1 + y/2)2 (1 + y/2)n
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 50
What is Price?
PRICE =1.5
+1.5
+1.5
+101.5
(1 + 0.01)1 (1 + 0.01)2 (1 + 0.01)3 (1 + 0.01)4
PRICE =1.5
+1.5
+1.5
+101.5
(1 + 0.015)1 (1 + 0.015)2 (1 + 0.015)3 (1 + 0.015)4
For example, consider a 2-Yr Bond, 3% Coupon,
3% Yield that pays semi-annually.
Price = $100.00
Price = $101.95
For the same cash flows, a 2% yield has the following price:
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 51
99 =1
+1
+1
+1
+1
+101
(1 + y/2)1 (1 + y/2)2 (1 + y/2)3 (1 + y/2)4 (1 + y/2)5 (1 + y/2)6
Let’s try 3.00% yield
Price = $97.15, which is less than the actual price of $99
so we must try a lower yield.
Let’s try 2.50% yield
Price = $98.56, price still too low.
Let’s try 2.35% yield
Price = $99.00, which equals the price, thus the yield is 2.35%.
What is Yield?
3-Yr Bond, 2% Coupon, $100 Face, $99.00 Price, Yield = ?
(remember, the periodic discount rate is ½ the annual yield)
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 52
9
Calculate Price
Module 2 Exercises
PRICE = CF1
+CF2
+…+CFn
( 1 + y/2)1 (1 + y/2)2 (1 + y/2)n
CF = Cash Flow
Y = Bond-Equivalent Yield
N = Number of Periods
Price is the sum of the present values
of future cash flow
For the following five bond exercises,
assume a principal of $1
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 53
TOTAL PV PRINCIPAL PRICE
$ / $ × 100 = $971,511
PRESENT
VALUE + + + + + =$9,852 $9,706 $9,563 $9,421 $9,282 $923,687
Calculate the Price of a 3-Yr BondExercise 2.1
10
3-Yr Bond, 2.00% Coupon, 3% Yield
INTEREST PAYMENT COUPON INTEREST PAYMENT
INTEREST PAYMENT = × ( ÷ 2 ) =
PRESENT VALUE OF
AN INTEREST PAYMENT
INTEREST PAYMENT YIELD ÷ 2
÷ ( 1 + )n
$1,000,000 0.02 $10,000
$10,000 0.015
INTEREST
PAYMENT
PERIOD 1 PERIOD 2 PERIOD 3 PERIOD 4 PERIOD 5 PERIOD 6
6-Mo 12-Mo 18-Mo 24-Mo 30-Mo 36-Mo
1 MM 97.15
$10,000 $10,000 $10,000 $10,000 $10,000
$1,010,000
PRINCIPAL +
INTEREST
NOTE: Chart is illustrative and is not to scale.
/1.093443
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 54
Calculate Using a Higher YieldExercise 2.2
11
3-Yr Bond, 2.00% Coupon, 5% Yield
PRESENT VALUE OF
AN INTEREST PAYMENT $10,000 ÷ ( 1 + )n0.025
INTEREST
PAYMENT$10,000 $10,000 $10,000 $10,000 $10,000
$1,010,000
NOTE: Chart is illustrative and is not to scale.
TOTAL PV PRICE
$ $917,378
PRESENT
VALUE + + + + + =$9,756 $9,518 $9,285 $9,059 $8,838 $870,922
PERIOD 1 PERIOD 2 PERIOD 3 PERIOD 4 PERIOD 5 PERIOD 6
6-Mo 12-Mo 18-Mo 24-Mo 30-Mo 36-Mo
91.73
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 55
Calculate Using a Lower YieldExercise 2.3
12
3-Yr Bond, 2.00% Coupon, 1% Yield
INTEREST
PAYMENT
PERIOD 1 PERIOD 2 PERIOD 3 PERIOD 4 PERIOD 5 PERIOD 6
6-Mo 12-Mo 18-Mo 24-Mo 30-Mo 36-Mo
$10,000 $10,000 $10,000 $10,000 $10,000
$1,010,000
PRESENT VALUE OF
AN INTEREST PAYMENT $10,000 ÷ ( 1 + )n0.005
TOTAL PV PRICE
$ $1,029,479
PRESENT
VALUE + + + + + =$9,950 $9,900 $9,851 $9,802 $9,753 $980,223
102.94
NOTE: Chart is illustrative and is not to scale.
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 56
Let’s Summarize What We’ve Done So Far
3-Yr Bond, 2% Coupon
Yield Price
0%
1% $102.95
2%
3% $97.15
4%
5% $91.74
6%
7%
8%
9%
10%
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 57
Other Yields Produce Other Prices
3-Yr Bond, 2% Coupon
Yield Price
0% $106.00
1% $102.95
2% $100.00
3% $97.15
4% $94.40
5% $91.74
6% $89.17
7% $86.68
8% $84.27
9% $81.95
10% $79.70
For bonds whose cash flows don’t
change with changes in interest
rates, there is only one price for
each yield. Likewise, there is only
one yield for each price. Or to put it
another way, there is only one price
yield relationship since there is only
possible cash flow.
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 58
$65
$70
$75
$80
$85
$90
$95
$100
$105
$110
0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15%
Let’s Graph the Relationship Between Yield and Price
3-Yr Bond, 2% Coupon
When rates go up, the price goes down
(the yield term is in the denominator).
PR
ICE
YIELD
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 59
$65
$70
$75
$80
$85
$90
$95
$100
$105
$110
0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15%
The Price – Yield Line is Not Straight
3-Yr Bond, 2% Coupon
PR
ICE
YIELD
1%
3%
5%Price Change
$5.80
Price Change
$5.41
Because there are exponents in the denominator, this line is curved. This means that
the change in price for an equal but opposite change in yield is not the same amount.
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 60
Calculate the Price of a 2-Yr BondExercise 2.4
13
2-Yr Bond, 5.00% Coupon, 4% Yield
TOTAL PV PRICE
$ $1,019,039
PRESENT
VALUE + + +$24,509 $24,029 $23,558 $946,943
INTEREST PAYMENT = × ( ÷ 2 )
PRESENT VALUE OF
AN INTEREST PAYMENT ÷ ( 1 + )n
$1,000,000 0.05
$25,000 0.02
INTEREST
PAYMENT
PERIOD 1 PERIOD 2 PERIOD 3 PERIOD 4
6-Mo 12-Mo 18-Mo 24-Mo
$25,000 $25,000 $25,000
$1,025,000
101.90
NOTE: Chart is illustrative and is not to scale.
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 61
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 62
Definition
Spread
The difference between two yields – commonly
between the yield on the instrument in question and
some benchmark rate (such as the similar maturity
U.S. Treasury rate).
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 63
Components of Spread?
3-YEAR
YIE
LD
Benchmark Treasury
(No Liquidity, Credit,
or Option Risk)
Interest Rate Risk
(Includes Current and
Future Inflation Expectations,
Future Monetary Policy, etc.)
Liquidity Risk
Spread
Yield
Option Risk
Credit Risk
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 64
The 3-Yr Treasury on Nov. 6, 2011 is yielding 0.46%
FNMA 2.69 Coupon, Nov. 6, 2014 maturing,
is offered at a spread of +29 bps over the 3-Yrs
So at yield of 0.46 + 0.29, or 0.75
This is the appropriate way to use spread
(as a mechanism for specifying a price)
Spread is Used as a Shorthand When Discussing Prices
But how is spread often (erroneously)
applied to investment thinking?
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 65
PRESENT
VALUE
Treasury Rate + Spread = Agency YieldExercise 2.5
14
3-Yr FNMA, 2.69% Coupon, Yield
$13,399 $13,349 $13,250 $13,200 $990,944$13,299
$1,013,450
YIELD
+ =
PRESENT VALUE OF
AN INTEREST PAYMENT ÷ ( 1 + )n
0.75%
$13,450 0.00375
TOTAL PV PRICE
$ $1,057,441
PERIOD 1 PERIOD 2 PERIOD 3 PERIOD 4 PERIOD 5 PERIOD 6
6-Mo 12-Mo 18-Mo 24-Mo 30-Mo 36-Mo
105.74
$13,450 $13,450 $13,450 $13,450 $13,450
0.46% 0.29%
NOTE: Chart is illustrative and is not to scale.
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 66
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 67
Quiz
A. The annual percentage return that is earned on a security, as
computed in accordance with standard industry practices
B. The discount rate used so that the present value of future defined
cashflows equals the price
C. Book income received from a security
Yield on a Bond is…
WRONG!
WRONG!
B. The discount rate used so that the present value of future defined
cash flows equals the price
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 68
In This Module
Current Practice in Fixed-Income Investing
Conventional Analysis: Risk and Reward
Yield – A Good Measure of Reward?
Yield – What is it Really?
Duration – A Good Measure of Risk?
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 69
Definition
Duration sounds like a measure of what?
Macaulay’s Duration Defined
The weighted average maturity of a bond’s cash
flows, where the present values of the cash flows
serve as the weights. The greater the duration of
the bond, the greater its percentage price volatility.
What is it used for?
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 70
1*PVCF1 + 2*PVCF2 + 3*PVCF + … + n*PVCFn
K*Price
1938 Macaulay Duration
Where:
K = Number of periods per year
n = Number of years to maturity multiplied by K
PVCFPD = Present value of cash flows
in period PD
NOTE: Graphic is illustrative. It is not to scale. Period 1 2 3 4 5
PV of Time
Weighted Interest*
PV of Time
Weighted Principal*
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 71
Example: 5-Yr Treasury 6% Coupon at a 6% Yield
PeriodCash
Flow
Present
Value
Period ×
Present Value
1 3 2.913 2.913
2 3 2.828 5.656
3 3 2.745 8.236
4 3 2.665 10.662
5 3 2.588 12.939
6 3 2.512 15.075
7 3 2.439 17.075
8 3 2.368 18.946
9 3 2.299 20.693
10 103 76.642 766.417
878.611
Price 100.000 [878.6 / (2×100)]
Duration 4.393
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 72
How Does Price Change as Yield Changes?
Note that as yield goes up, the price goes down and as
yield goes down the price goes up. We saw previously that
these price changes for equal but opposite yield changes
are not the same.
It would be nice to have a formula to quantify this rate
of change of price as yield changes. It turns out, a slight
tweak to the Macaulay Duration formula gives this rate
of change of price formula results in a formula, called
Modified Duration, that does this correctly.
PRICE = CF1
+CF2
+…+CFn
( 1 + y/2)1 (1 + y/2)2 (1 + y/2)n
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 73
Where:
K = Number of periods per year
Modified Duration =Macaulay Duration
(1+ yield / K)
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 74
Definition
Modified Duration
The percentage price change of a security for a given
change in yield. The higher the modified duration of a
security, the higher its risk.
Therefore,
If I had a duration of 1.00 and rates moved
100 bps I would expect a 1% price change.
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 75
Modified Duration Examples
5-Yr Treasury 6.00% Coupon (semi-annual coupon) at a 6.00% Yield
Macaulay Duration = 4.393
Modified Duration = 4.393 / 1.03
Modified Duration = 4.265
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 76
What Does Duration Tell Us?
I am considering purchasing one of 3 bonds on 5/1/2013:
“Hey…I need some advice!”
Option AOR
Option BOR
Option C
Yield 0.82% 1.15% 1.26%
w/Modified Duration 4.66 0.99 3.78
What does the modified duration suggest the price
will do if interest rates rise by 100 bps?
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 77
In Fact, We Did Experience a Rate Rise
3 Month Period ~7 &10 years Rates up 100 bps, 5 years up 84 bps, 1 year Unchanged
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 78
Bond A: 5-Yr Bullet Went from $100.31 to $96.473
Modified Duration: 4.66
Expected Change = 0.84 × 4.66 = 3.91%
Actual Price Decline: 3.83%
What Actually Happened to the Prices?
Bond B: 5-Yr NC1 Went from $100 to $97.15
Modified Duration: 0.99
Expected Change = 0 × 0.99 = 0
Actual Price Decline: 2.85%
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 79
Bond C:15 Year 2.5% PoolWent from $104.59 to $99.34
Modified Duration: 3.78
Expected Change = 0.50 × 3.78 = 1.88%
Actual Price Decline: 5.25%
Modified Duration —
Not a Great Predictor for MBS, Either
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 80
In general Duration measures the price sensitivity
of a bond to a small change in interest rates.
For securities such as MBS, Duration measures such
as “Modified Duration” and another well known formula
“Macaulay Duration” have little meaning when it comes
to interest risk management. The formulas are limited
since they assume cash flows do not change if
interest rates change. In this case these formulas
are inappropriate.IVAN BANDIC, MANAGING DIRECTOR RBC CAPITAL MARKETS
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 81
1*PVCF1 + 2*PVCF2 + 3*PVCF + … + n*PVCFn
K*Price
Problem With Duration
Where:
K = Number of periods per year
n = Number of years to maturity multiplied by K
PVCFPD = Present value of cash flows
in period PD
NOTE: Graphic is illustrative. It is not to scale. Period 1 2 3 4 5
What if cash flows change when interest rates change?
2.70
PV of Time
Weighted Interest*
PV of Time
Weighted Principal*
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 82
Problem With Duration
PV of Time
Weighted Interest*
PV of Time
Weighted Principal*
Where:
K = Number of periods per year
n = Number of years to maturity multiplied by K
PVCFPD = Present value of cash flows
in period PD
NOTE: Graphic is illustrative. It is not to scale. Period 1 2 3 4 52.70
What if cash flows change when interest rates change?
1*PVCF1 + 2*PVCF2 + 3*PVCF + … + n*PVCFn
K*Price
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 83
What is the Duration of a 10-Yr NC 1 Agency?
FHLB 3.05 Sep 9, 2020
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 84
What is the Duration of a 10-year NC 1 Agency?
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 85
Duration =V- - V+
2 Vo (∆y)
Effective Duration
Used for Bonds with Embedded Options
Where:
∆ y = Change in the yield of the bond (in decimal form)
V- = Estimated value of the bond per $100 of par value
if the yield is decreased by ∆y
V+ = Estimated value of the bond per $100 of par value
if the yield is increased by ∆y
Vo = Initial price of the bond (per $100 of the par value)
We will see that calculating scenario returns
is a better way to see the effect of duration.
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 86
Words of Wisdom from a Master Investor
Academics, however, like to define investment ‘risk’
(differently) … In their hunger for a single statistic to
measure risk … they forget a fundamental principle:
It is better to be approximately right than
precisely wrong.
WARREN BUFFETTAMERICAN BUSINESS MAGNATE,
INVESTOR and PHILANTHROPIST
Module 2: The Use and Abuse of Conventional Analytics© 2016 Performance Trust. All Rights Reserved. 87
Duration, like average life, is a tool that measures the “risk” of a bond.
Duration runs into problems when it comes to securities with options,
changing cash flows, or large rate changes.
Duration makes no attempt to measure reward or return.
What is better…
Duration
a 5-Yr or a 1-Yr?
Summary
Following conventional analytics is not in the portfolio manager’s best interest.
Yield is a pricing mechanism and “not what you get.”
© 2016 Performance Trust Capital Partners, LLC (which, along with its affiliates, is referred to
as “Performance Trust”). All Rights Reserved. This material is for your internal use only and may
not be disclosed to third parties. The content is the proprietary and confidential material of
Performance Trust and so designated pursuant to a confidentiality agreement between the
intended recipient and Performance Trust. The research and other information provided herein has
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