10 BOND PORTFOLIO MANAGEMENT
BOND PORTFOLIO
MANAGEMENT
5 STEPS INVOLVED IN THE
MANAGEMENT INVESTMENT PROCESS
1. SETTING INVESTMENT OBJECTIVES
2. ESTABLISHING AN INVESTMENT POLICY
3. SELECTING A PORTFOLIO STRATEGY
4. SELECTING ASSETS
5. MEASURING AND EVALUATING PERFORMANCE
1.SETTING INVESTMENT OBJECTIVES
•Investment objective will vary by type of financial institution :
•Life insurance
•Pension fund
•Banks
•Investment companies
•HF
2. ESTABLISHING AN INVESTMENT POLICY
•Setting asset allocation (cash, equities, fixed-income…)
•Regularly constraints (no bonds Convexity bullet
Which portfolio is more volatile ?
Barbell for a decrease in rates
DURATION VS CONVEXITY
For 2 portfolios with the same duration, the greater the
convexity, the better the performance of a bond,
when yield changes.
What is the dollar yield to maturity of the bullet portfolio?
9.25%
What is the dollar yield to maturity of the barbell portfolio?
0.502 (8.50%) + 0.498 (9.50%) = 8.998%
YTM bullet > YTM barbell
ANALYSIS CONCLUSION
•Same duration = 6.434
•Yield bullet > Yield barbell
•Convexity barbell > Convexity Bullet
Chosing the barbell portfolio is refered to The Cost of Convexity
Giving up yield for better convexity
…...6-MONTH HORIZON
(hand out)
Which portfolio (bullet or barbell) should a portfolio manager
choose with a 6-month investment horizon ?
Difference in dollar return = bullet total return - barbell total
return
FOR A PARALLEL SHIFT IN YIELDS WHICH PORTFOLIO
OUTPERFORMS THE OTHER WHEN YIELD CHANGE BY
MORE THAN 100 BP ?
PARALLEL SHIFT
•When yield changes by more than 100BP, the barbell portfolio
outperforms the bullett portfolio (and vice versa)
Even with parallel shift in yield curve 2 portfolios with the same
duration will not give the same performance
Different convexity
With all other things beeing equal, the market pays more for
convexity through higher prices
PARALLEL SHIFT
•If the yield changes by less than 100BP (up or down), the
bullet portfolio will provide a better total return.
Convexity gives more accurate information on bond sensitivity
for large variation in yields.
YIELD SPREAD
STRATEGIES
•Positioning a portfolio to capitalize on change in yield spreads
between sectors of the bond market
•Yield spread betwen the 2-year and 10-year Treasuries
(intermarket spread swap)
CREDIT SPREAD
•Credit spread between Treasury and non-Treasury widens or narrows
in a declining or contracting economy.
Widens why?
Less revenues for companies
debt
repayment problems
less credibility
more risk
wider spreads
IMPORTANCE OF
DOLLAR DURATION
P = 80
Dur = 5
A
P = 90
Dur = 4
B
For a 100BP change, Bond A will vary by 5% that is $40
For a 100BP change, Bond B will vary by 4% that is $36
Suppose that a portfolio manager owns $10 million of par value of
Bond A and Bond B which has a market value of $8 million
$9 million
The dollar duration of Bond A per 100BP change in yield for the
$8 million market value is $400 000 that is 5% x $8 million
The dollar duration of Bond B per 100BP change in yield for the
$9 million market value is $360 000 that is 4% x $9 million
•Suppose that the portfolio manager wants to exchange Bond A that
it owns in his portfolio for Bond B
•He needs to keep the same interest rate exposure (same duration)
for Bond B that he currently holds for Bond A
?
What quantity of Bond B must he purchase to keep his dollar
Duration the same ?
1. If he buys $10 million of par value of Bond B and therefore
$9 million of market value of Bond B(90% of face value),
the dollar change for a 100 BP change in rates would be only
$360 000
2. If he purchases $10 million of market value of Bond B, the dollar
change for a 100BP change in rates would be $ 400 000
Because Bond B is trading at 90, $11.1 million of par value
of Bond B must be purchased to keep the dollar duration the
same
Mathematically….
Let:
$DA = dollar duration per 100BP change in yield for Bond A
for the market value of Bond A held
MDB = Modified duration for Bond B
MVB = Market value of Bond B
Then the following equation sets the dollar duration for Bond A equal
to the dollar duration of Bond B :
MDB
$DA = ------------- MVB and then solving for MVB
THE USE OF LEVERAGE
•A portfolio that does not contain any leverage is called an
unlevered portfolio.
•A portfolio that contains leverage is called a levered portfolio.
Why use leverage in any investment ?
What are the risk associated with leverage investing
DURATION OF A
LEVERAGED PORTFOLIO
•Portfolio of $100 million invested in a bond with a duration of 10
•Borrows $300 million and invest it in the same bond
Total = $400 million
What if rates change by 100BP ?
Changes by $40 million
The portfolio manager is interested in his equity ($100 million), not
the levered part of his investment.
The proper way to measure the portfolio’s duration is relative to the
unlevered amount of equity because the the manager is concerned
with the risk exposure relative to his equity
The duration of the unlevered portfolio = 10
Speculating on Interest Rates
•A portfolio manager who wants to speculate on an increase in
interest rates will buy/sell interest rate futures .
sell
•
3 advantages of using futures :
1. Lower transaction cost
2. Easier to sell short on futures than in the cash Treasury market
3. Margin requirement are lower
Controlling the interest rate risk
of a portfolio
•Interest rate futures can be used to adjust the durationof a portfolio.
•Suppose a portfolio manager wishes to increase the duration of his
portfolio from 5 years to 10 years using futures.
How many contracts should he buy/sell? buy
(DTarget - Dinitial ) Pvalue
Approximate # of contracts = ----------------------------------------------(to reach a new duration level)
D asset underlying future contract x Valuefuture contract
BOND
A
FV
DUR
Di =10.8
BOND
B
BOND
C
$2 000 000 $3 000 000 $5 000 000
9
10
12
100
100
100
DT = 1.2 x 10.8 = 12.96
Buy 17 contracts
The portfolio manager expect a decrease in interest rate.
Increase duration
•What should he do regarding duration ?
•He wishes to modify the duration of his portfolio by 20%
How many futures contracts should he buy/sell knowing that
the contract trades at 103 ? (20-year 8% coupon bond yielding 6%
has a modified duration of 13)
HEDGING USING
INTEREST RATE FUTURES
In bond portfolio management, the bond to be hedged is not identical
to the bond underlying the futures contract
If rates are expected to go up, and a portfolio manager wishes to
hedge his long position in bonds, he would short interest rate
futures.
•How many contracts should he short ?
Par value to be hedged
Hedge ratio x ----------------------------Par value of contract
Par value to be hedged
Contract amount = Hedge ratio x ----------------------------Par value of contract
Duration of bond to be hedged
Hedge ratio = -----------------------------------------Duration of hedging instrument
If the bond to be hedged is more volatile than the hedging instrument,
more
more/less of the hedging instrument will be needed.
BOND
A
FV
DUR
BOND
B
BOND
C
$2 000 000 $3 000 000 $5 000 000
9
10
12
PRICE
90
110
100
Weight:
17 ,82%
32,68%
49,50%
Portfolio Value = 10,1Million
Duration : (9 x 17,82%) + (32,68% x 10) + (12 x 49,50%) =10.82
You need to short 84 contracts (see previous page for formula)
Consider porfolio’s value of $95 million (par value $100 million).
Volatility of the portfolio is 16% and the volatility of the contract is 13%.
How many contracts should be bought/sold to hedge the portfolio?
0.16/ 0.13 x 100 million/$100 000 = 1231 contracts (always round up
MANAGEMENT
5 STEPS INVOLVED IN THE
MANAGEMENT INVESTMENT PROCESS
1. SETTING INVESTMENT OBJECTIVES
2. ESTABLISHING AN INVESTMENT POLICY
3. SELECTING A PORTFOLIO STRATEGY
4. SELECTING ASSETS
5. MEASURING AND EVALUATING PERFORMANCE
1.SETTING INVESTMENT OBJECTIVES
•Investment objective will vary by type of financial institution :
•Life insurance
•Pension fund
•Banks
•Investment companies
•HF
2. ESTABLISHING AN INVESTMENT POLICY
•Setting asset allocation (cash, equities, fixed-income…)
•Regularly constraints (no bonds Convexity bullet
Which portfolio is more volatile ?
Barbell for a decrease in rates
DURATION VS CONVEXITY
For 2 portfolios with the same duration, the greater the
convexity, the better the performance of a bond,
when yield changes.
What is the dollar yield to maturity of the bullet portfolio?
9.25%
What is the dollar yield to maturity of the barbell portfolio?
0.502 (8.50%) + 0.498 (9.50%) = 8.998%
YTM bullet > YTM barbell
ANALYSIS CONCLUSION
•Same duration = 6.434
•Yield bullet > Yield barbell
•Convexity barbell > Convexity Bullet
Chosing the barbell portfolio is refered to The Cost of Convexity
Giving up yield for better convexity
…...6-MONTH HORIZON
(hand out)
Which portfolio (bullet or barbell) should a portfolio manager
choose with a 6-month investment horizon ?
Difference in dollar return = bullet total return - barbell total
return
FOR A PARALLEL SHIFT IN YIELDS WHICH PORTFOLIO
OUTPERFORMS THE OTHER WHEN YIELD CHANGE BY
MORE THAN 100 BP ?
PARALLEL SHIFT
•When yield changes by more than 100BP, the barbell portfolio
outperforms the bullett portfolio (and vice versa)
Even with parallel shift in yield curve 2 portfolios with the same
duration will not give the same performance
Different convexity
With all other things beeing equal, the market pays more for
convexity through higher prices
PARALLEL SHIFT
•If the yield changes by less than 100BP (up or down), the
bullet portfolio will provide a better total return.
Convexity gives more accurate information on bond sensitivity
for large variation in yields.
YIELD SPREAD
STRATEGIES
•Positioning a portfolio to capitalize on change in yield spreads
between sectors of the bond market
•Yield spread betwen the 2-year and 10-year Treasuries
(intermarket spread swap)
CREDIT SPREAD
•Credit spread between Treasury and non-Treasury widens or narrows
in a declining or contracting economy.
Widens why?
Less revenues for companies
debt
repayment problems
less credibility
more risk
wider spreads
IMPORTANCE OF
DOLLAR DURATION
P = 80
Dur = 5
A
P = 90
Dur = 4
B
For a 100BP change, Bond A will vary by 5% that is $40
For a 100BP change, Bond B will vary by 4% that is $36
Suppose that a portfolio manager owns $10 million of par value of
Bond A and Bond B which has a market value of $8 million
$9 million
The dollar duration of Bond A per 100BP change in yield for the
$8 million market value is $400 000 that is 5% x $8 million
The dollar duration of Bond B per 100BP change in yield for the
$9 million market value is $360 000 that is 4% x $9 million
•Suppose that the portfolio manager wants to exchange Bond A that
it owns in his portfolio for Bond B
•He needs to keep the same interest rate exposure (same duration)
for Bond B that he currently holds for Bond A
?
What quantity of Bond B must he purchase to keep his dollar
Duration the same ?
1. If he buys $10 million of par value of Bond B and therefore
$9 million of market value of Bond B(90% of face value),
the dollar change for a 100 BP change in rates would be only
$360 000
2. If he purchases $10 million of market value of Bond B, the dollar
change for a 100BP change in rates would be $ 400 000
Because Bond B is trading at 90, $11.1 million of par value
of Bond B must be purchased to keep the dollar duration the
same
Mathematically….
Let:
$DA = dollar duration per 100BP change in yield for Bond A
for the market value of Bond A held
MDB = Modified duration for Bond B
MVB = Market value of Bond B
Then the following equation sets the dollar duration for Bond A equal
to the dollar duration of Bond B :
MDB
$DA = ------------- MVB and then solving for MVB
THE USE OF LEVERAGE
•A portfolio that does not contain any leverage is called an
unlevered portfolio.
•A portfolio that contains leverage is called a levered portfolio.
Why use leverage in any investment ?
What are the risk associated with leverage investing
DURATION OF A
LEVERAGED PORTFOLIO
•Portfolio of $100 million invested in a bond with a duration of 10
•Borrows $300 million and invest it in the same bond
Total = $400 million
What if rates change by 100BP ?
Changes by $40 million
The portfolio manager is interested in his equity ($100 million), not
the levered part of his investment.
The proper way to measure the portfolio’s duration is relative to the
unlevered amount of equity because the the manager is concerned
with the risk exposure relative to his equity
The duration of the unlevered portfolio = 10
Speculating on Interest Rates
•A portfolio manager who wants to speculate on an increase in
interest rates will buy/sell interest rate futures .
sell
•
3 advantages of using futures :
1. Lower transaction cost
2. Easier to sell short on futures than in the cash Treasury market
3. Margin requirement are lower
Controlling the interest rate risk
of a portfolio
•Interest rate futures can be used to adjust the durationof a portfolio.
•Suppose a portfolio manager wishes to increase the duration of his
portfolio from 5 years to 10 years using futures.
How many contracts should he buy/sell? buy
(DTarget - Dinitial ) Pvalue
Approximate # of contracts = ----------------------------------------------(to reach a new duration level)
D asset underlying future contract x Valuefuture contract
BOND
A
FV
DUR
Di =10.8
BOND
B
BOND
C
$2 000 000 $3 000 000 $5 000 000
9
10
12
100
100
100
DT = 1.2 x 10.8 = 12.96
Buy 17 contracts
The portfolio manager expect a decrease in interest rate.
Increase duration
•What should he do regarding duration ?
•He wishes to modify the duration of his portfolio by 20%
How many futures contracts should he buy/sell knowing that
the contract trades at 103 ? (20-year 8% coupon bond yielding 6%
has a modified duration of 13)
HEDGING USING
INTEREST RATE FUTURES
In bond portfolio management, the bond to be hedged is not identical
to the bond underlying the futures contract
If rates are expected to go up, and a portfolio manager wishes to
hedge his long position in bonds, he would short interest rate
futures.
•How many contracts should he short ?
Par value to be hedged
Hedge ratio x ----------------------------Par value of contract
Par value to be hedged
Contract amount = Hedge ratio x ----------------------------Par value of contract
Duration of bond to be hedged
Hedge ratio = -----------------------------------------Duration of hedging instrument
If the bond to be hedged is more volatile than the hedging instrument,
more
more/less of the hedging instrument will be needed.
BOND
A
FV
DUR
BOND
B
BOND
C
$2 000 000 $3 000 000 $5 000 000
9
10
12
PRICE
90
110
100
Weight:
17 ,82%
32,68%
49,50%
Portfolio Value = 10,1Million
Duration : (9 x 17,82%) + (32,68% x 10) + (12 x 49,50%) =10.82
You need to short 84 contracts (see previous page for formula)
Consider porfolio’s value of $95 million (par value $100 million).
Volatility of the portfolio is 16% and the volatility of the contract is 13%.
How many contracts should be bought/sold to hedge the portfolio?
0.16/ 0.13 x 100 million/$100 000 = 1231 contracts (always round up