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Chapter 14
Revision of the Fixed-Income Portfolio
Portfolio Construction, Management, & Protection, 4e, Robert A. StrongCopyright ©2006 by South-Western, a division of Thomson Business & Economics. All rights reserved.
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There are no permanent changes because change itself is permanent. It behooves the industrialist to
research and the investor to be vigilant.
Ralph L. Woods
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Outline Introduction Passive versus Active Management
Strategies Bond Convexity
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Introduction Fixed-income security management is
largely a matter of altering the level of risk the portfolio faces:• Interest rate risk• Default risk• Reinvestment rate risk
Interest rate risk is measured by duration
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Passive versus Active Management Strategies
Passive Strategies Active Strategies Risk of Barbells and Ladders Bullets versus Barbells Swaps Forecasting Interest Rates Volunteering Callable Municipal Bonds
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Passive Strategies Buy and Hold Indexing
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Buy and Hold Bonds have a maturity date at which their
investment merit ceases
A passive bond strategy still requires the periodic replacement of bonds as they mature
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Indexing Indexing involves an attempt to replicate
the investment characteristics of a popular measure of the bond market
Examples are:• Salomon Brothers Corporate Bond Index• Lehman Brothers Long Treasury Bond Index
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Indexing (cont’d) The rationale for indexing is market
efficiency• Managers are unable to predict market
movements and attempts to time the market are fruitless
A portfolio should be compared to an index of similar default and interest rate risk
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Active Strategies Laddered Portfolio Barbell Portfolio Other Active Strategies
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Laddered Portfolio In a laddered strategy, the fixed-income
dollars are distributed throughout the yield curve
A laddered strategy eliminates the need to estimate interest rate changes
For example, a $1 million portfolio invested in bond maturities from 1 to 25 years (see next slide)
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Laddered Portfolio (cont’d)
05,000
10,000
15,000
20,000
25,00030,000
35,000
40,000
45,000
50,000
1 3 5 7 9 11 13 15 17 19 21 23 25Years Until Maturity
Par
Val
ue H
eld
($)
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Barbell Portfolio The barbell strategy differs from the laddered
strategy in that less amount is invested in the middle maturities
For example, a $1 million portfolio invests $70,000 par value in bonds with maturities of one to five and twenty-one to twenty-five years, and $20,000 par value in bonds with maturities of six to twenty years (see next slide)
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Barbell Portfolio (cont’d)
05,000
10,000
15,000
20,000
25,00030,000
35,000
40,000
45,000
50,000
1 3 5 7 9 11 13 15 17 19 21 23 25Years Until Maturity
Par
Val
ue H
eld
($)
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Barbell Portfolio (cont’d) Managing a barbell portfolio is more complicated
than managing a laddered portfolio Each year, the manager must replace two sets of
bonds:• The one-year bonds mature, and the proceeds are used
to buy 25-year bonds
• The twenty-one-year bonds become twenty-year bonds, and $50,000 par value are sold and applied to the purchase of $50,000 par value of five-year bonds
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Other Active Strategies Identify bonds that are likely to experience
a rating change in the near future• An increase in bond rating pushes the price up
• A downgrade pushes the price down
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Risk of Barbells and Ladders Interest Rate Risk Reinvestment Rate Risk Reconciling Interest Rate and Reinvestment
Rate Risks
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Interest Rate Risk Duration increases as maturity increases
The increase in duration is not linear• Malkiel’s theorem about the decreasing
importance of lengthening maturity• e.g., the difference in duration between two-
and one-year bonds is greater than the difference in duration between twenty-five- and twenty-four-year bonds
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Reinvestment Rate Risk The barbell portfolio requires a reinvestment each
year of $70,000 in par value The laddered portfolio requires the reinvestment
each year of $40,000 in par value
Declining interest rates favor the laddered strategy Rising interest rates favor the barbell strategy
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Reconciling Interest Rate and Reinvestment Rate Risks
The general risk comparison:
Laddered favoredBarbell favoredReinvestment Rate Risk
Laddered favoredBarbell favoredInterest Rate Risk
Falling Interest RatesRising Interest Rates
(This assumes the duration of the laddered portfolio is greater than the duration of the barbell portfolio.)
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Reconciling Interest Rate and Reinvestment Rate Risks (cont’d)
The relationships between risk and strategy are not always applicable:• It is possible to construct a barbell portfolio
with a longer duration than a laddered portfolio– e.g., include all zero coupon bonds in the barbell
portfolio
• When the yield curve is inverting, its shifts are not parallel
– A barbell strategy is safer than a laddered strategy
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Bullets versus Barbells A bullet strategy is one in which the bond
maturities cluster around one particular maturity on the yield curve
It is possible to construct bullet and barbell portfolios with the same durations but with different interest rate risks• Duration only works when yield curve shifts are
parallel
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Bullets versus Barbells (cont’d)
A heuristic on the performance of bullets and barbells:• A barbell strategy will outperform a bullet
strategy when the yield curve flattens
• A bullet strategy will outperform a barbell strategy when the yield curve steepens
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Swaps Purpose Substitution Swap Intermarket or Yield Spread Swap Bond-Rating Swap Rate Anticipation Swap
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Purpose In a bond swap, a portfolio manager
exchanges an existing bond or set of bonds for a different issue
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Purpose (cont’d) Bond swaps are intended to:
• Increase current income• Increase yield to maturity• Improve the potential for price appreciation
with a decline in interest rates• Establish losses to offset capital gains or
taxable income
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Substitution Swap In a substitution swap, the investor
exchanges one bond for another of similar risk and maturity to increase the current yield• e.g., selling an 8 percent coupon for par and
buying an 8 percent coupon for $980 increases the current yield by 16 basis points
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Substitution Swap (cont’d) Profitable substitution swaps are
inconsistent with market efficiency
Obvious opportunities for substitution swaps are rare
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Intermarket or Yield Spread Swap
The intermarket or yield spread swap involves bonds that trade in different markets• e.g., government versus corporate bonds
Small differences in different markets can cause similar bonds to behave differently in response to changing market conditions
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Intermarket or Yield Spread Swap (cont’d)
In a flight to quality, investors become less willing to hold risky bonds• As investors buy safe bonds and sell more risky
bonds, the spread between their yields widens Flight to quality can be measured using the
confidence index• The ratio of the yield on AAA bonds to the
yield on BBB bonds
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Bond-Rating Swap A bond-rating swap is really a form of
intermarket swap
If an investor anticipates a change in the yield spread, he can swap bonds with different ratings to produce a capital gain with a minimal increase in risk
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Rate Anticipation Swap In a rate anticipation swap, the investor
swaps bonds with different interest rate risks in anticipation of interest rate changes• Interest rate decline: swap long-term premium
bonds for discount bonds
• Interest rate increase: swap discount bonds for premium bonds or long-term bonds for short-term bonds
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Forecasting Interest Rates Few professional managers are consistently
successful in predicting interest rate changes
Managers who forecast interest rate changes correctly can benefit• e.g., increase the duration of a bond portfolio if
a decrease in interest rates is expected
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Volunteering Callable Municipal Bonds
Callable bonds are often retired at par as part of the sinking fund provision
If the bond issue sells in the marketplace below par, it is possible:• To generate capital gains for the client
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Bond Convexity (Advanced Topic)
The Importance of Convexity Calculating Convexity General Rules of Convexity Using Convexity
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The Importance of Convexity Convexity is the difference between the
actual price change in a bond and that predicted by the duration statistic
In practice, the effects of convexity are minor
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The Importance of Convexity (cont’d)
The first derivative of price with respect to yield is negative• Downward sloping curves
The second derivative of price with respect to yield is positive• The decline in bond price as yield increases is
decelerating• The sharper the curve, the greater the convexity
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The Importance of Convexity (cont’d)
Greater Convexity
Yield to Maturity
Bon
d P
rice
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The Importance of Convexity (cont’d)
As a bond’s yield moves up or down, there is a divergence from the actual price change (curved line) and the duration-predicted price change (tangent line)• The more pronounced the curve, the greater the
price difference
• The greater the yield change, the more important convexity becomes
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The Importance of Convexity (cont’d)
Yield to Maturity
Bon
d P
rice
Error from using duration only
Current bond price
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Calculating Convexity The percentage change in a bond’s price
associated with a change in the bond’s yield to maturity:
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2
1 1 Error( )
2
where bond price
yield to maturity
dP dP d PdR dR
P P dR P dR P
P
R
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Calculating Convexity (cont’d) The second term contains the bond
convexity:
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2
1Convexity ( )
2
d PdR
P dR
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Calculating Convexity (cont’d) Modified duration is related to the
percentage change in the price of a bond for a given change in the bond’s yield to maturity• The percentage change in the bond price is
equal to the negative of modified duration multiplied by the change in yield
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Calculating Convexity (cont’d) Modified duration is calculated as follows:
Macaulay duration
Modified duration1 Annual yield to maturity / 2
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General Rules of Convexity There are two general rules of convexity:
• The higher the yield to maturity, the lower the convexity, everything else being equal
• The lower the coupon, the greater the convexity, everything else being equal
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Using Convexity Given a choice, portfolio managers should
seek higher convexity while meeting the other constraints in their bond portfolios• They minimize the adverse effects of interest
rate volatility for a given portfolio duration