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Chapter 16 Revision of the Fixed-Income Portfolio. 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. Outline. Introduction Passive versus active management strategies

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slide2
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

outline
Outline
  • Introduction
  • Passive versus active management strategies
  • Bond convexity
introduction
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
passive versus active management strategies
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
passive strategies
Passive Strategies
  • Buy and hold
  • Indexing
buy and hold
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
indexing
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
indexing cont d
Indexing (cont’d)
  • The rationale for indexing is market efficiency
    • Managers are unable to predict market movements and that attempts to time the market are fruitless
  • A portfolio should be compared to an index of similar default and interest rate risk
active strategies
Active Strategies
  • Laddered portfolio
  • Barbell portfolio
  • Other active strategies
laddered portfolio
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)
laddered portfolio cont d
Laddered Portfolio (cont’d)

Par Value Held ($ in Thousands)

Years Until Maturity

barbell portfolio
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 1 to 5 and 21 to 25 years, and $20,000 par value in bonds with maturities of 6 to 20 years (see next slide)
barbell portfolio cont d
Barbell Portfolio (cont’d)

Par Value Held ($ in Thousands)

Years Until Maturity

barbell portfolio cont d15
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 21-year bonds become 20-years bonds, and $50,000 par value are sold and applied to the purchase of $50,000 par value of 5-year bonds
other active strategies
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
risk of barbells and ladders
Risk of Barbells and Ladders
  • Interest rate risk
  • Reinvestment rate risk
  • Reconciling interest rate and reinvestment rate risks
interest rate risk
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 2- and 1-year bonds is greater than the difference in duration between 25- and 24-year bonds
interest rate risk cont d
Interest Rate Risk (cont’d)
  • Declining interest rates favor a laddered strategy
  • Increasing interest rates favor a barbell strategy
reinvestment rate risk
Reinvestment Rate Risk
  • The barbell portfolio requires a reinvestment each year of $70,000 par value
  • The laddered portfolio requires the reinvestment each year of $40,000 par value
  • Declining interest rates favor the laddered strategy
  • Rising interest rates favor the barbell strategy
reconciling interest rate reinvestment rate risks22
Reconciling Interest Rate & Reinvestment Rate Risks
  • 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
bullets versus barbells
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
bullets versus barbells cont d
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
swaps
Swaps
  • Purpose
  • Substitution swap
  • Intermarket or yield spread swap
  • Bond-rating swap
  • Rate anticipation swap
purpose
Purpose
  • In a bond swap, a portfolio manager exchanges an existing bond or set of bonds for a different issue
purpose cont d
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
substitution swap
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% coupon for par and buying an 8% coupon for $980 increases the current yield by 16 basis points
substitution swap cont d
Substitution Swap (cont’d)
  • Profitable substitution swaps are inconsistent with market efficiency
  • Obvious opportunities for substitution swaps are rare
intermarket or yield spread swap
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
intermarket or yield spread swap cont d
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
bond rating swap
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
rate anticipation swap
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
forecasting interest rates
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 is a decrease in interest rates is expected
volunteering callable municipal bonds
Volunteering Callable Municipal Bonds
  • Callable bonds are often retied 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
    • If the bonds are offered to the municipality below par but above the market price
bond convexity
Bond Convexity
  • The importance of convexity
  • Calculating convexity
  • General rules of convexity
  • Using convexity
the importance of convexity
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
the importance of convexity cont d
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
the importance of convexity cont d39
The Importance of Convexity (cont’d)

Greater Convexity

Bond Price

Yield to Maturity

the importance of convexity cont d40
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
the importance of convexity cont d41
The Importance of Convexity (cont’d)

Error from using

duration only

Bond Price

Current bond

price

Yield to Maturity

calculating convexity
Calculating Convexity
  • The percentage change in a bond’s price associated with a change in the bond’s yield to maturity:
calculating convexity cont d
Calculating Convexity (cont’d)
  • The second term contains the bond convexity:
calculating convexity cont d44
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
calculating convexity cont d45
Calculating Convexity (cont’d)
  • Modified duration is calculated as follows:
general rules of convexity
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
using convexity
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