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## Chapter 16 Revision of the Fixed-Income Portfolio

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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

Outline

- Introduction
- Passive versus active management strategies
- Bond convexity

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 strategies
- Active strategies
- Risk of barbells and ladders
- Bullets versus barbells
- Swaps
- Forecasting interest rates
- Volunteering callable municipal bonds

Passive Strategies

- Buy and hold
- Indexing

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 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)

- 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

- Laddered portfolio
- Barbell portfolio
- Other active strategies

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)

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)

- 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

- 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

- Interest rate risk
- Reinvestment rate risk
- Reconciling interest rate and reinvestment rate risks

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)

- Declining interest rates favor a laddered strategy
- Increasing interest rates favor a barbell strategy

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 Risks

- The general risk comparison:

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

- 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)

- 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

- Purpose
- Substitution swap
- Intermarket or yield spread swap
- Bond-rating swap
- Rate anticipation swap

Purpose

- In a bond swap, a portfolio manager exchanges an existing bond or set of bonds for a different issue

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

- 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)

- Profitable substitution swaps are inconsistent with market efficiency
- Obvious opportunities for substitution swaps are rare

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)

- 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

- 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

- 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

- 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

- 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

- The importance of convexity
- Calculating convexity
- General rules of convexity
- Using 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 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’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’d)

Error from using

duration only

Bond Price

Current bond

price

Yield to Maturity

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)

- The second term contains the bond convexity:

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’d)

- Modified duration is calculated as follows:

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

- 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

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