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Fixed Income , Bonds


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Chapter 16 Revision of the Fixed-Income Portfolio:

1 Chapter 16 Revision of the Fixed-Income Portfolio

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2 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


3 Outline Introduction Passive versus active management strategies Bond convexity


4 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:

5 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:

6 Passive Strategies Buy and hold Indexing

Buy and Hold:

7 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


8 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):

9 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:

10 Active Strategies Laddered portfolio Barbell portfolio Other active strategies

Laddered Portfolio:

11 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):

12 Laddered Portfolio (cont’d) Years Until Maturity Par Value Held ($ in Thousands)

Barbell Portfolio:

13 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):

14 Barbell Portfolio (cont’d) Years Until Maturity Par Value Held ($ in Thousands)

Barbell Portfolio (cont’d):

15 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:

16 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:

17 Risk of Barbells and Ladders Interest rate risk Reinvestment rate risk Reconciling interest rate and reinvestment rate risks

Interest Rate Risk:

18 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):

19 Interest Rate Risk (cont’d) Declining interest rates favor a laddered strategy Increasing interest rates favor a barbell strategy

Reinvestment Rate Risk:

20 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:

21 Reconciling Interest Rate & Reinvestment Rate Risks The general risk comparison: Rising Interest Rates Falling Interest Rates Interest Rate Risk Barbell favored Laddered favored Reinvestment Rate Risk Barbell favored Laddered favored

Reconciling Interest Rate & Reinvestment Rate Risks:

22 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:

23 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):

24 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


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


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

Purpose (cont’d):

27 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:

28 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):

29 Substitution Swap (cont’d) Profitable substitution swaps are inconsistent with market efficiency Obvious opportunities for substitution swaps are rare

Intermarket or Yield Spread Swap:

30 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):

31 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:

32 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:

33 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:

34 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:

35 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:

36 Bond Convexity The importance of convexity Calculating convexity General rules of convexity Using convexity

The Importance of Convexity:

37 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):

38 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):

39 The Importance of Convexity (cont’d) Greater Convexity Yield to Maturity Bond Price

The Importance of Convexity (cont’d):

40 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):

41 The Importance of Convexity (cont’d) Yield to Maturity Bond Price Error from using duration only Current bond price

Calculating Convexity:

42 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):

43 Calculating Convexity (cont’d) The second term contains the bond convexity:

Calculating Convexity (cont’d):

44 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):

45 Calculating Convexity (cont’d) Modified duration is calculated as follows:

General Rules of Convexity:

46 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:

47 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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