MANAGINGTHE FIXED INCOME PORTFOLIO

CHAPTER NINETEEN

Practical Investment Management

Robert A. Strong

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Outline

Fixed Income Security Risk Default Risk Reinvestment Rate Risk Interest Rate Risk

Duration Duration Measures Applying Duration

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Outline

Convexity Problems with Duration Simple Convexity An Example Using Convexity

Management Strategies Active vs. Passive Management Classic Passive Management Strategies The Risk of Barbells and Ladders Indexing Active Management

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Fixed Income Security Risk

Default risk, or credit risk, is the possibility that a borrower will be unable to repay principal and interest as agreed upon in the loan document.

Reinvestment rate risk refers to the possibility that the cash coupons received will be reinvested at a rate different from the bond’s stated rate.

Interest rate risk refers to the chance of loss because of adverse movements in the general level of interest rates.

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Interest Rate Risk : Malkiel’s Theorems

Malkiel’s theorems are a set of relationships among bond prices, time to maturity, and interest rates.

Theorem One : Bond prices move inversely with yields.

Theorem Two : Long-term bonds have more risk.

Theorem Three : Higher coupon bonds have less risk.

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Interest Rate Risk : Malkiel’s Theorems

Theorem Four : The importance of theorem two diminishes with time.

Theorem Five : Capital gains from an interest rate decline exceed the capital loss from an equivalent interest rate increase.

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Interest Rate Risk : Malkiel’s Theorems

Insert Table 19-1 here.

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Interest Rate Risk : Malkiel’s Theorems

Bond A : matures in 8 years, 9.5% coupon Bond B : matures in 15 years, 11% coupon Which price will rise more if interest rates fall?

Apparent contradictions can be reconciled by computing a statistic called duration.

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Duration

For a noncallable security, duration is the weighted average time until abond’s cash flows are received.

Duration is not limited to bond analysis. It can be determined for any cash flow stream.

Duration is a direct measure of interest rate risk. The higher it is, the higher is the risk.

Thinking of duration as a measure of time can be misleading if the life or the payments of the bond are uncertain.

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D

C t

1 R tt1

N

t

Pwhere D = duration Ct = cast flow at time t R = yield to maturity (per period) P = current price of bond N = number of periods until maturity t = period in which cash flow is received

Duration Measures

Macaulay duration is the time-value-of-money-weighted, average number of years necessary to recover the initial cost of the security.

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Duration Measures

P

R

FN

RR

RNRRC

DNN

N

t

11

112

1

where F = face value (par value) of the bondand all other variables are as previously defined.

Chua’s closed-form duration is less cumbersome because it has no summation requirement.

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Duration Measures

PR

NC

R

C

R

C

RPdR

dPN

N 1

11

2

11

112

21

1

21 R+

DD Macaulay

modified

Modified duration measures the percentage change in bond value associated with a one-point change in interest rates.

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Duration Measures

Deffective

P PP0 R R

where P- = price of bond associated with a decline of x basis points P+ = price of bond associated with a rise of x basis points R- = initial yield minus x basis points R+ = initial yield plus x basis points P0 = initial price of the bond

Effective duration is a measure of price sensitivity calculated from actual bond prices associated with different interest rates. It is a close approximation of modified duration for small yield changes.

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Dollar duration determines the dollar amount associated with a percentage price change.

Duration Measures

Ddollar = - x modifiedduration

bond price as apercentage of par

Pnew = Pold + (Ddollar x change in yield)

The price value of a basis point is the dollar price change in a bond associated with a single basis point change in the bond’s yield.

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Applying Duration

The yield curve experiences a parallel shift when interest rates at each maturity change by the same amount.

Duration is especially useful in determining the relative riskiness of two or more bonds when visual inspection of their characteristics makes it unclear which is more vulnerable to changing interest rates.

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Applying Duration

Insert Table 19-2 here.

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Problems with Duration

The bond price - bond yield relationship is not linear.p

rice

yield to maturity

Graphically, duration is the tangent to the current point on the price-yield curve. Its absolute value declines as yield to maturity rises.

Duration is a first derivative statistic. Hence, when the change is large, estimates made using the derivative alone will contain errors.

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Problems with Duration

Insert Figure 19-1 here.

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Problems with Duration

Insert Figure 19-2 here.

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Problems with Duration

Insert Figure 19-3 here.

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Convexity

N

tNt

t

R

FNN

R

Ctt

PConvexity

122 1

1

1

11

Convexity measures the difference between the actual price and that predicted by duration, i.e. the inaccuracy of duration.

The more convex the bond price-YTM curve, the greater is the convexity.

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Convexity

Insert Figure 19-4 here.

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Convexity : An Example

Price forecasting accuracy is enhanced by incorporating the effects of convexity.

Suppose a bond has a 15-year life, an 11% coupon, and a price of 93%. Macaulay duration = 7.42, yield-to-maturity = 12.00%, modified duration = 7.00, convexity = 97.71.

If YTM rises to 12.50%, new price= 89.95% Actual price change = - 3.28% Price change predicted by duration = - 3.50% Price change predicted by duration and convexity = - 3.38%

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Using Convexity

yield to maturity

bo

nd

pri

ce

No matter what happens to interest rates, the bond with the greater convexity fares better. It dominates the competing investment.

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Using Convexity

Insert Figure 19-6 here.

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Management Strategies

An active strategy is one in which the investment manager seeks to improve the rate of return on the portfolio by anticipating events in the marketplace.

A passive strategy is one in which the portfolio is largely left alone after its construction. Changes are made when securities mature or are called, but normally not for any other reason.

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Classic Passive Management Strategies

A laddered strategy distributes fixed income dollars throughout the yield curve.p

ar

va

lue

maturity

maturity

pa

r v

alu

e

A barbell strategy differs from the laddered strategy in that less investment is made in the middle maturities.

A credit barbell is a bond portfolio containing a mix of high-grade and low-grade securities.

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Classic Passive Management Strategies

Insert Figure 19-7 here.

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Classic Passive Management Strategies

Insert Figure 19-8 here.

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Classic Passive Management Strategies

Insert Figure 19-9 here.

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Classic Passive Management Strategies

Insert Figure 19-10 here.

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If durationladdered portfolio > durationbarbell portfolio ,

The Risk of Barbells and Ladders

Yield curve inversion means short-term rates are rising faster than long-term rates. Duration as a pure measure of interest rate risk only works for parallel shifts in the yield curve.

rising interest rate falling interest rate

interest rate barbell ladder risk favored favored

reinvestment barbell ladder rate risk favored favored

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Passive Management Strategies

Indexing is predicated upon managers being unable to consistently predict market movements.

Indexing involves attempting to replicate the investment characteristics of a popular measure of the bond market.

The two best-known bond indexes are probably the Merrill Lynch Corporate Bond Index and the Lehman Brothers Bond Index.

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Active Management Strategies

Active management techniques frequently involve a bond swap, which is usually intended to do one of four things: 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

Active management strategies fall into four broad categories.

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Strategy 1 : Duration Management

Duration management techniques involve creating a structured portfolio - a collection of securities with characteristics that will accommodate a specific need or objective.

A key concept is immunization - a technique that seeks to reduce or eliminate the interest rate risk in a portfolio.

Bank immunization is achieved when the total dollar duration of a financial institution’s rate sensitive assets equals the total dollar duration of its rate sensitive liabilities.

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Strategy 1 : Duration Management

Bullet immunization seeks to ensure that a specific sum of money will be available at a point or series of points in the future. Cash matching is the special case when cash is generated exactly in line with cash demands.

Another practice, known as duration matching, aims to get interest rate risk and reinvestment rate risk to cancel each other out.

A dedicated portfolio is a separate portfolio that will generate cash equal to or greater than some required amount.

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Active Management Strategies

Strategy 2 : Yield Curve Reshaping If lower interest rates are expected, long-term

premium bonds may be exchanged for long-term discount bonds, for example.

Strategy 3 : Sector Selection Differences in market sectors sometimes cause

otherwise similar bonds to behave differently in response to market changes.

Strategy 4 : Issue Selection Analysts try to correctly anticipate bond rating

changes or make profitable substitution swaps.

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Review

Fixed Income Security Risk Default Risk Reinvestment Rate Risk Interest Rate Risk

Duration Duration Measures Applying Duration

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Review

Convexity Problems with Duration Simple Convexity An Example Using Convexity

Management Strategies Active vs. Passive Management Classic Passive Management Strategies The Risk of Barbells and Ladders Indexing Active Management