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Fixed-IncomeFixed-IncomePortfolio ManagementPortfolio Management

Chapter 16Chapter 16

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Active strategy- Trade on interest rate predictions

- Trade on market inefficiencies Passive strategy

- Control risk

- Balance risk and return

Managing Fixed Income Securities: Managing Fixed Income Securities: Basic StrategiesBasic Strategies

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Inverse relationship between price and yield An increase in a bond’s yield to maturity

results in a smaller price decline than the gain associated with a decrease in yield

Long-term bonds tend to be more price sensitive than short-term bonds

Bond Pricing RelationshipsBond Pricing Relationships

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As maturity increases, price sensitivity increases at a decreasing rate

Price sensitivity is inversely related to a bond’s coupon rate

Price sensitivity is inversely related to the yield to maturity at which the bond is selling

Bond Pricing Relationships (cont’d)Bond Pricing Relationships (cont’d)

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A measure of the effective maturity of a bond The weighted average of the times until each payment is received,

with the weights proportional to the present value of the payment Duration is shorter than maturity for all bonds except zero coupon

bonds Duration is equal to maturity for zero coupon bonds

DurationDuration

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t tt

w CF y ice ( )1 Pr

twtDT

t

1

CF Cash Flow for period tt

Duration: CalculationDuration: Calculation

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8%Bond

Timeyears

Payment PV of CF(10%)

Weight C1 XC4

.5 40 38.095 .0395 .0198

1 40 36.281 .0376 .0376

1.5

2.0

40

1040

sum

34.553

855.611

964.540

.0358

.8871

1.000

.0537

1.7742

1.8853

Duration Calculation: Duration Calculation: Example using Table 16.3Example using Table 16.3

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Price change is proportional to duration and not to maturity

P/P = -D x [(1+y) / (1+y)

D* = modified duration

D* = D / (1+y)

P/P = - D* x y

Duration/Price RelationshipDuration/Price Relationship

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Rules for DurationRules for Duration

Rule 1 The duration of a zero-coupon bond equals its time to maturity

Rule 2 Holding maturity constant, a bond’s duration is higher when the coupon rate is lower

Rule 3 Holding the coupon rate constant, a bond’s duration generally increases with its time to maturity

Rule 4 Holding other factors constant, the duration of a coupon bond is higher when the bond’s yield to maturity is lower

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Rules for Duration (cont’d)Rules for Duration (cont’d)

Rules 5 The duration of a level perpetuity is equal to:

Rule 6 The duration of a level annuity is equal to:

1)1(

1

Ty

T

y

y

y

y)1(

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Rules for Duration (cont’d)Rules for Duration (cont’d)

Rule 7 The duration for a corporate bond is equal to:

yyc

ycTy

y

yT

]1)1[(

)()1(1

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Bond-Index Funds Immunization of interest rate risk

- Net worth immunizationDuration of assets = Duration of liabilities

- Target date immunizationHolding Period matches Duration

Cash flow matching and dedication

Passive ManagementPassive Management

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Yield

Price

Duration

Pricing Error from convexity

Duration and ConvexityDuration and Convexity

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Correction for ConvexityCorrection for Convexity

n

tt

t tty

CF

yPConvexity

1

22

)()1()1(

1

Correction for Convexity:

])([21 2yConveixityyD

P

P

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Substitution swap Intermarket swap Rate anticipation swap Pure yield pickup Tax swap

Active Bond Management: Active Bond Management: Swapping StrategiesSwapping Strategies

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Maturity

Yield to Maturity %

3 mon 6 mon 9 mon

1.5 1.25 .75

Yield Curve RideYield Curve Ride

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Contingent ImmunizationContingent Immunization

Combination of active and passive management

Strategy involves active management with a floor rate of return

As long as the rate earned exceeds the floor, the portfolio is actively managed

Once the floor rate or trigger rate is reached, the portfolio is immunized