Essentials of Investments

© 2001 The McGraw-Hill Companies, Inc. All rights reserved.

Fourth Edition

Irwin / McGraw-Hill

Bodie • Kane • Marcus1

Chapter 11

Managing Fixed-Income Investments

Essentials of Investments

© 2001 The McGraw-Hill Companies, Inc. All rights reserved.

Fourth Edition

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Bodie • Kane • Marcus2

Managing Fixed Income Securities: Basic Strategies

• Active strategy– Trade on interest rate predictions– Trade on market inefficiencies

• Passive strategy– Control risk– Balance risk and return

Essentials of Investments

© 2001 The McGraw-Hill Companies, Inc. All rights reserved.

Fourth Edition

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Bond Pricing Relationships

• 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

Essentials of Investments

© 2001 The McGraw-Hill Companies, Inc. All rights reserved.

Fourth Edition

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Bond Pricing Relationships (cont.)

• 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

Essentials of Investments

© 2001 The McGraw-Hill Companies, Inc. All rights reserved.

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Duration• 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

Essentials of Investments

© 2001 The McGraw-Hill Companies, Inc. All rights reserved.

Fourth Edition

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Duration: Calculation

t tt

w CF y ice ( )1 Pr

D t wt

T

t

1

CF Cash Flow for period tt

Essentials of Investments

© 2001 The McGraw-Hill Companies, Inc. All rights reserved.

Fourth Edition

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Bodie • Kane • Marcus7

Duration Calculation

8%Bond

Timeyears

Payment PV of CF(10%)

Weight C1 XC4

1 80 72.727 .0765 .0765

2 80 66.116 .0690 .1392

Sum

3 1080 811.420

950.263

.8539

1.0000

2.5617

2.7774

Essentials of Investments

© 2001 The McGraw-Hill Companies, Inc. All rights reserved.

Fourth Edition

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Bodie • Kane • Marcus8

Duration/Price Relationship

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

Essentials of Investments

© 2001 The McGraw-Hill Companies, Inc. All rights reserved.

Fourth Edition

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Bodie • Kane • Marcus9

Uses of Duration

• Summary measure of length or effective maturity for a portfolio

• Immunization of interest rate risk (passive management)– Net worth immunization– Target date immunization

• Measure of price sensitivity for changes in interest rate

Essentials of Investments

© 2001 The McGraw-Hill Companies, Inc. All rights reserved.

Fourth Edition

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Bodie • Kane • Marcus10

Pricing Error from Convexity

Price

Yield

Duration

Pricing Error from

Convexity

Essentials of Investments

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Correction for Convexity

)(21 2yConvexityyD

P

P

Modify the pricing equation:

Convexity is Equal to:

N

tt

t tty

CFP 1

22 )1(y)(1

1

Where: CFt is the cashflow (interest and/or principal) at time t.

Essentials of Investments

© 2001 The McGraw-Hill Companies, Inc. All rights reserved.

Fourth Edition

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Bodie • Kane • Marcus12

Active Bond Management: Swapping Strategies

• Substitution swap

• Intermarket swap

• Rate anticipation swap

• Pure yield pickup

• Tax swap