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CHAPTER 16 CHAPTER 16 Investments Investments Managing Bond Managing Bond Portfolios Portfolios Slides by Slides by Richard D. Johnson Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin McGraw-Hill/Irwin Cover image

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Page 1: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

CHAPTER 16CHAPTER 16

InvestmentsInvestments

Managing Bond Managing Bond PortfoliosPortfolios

Slides bySlides by

Richard D. JohnsonRichard D. Johnson

Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reservedCopyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/IrwinMcGraw-Hill/Irwin

Cover image

Page 2: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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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 Relationships

Page 3: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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Figure 16.1 Change in Bond Price as a Function of Change in Yield to Maturity

Page 4: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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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)

Page 5: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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Table 16.1 Prices of an 8% Coupon Bond (Coupons Paid Semiannually)

Page 6: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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Table 16.2 Prices of Zero-Coupon Bond (Coupons Paid Semiannually)

Page 7: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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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.

Duration

Page 8: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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Figure 16.2 Cash Flows Paid by 9% Coupon, Annual Payment

Bond with an 8-Year Maturity and 10% Yield to Maturity

Page 9: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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t tt

w CF y ice ( )1 Pr

twtDT

t

1

CF CashFlow for period tt

Duration: Calculation

Page 10: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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Spreadsheet 16.1 Calculating the Duration of Two Bonds

Page 11: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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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 Relationship

Page 12: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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Rules 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.

Rules 5 The duration of a level perpetuity is equal to: (1+y) / y

Page 13: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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Figure 16.3 Bond Duration versus Bond Maturity

Page 14: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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Table 16.3 Bond Duration (Initial Bond Yield 8% APR)

Page 15: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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Figure 16.4 Bond Price Convexity (30-Year Maturity, 8% Coupon; Initial Yield to Maturity = 8%

Page 16: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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Correction for Convexity

n

tt

t tty

CF

yPConvexity

1

22

)()1()1(

1

Correction for Convexity:

])([21 2yConveixityyD

P

P

Page 17: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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Figure 16.5 Convexity of Two Bonds

Page 18: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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Figure 16.6 Price –Yield Curve for a Callable Bond

Page 19: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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Figure 16.7 Price – Yield Curve for a Mortgage-Backed Security

Page 20: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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Figure 16.8 Panel AP: Cash Flows to Whole Mortgage Pool; Panels B – D Cash Flows to Three Tranches

Page 21: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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Bond-Index FundsImmunization of interest rate risk:

– Net worth immunizationDuration of assets = Duration of liabilities

– Target date immunizationHolding Period matches Duration

Cash flow matching and dedication

Passive Management

Page 22: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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Figure 16.9 Stratification of Bonds into Cells

Page 23: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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Table 16.4 Terminal value of a Bond Portfolio After 5 Years (All Proceeds Reinvested)

Page 24: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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Figure 16.10 Growth of invested Funds

Page 25: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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Figure 16.11 Immunization

Page 26: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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Table 16.5 Market Value of Balance Sheet

Page 27: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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Substitution swapIntermarket swapRate anticipation swapPure yield pickupTax swap

Active Management: Swapping Strategies

Page 28: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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Maturity

Yield to Maturity %

3 mon 6 mon 9 mon

1.5 1.25 .75

Yield Curve Ride

Page 29: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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Contingent Immunization

A combination of active and passive management.

The 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.

Page 30: CHAPTER 16 Investments Managing Bond Portfolios Slides by Richard D. Johnson Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

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Figure 16.12 Contingent Immunization


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