McGraw-Hill/Irwin Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 16 Managing Bond Portfolios

16-2 Active strategy Trade on interest rate predictions Trade on market inefficiencies Passive strategy Control risk Balance risk and return Basic Strategies

16-3 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

16-4 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)

16-5 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

16-6 Duration: Calculation

16-7 8% Bond Time years PaymentPV of CF (10%) WeightC1 X C sum Duration Calculation: Spreadsheet 16.1

16-8 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

16-9 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.

16-10 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:

16-11 Rules for Duration (cont’d) Rule 7 The duration for a corporate bond is equal to:

16-12 Yield Price Duration Pricing Error from convexity Duration and Convexity

16-13 Correction for Convexity Correction for Convexity:

16-14 Bond-Index Funds Immunization of interest rate risk: Net worth immunization Duration of assets = Duration of liabilities Target date immunization Holding Period matches Duration Cash flow matching and dedication Passive Management

16-15 Substitution swap Inter-market swap Rate anticipation swap Pure yield pickup Tax swap Active Management: Swapping Strategies

16-16 Maturity Yield to Maturity % 3 mon 6 mon 9 mon Yield Curve Ride

16-17 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.

16-18 Interest Rate Swaps Contract between two parties to exchange a series of cash flows One party pays a fixed rate and receives a variable rate One party pays a variable rate and receives a fixed rate Payments based on notional principal

16-19 Swap Example Figure Swap Dealer Company B Company A LIBOR 7% 6.95%7.05%