1. Chapter 11 Managing Bond Portfolios 1

2. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Interest Rate Risk A change in market interest rates causes: ◦Bond prices to change in opposite direction ◦Reinvestment income to change in same direction 2

3. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Interest Rate Risk For example, a decrease in market interest rates results in: ◦Higher bond prices (capital gain, if the bond is sold) ◦Lower reinvestment income (reducing terminal value and realized compound yield if bond is held) 3

4. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Bond Pricing Relationships All bond prices are inversely related to market interest rates However, long-term bonds tend to be more price sensitive than short-term bonds 4

5. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Bond Pricing Relationships (cont.) Other factors affect bond price sensitivity to a change in yield, including: ◦Coupon rate (high coupon, less sensitive) ◦Level of interest rates (high rates, less sensitive) ◦A decrease in YTM has a slightly bigger impact on price than an increase in yield of the same size 5

6. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Duration Duration is a better way to measure bond price sensitivity than maturity

7. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Duration There are two types of duration: ◦Macaulay’s duration (D) ◦Modified duration (D*)

8. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Duration Modified duration (D*) measures a bond’s price sensitivity to changes in yield Macaulay’s duration (D) is used to immunize a bond portfolio from interest rate risk

9. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Duration Macaulay’s duration (D) is a weighted average of the time until cash flows from a bond are received ◦D = maturity for zero coupon bonds ◦D < maturity for coupon bonds

10. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Calculating Duration Macaulay’s D (D): D = [ (PV of CFt) x t] / Bond Price Modified D (D*) D* = D / (1+y) Where y is the YTM on the bond

11. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Using Duration Modified D (D*) measures the sensitivity of a bond’s price to a change in y: P / P = Percentage  in bond price = -D* y

12. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Using Duration (cont.) D* is a linear approximation to a nonlinear relationship. As a result, it does not measure the change in bond price exactly. 12

13. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Pricing Error from Convexity Price Yield Duration Pricing Error from Convexity 13

14. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Uses of Duration A bond portfolio is immunized if a change in interest rates does not affect its terminal value. To immunize a bond portfolio, set D = investment horizon For an immunized portfolio, the change in bond value is just offset by the change in reinvestment income 14

15. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Active Bond Management: Swapping Strategies Substitution swap Intermarket swap Rate anticipation swap Pure yield pickup Tax swap 15