Bond Portfolio Management

1. Bond Portfolio Management • Term Structure • Yield Curve • Expected return versus forward rate • Term structure theories • Managing bond portfolios • Duration • Convexity • Immunization and trading strategy

2. Overview of Term Structure • The relationship between yield to maturity and maturity. • Information on expected future short term rates can be implied from yield curve. • The yield curve is a graph that displays the relationship between yield and maturity. • Three major theories are proposed to explain the observed yield curve.

3. Figure 15.1 Treasury Yield Curves 1). Pure yield curve; 2). on-the-run yield curve (page 485)

4. Table 15.1 1-year rate is 5%, 2-year rate is 6%, 3-year rate is 7%, 4-year rate is 8%. Compute the yield to maturity of a 3-year coupon bond with a coupon rate of 10%.

5. Forward Rates from Observed Rates fn = one-year forward rate for period n yn = yield for a security with a maturity of n

6. Example: page 487 4 yr = 8.00% 3yr = 7.00% f4 = ?

7. Downward Sloping Spot Yield Curve Zero-Coupon RatesBond Maturity 12% 1 11.75% 2 11.25% 3 10.00% 4 9.25% 5

8. Forward Rates Downward Sloping Y C 1yr Forward Rates 1yr= = 0.115006 2yrs= = 0.102567 3yrs= = 0.063336 4yrs= = 0.063008

9. Theories of Term Structure • Expectation Theory • Forward rate = expected rate (page 494) • Liquidity Premium Theory • Upward bias over expectations • Equation 15.8 on page 499

10. Figure 15.4 Yield Curves

11. Figure 15.4 Yield Curves (Concluded)

12. Figure 15.6: Term Spread

13. 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.

14. Figure 16.2 Cash Flows Paid by 9% Coupon, Annual Payment Bond with an 8-Year Maturity and 10% Yield to Maturity

15. Duration: Calculation

16. Example: Duration See page 516-517.

17. 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

18. 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

19. Figure 16.3 Bond Duration versus Bond Maturity

20. Correction for Convexity Correction for Convexity:

21. Figure 16.5 Convexity of Two Bonds Which bond does you prefer?

22. Figure 16.6 Price –Yield of a Callable Bond Negative convexity: page 526; mortgage has the similar feature (page 526, 528)

23. Passive Management • Bond-Index Funds • Lehman Aggregate Bond index • Salomon Smith Barney Broad Investment Grade (BIG) Index • Merrill Lynch U.S. Broad Market Index • 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 • Covered in fixed income class

24. Immunization • Price risk • Reinvestment • Immunization is the point that two effects are cancelled out.

25. Active Management: Swapping Strategies • The key idea is to predict the interest rate movement • Or simply riding on the yield curve

26. Yield Curve Ride Yield to Maturity % 1.5 1.25 .75 Maturity 3 mon 6 mon 9 mon