Financial Management

CH 16 CFA PROBLEMS 1. a. The call feature provides a valuable option to the issuer, since it can buy back the bond at a specified call price even if the present value of the scheduled remaining payments is greater than the call price. The investor will demand, and the issuer will be willing to pay, a higher yield on the issue as compensation for this feature. The call feature reduces both the duration (interest rate sensitivity) and the convexity of the bond. If interest rates fall, the increase in the price of the callable bond will not be as large as it would be if the bond were noncallable. Moreover, the usual curvature that characterizes price changes for a straight bond is reduced by a call feature. The price-yield curve (see Figure 16.6) flattens out as the interest rate falls and the option to call the bond becomes more attractive. In fact, at very low interest rates, the bond exhibits negative convexity. Bond price decreases by $80.00, calculated as follows: 10 × 0.01 × 800 = 80.00 b. c. d. ½ × 120 × (0.015)2 = 0.0135 = 1.35% 9/1.10 = 8.18 (i)

b.

2.

a.

e. f. 3. a. b.

(i) (iii) Modified duration =

Macaulay duration 10 = = 9.26 years 1 + YTM 1.08

For option-free coupon bonds, modified duration is a better measure of the bond’s sensitivity to changes in interest rates. Maturity considers only the final cash flow, while modified duration includes other factors, such as the size and timing of coupon payments, and the level of interest rates (yield to maturity). Modified duration indicates the approximate percentage change in the bond price for a given change in yield to maturity. i. Modified duration increases as the coupon decreases. ii. Modified duration decreases as maturity decreases. Convexity measures the curvature of the bond’s price-yield curve. Such curvature means that the duration rule for bond price change (which is based only on the slope of the curve at the original yield) is only an approximation. Adding a term to account for...