Consider a 30-year corporate bond paying 9 percent semi-annual coupon. The curre

Question

Consider a 30-year corporate bond paying 9 percent semi-annual coupon. The current yield to maturity is 11 percent. (20 points) a. Find the modified duration. (6 points) b. Refer to part a. If the interest increases by 25 basis points, what is the exact change in price? (3 points) c. Refer to part b. If the interest increases by 25 basis points, what is the approximate change in price? (3 points) d. What is the error of approximation? (3 points) e. Using 25 basis point interest rate changes, approximate the modified duration.

Explanation / Answer

Maturity 30 YTM 11% Coupon 4.5 N 60 Price 82.55 Assuming face value as 100 The duration of bond is 9.39 Modified duration is duration/(1+Yield/k) where k is coupon frequency 8.900473934 b, the change in price is basis point change in yield* duration 0.022251185 so the price will decrease if interest rate increases c. If interest rate increases by 25 basis point more the change in price will be 0.04450237 d.If interest rate directly increases by 50bps the change in price will be 0.04450237 So the error is 0.00000000 e. 9.3

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