1. Consider a 4% coupon 30-year option-free bond selling at 72.3244 and yielding 6%. If the yield is decreased by 20 basis points, the price would increase to 74.5492. If the yield increases by 20 basis points, the price would decrease to 70.1988.
a. Calculate the modified duration.
b. What does this number tell us?
c. What would be the approximate dollar price change for a 50 basis point change in yield?
2. Using the same numbers as in question 3, answer the following questions:
a. What is the convexity measure for this bond?
b. Suppose yields change by 200 basis points, what is the percentage price change using duration by itself? What is the percentage price change due to convexity?