There is a 7 year maturity bond that makes semiannual coupon payments and has a coupon rate of 1.875%, a face value of 1000, and a yield to maturity of 1.89% trading in the market.
a. Calculate the duration (Macaulay duration) for the bond.
b. Describe intuitively what the bond’s Macaulay duration measures. If the bond was a zero coupon bond, what would have been its Macaulay duration? c. Calculate the modified duration of the bond.
d. If the market yield increases by 50 basis points (0.5 percent), what is the percentage change in the bond’s price as predicted using the bond’s duration (calculated in c.)?
e. Now calculate the bond price before and after the change in yield directly (hint: you can use the Excel spreadsheet in PS6.xlsx to do this.) How good is the approximation of the bond’s price change you used in d.?
f. Is the predicted price higher or lower than the actual price? Is this what you expected?