Suppose you are a fixed income analyst for a hedge fund. Your team forecasts that long term Treasury rates will decrease today by 0.25%. In order to capitalize off of this expected change, the fund is looking to buy 3.25% Treasury Bonds today (settle is 11/11/2020). The price is quoted at 119.75 and the maturity is 2/14/2045.

a. What is the Modified Duration of this bond? (9 points)

b. The hedge fund manager is in a hurry and so asks you: Using the modified duration, what is the approximate percent change in bond value if the forecasted change in rates is correct today? (9 points)

c. Afterwards, you decide to calculate the exact percent change in bond value if the forecasted change in rates is correct today. What is this answer? (9 points)

d. From your general understanding of Malkiels theorems, explain why the approximate method in part b underestimates the exact method used in part c