Interest Rate Risk:
Consider a 10-year zero coupon bond.
A. Using the bond pricing equation, P(y), illustrate the derivation (using calculus) of this bond's modified duration. Note: the correct answer is an equation, not a number.
B. Assuming the yield-to-maturity is 7%, compute the bond's modified duration.
C. Use your answer to part B to estimate the price of the bond and the percentage price change if
interest rates instantaneously rise to 8%.
D. Use your answer to part B to estimate the price of the bond and the percentage price change if
interest rates instantaneously decline to 6%.
E. How do the estimates from C. and D. compare to the true prices using the bond pricing
equation P(y) if yields change to 8% and 6%? Is the estimate more accurate for part C. or D., and why?