Duration and Convexity

Your research department reports continuously compounded interest rates as

Maturity (Years) ---Interest Rate (%)

0.5---1.00

1.0---1.50

1.5---2.00

2.0---2.00

(e) Construct a hedge portfolio of 1 coupon bond, and k₁ one-year zero coupon bonds and k₂ two-year zero coupon bonds, that has zero duration and convexity. What are the values of k₁ and k₂?

(f) Suppose that the yield curve shifts upward with dr = 1%. Recalculate P_c(0,2), P_z(0,1) and P_z(0,2) and use this to calculate the change in the values of the hedge portfolios constructed in (d) and (e). Comment on the result.