We have a portfolio of bonds which has duration equal to 10 years and convexity of 25. The goal is to manage interest rate risk here. As a tool to manage the IR risk, we have three zero coupon bonds with maturities of 2,4 and 6 years. Based on this information and by assuming the continuous compounding frequency, answer the following:

a) What would be the best strategy to immunize the portfolio against IR risk if I want to use the 2 and 4-year zeros as hedging instruments?

b) How would your answer change if I try to go for the 4 and 6-year bonds as hedging instruments?

c) How would your answers change if there is a 1 percent change in interest rate?

d) Now, assume that you want to hedge the IR risk using all three bonds. What is the combination of bonds you need to use here?

e) What is the effect of increasing the number of assets in the hedging portfolio on the number of solutions, in comparison to parts a and b?