Investment Theory

3. A pension plan would like to shield its liabilities, due in exactly 3 years, from interest rate fluctuations. The current YTM is 10%. The strategies it is considering are:

1. Purchase a 10-year bond with 9% coupon rate (hold it for 3 years)
2. Purchase a 1-year zero coupon and then roll it over (twice)
3. Purchase a 4-year bond with 34.85% coupon (hold it for 3 years)

What is the Macaulay duration of each alternative? Which immunizes the portfolio?