Assume you have the following four securities that you can use for hedging. The key rates 01 for these securities are given in the table below. Assume key rates 01 are spot rates for the corresponding time periods (2, 5, 10, and 30 years). Note that such assumption is different from the assumption in lectures where key rates were YTM on par bonds.

Security 2-year key 5-year key 10-year key 30-year key A1 20 0 0 0 A2 0 50 10 0 A3 0 0 5 0 A4 0 0 10 20

a) (1 point) If you want to hedge a 2-year coupon-paying bond, which of the above securities (A1, A2,

A3, A4) you should use? No justification is needed just list all required securities.

b) (1 point) If you want to hedge a 5-year coupon-paying bond, which of the above securities (A1, A2,

A3, A4) you should use? No justification is needed just list all required securities.

c) (3 points) How should you hedge your portfolio that has the 5-year key rate of 100? Specify the exact

number of each security (A1, A2, A3, A4) in your hedging portfolio