Suppose you own $50 mn (face value) of the Notes maturing on 12/31/2023 (with 2.625 coupon rate, duration 4.72, convexity 23.09, and price $100.523438) and are worried that the price of these notes might go down when the interest rates go up.

(a) You decide to hedge your position using the Note maturing on 12/31/2020 (with 2.5 coupon rate, duration 1.96, and price $100.019531). Compute the duration hedge, i.e., what is the face value of the hedging position.

(b)  Suppose you want to hedge duration and convexity at the same time and use 3.5-year Notes (maturing on 06/30/2022 with 1.75 coupon rate, duration 3.41, convexity 11.81, and price $97.585938) and 7-year notes (maturing on 12/31/2025 with 2.625 coupon rate, duration 6.44, convexity 43.71, and price $100.25) as your hedging instruments. Compute the hedging position (face values of each security).