An investor holds a portfolio of Treasury bonds with various possible maturities. Its characteristics are given as follows: price of $5,583.95, YTM of 6%, Modified duration of 9.43, relative convexity of 97.90. Two Treasure bonds are used as hedging instruments with the following features: Bond A has a price of $49.70, YTM of 6%, Modified duration of 11.32, relative convexity of 138.84; Bond B has a price of $39.36, YTM of 6%, Modified duration of 15.09, relative convexity of 242.08. Coupon frequency and compounding frequency are assumed to be annual. What is the number of hedging instruments the investor needs to buy or sell to implement a duration and convexity hedge? Assume a parallel shift in the yield curve.

• A . The investor needs to sell 140.26 units of bond A and sell 44.20 units of bond B.
• B. The investor needs to sell 140.26 units of bond A and buy 44.20 units of bond B.
• C. The investor needs to sell 79.97 units of bond A and sell 44.20 units of bond B.
• D. The investor needs to sell 79.97 units of bond A and sell 29.55 units of bond B.