Problem 1 (15 points) Suppose that at time to a bank is considering the purchase of a 2-year zero-coupon bond at a price B(to,T2), where T2 = to +2. The bank can fund this transaction either by using 6-month zero-coupon bond B(to, Tos), where T2 = to + 0.5. or by selling short a 3-period zero-coupon bond B(to, T3), where T3 = to + 3 or a combination of both. Assume that the zero-coupon yield is flat at y = 5% and that the shifts are parallel. How should the bank proceed given that it wants to have the total position insensitive to first-order changes in the yield