1. Carter Bank, which has a positive duration gap, anticipates the need to borrow some funds for next year; however, it wants to lock in today's short-term borrowing rate just in case it rises next year. Carter decides to purchase a loan (a short-term bond, Bpv) today and, rather than use cash to pay for it, finances it by borrowing at today's current short-term borrowing rate of Prepo=4%. Carter also enters into a futures contract with a pension (hedge) fund, agreeing to deliver the bond at a price of $1,025 in the future in exchange for the cash funds next period. The futures contract requires the pension fund to pay $1,025 cash to Carter Bank when Bpv is delivered. Because the pension fund would not own Bpy until then, it would forgo the zero-rate payment (e.g., the pull-to-par component when a zero trades at a discount), which is calculated based on $1,000 face value and a rzero=3%. a. From Carter's point of view, is the carry (i.e., net financing cost) positive or negative? Show your work. What might the carry suggest about the slope of the yield curve? Explain. b. Compute the implied futures price of the bond. Show your work. c. Based upon the futures contract price of $1,025, does the Law of One Price hold? Explain. d. What might cause the actual price of a futures contract to differ from its implied theoretical price? e. Who profits at the settlement date from this agreement-Carter or the hedge fund? Explain. f. Define the implied repo rate, then solve for the implied repo rate at a futures price of $1,025. 1. Carter Bank, which has a positive duration gap, anticipates the need to borrow some funds for next year; however, it wants to lock in today's short-term borrowing rate just in case it rises next year. Carter decides to purchase a loan (a short-term bond, Bpv) today and, rather than use cash to pay for it, finances it by borrowing at today's current short-term borrowing rate of Prepo=4%. Carter also enters into a futures contract with a pension (hedge) fund, agreeing to deliver the bond at a price of $1,025 in the future in exchange for the cash funds next period. The futures contract requires the pension fund to pay $1,025 cash to Carter Bank when Bpv is delivered. Because the pension fund would not own Bpy until then, it would forgo the zero-rate payment (e.g., the pull-to-par component when a zero trades at a discount), which is calculated based on $1,000 face value and a rzero=3%. a. From Carter's point of view, is the carry (i.e., net financing cost) positive or negative? Show your work. What might the carry suggest about the slope of the yield curve? Explain. b. Compute the implied futures price of the bond. Show your work. c. Based upon the futures contract price of $1,025, does the Law of One Price hold? Explain. d. What might cause the actual price of a futures contract to differ from its implied theoretical price? e. Who profits at the settlement date from this agreement-Carter or the hedge fund? Explain. f. Define the implied repo rate, then solve for the implied repo rate at a futures price of $1,025