1. Assume all rates are annualized with semi-annual compounding. Please be explicit about how you derive your results and round to four decimals after the comma.
(Part I) At time 0, Investor A enters into a forward contract, at no cost, to buy, at time 2, $100,000 par of a zero maturing at time 3. The forward price this investor locks in to pay at time 2 is $91,000.
a. What forward rate does this investor lock in at time 0, through this forward contract, for lending from time 2 to time 3?
(Part II) At time 1, the spot price of $1 par of a zero maturing at time 2 is 0.95 and the spot price of $1 par of a zero maturing at time 3 is 0.91.
a. At time 1, what is the forward price an investor could lock in to pay, at time 2, for $100,000 par of a zero maturing at time 3?
b. What is the value, at time 1, of Investor A's position in the forward contract from Part I?
2. Suppose you have a short position in a 30-year 5%-coupon bond and a long position in a zerocoupon bond with exactly the same market value and duration. If all zero rates fall by 25 basis points, will your net position rise or fall in value? Explain.