Forward interest rate arbitrage:
3) You are given the following information: at t = 0, the price of a 10-year zero coupon bond with FV = $10,000 is $7,000; r0,3 = 5%; f3,12 = 6%.
a) What should f10,5 be assuming there is no arbitrage?
b) Suppose a financial institution is quoting a rate of f10,5 = 11%. Describe how you would construct an arbitrage strategy. Assume that part of your strategy involves buying or selling $1 worth of the 10-year zero coupon bond, and also either borrowing or lending $1 at a rate of r0,3 = 5%. Construct the arbitrage in such a way that your profit is realized at t = 15, and the net cash flows at all other points in time are 0. You must specify for each rate r0,3 = 5%, f3,12 = 6%, and f10,5 = 11% whether you are borrowing or lending at that rate, and how much. Make sure to also specify if you are buying or shorting $1 worth of the bond.
c) What is the magnitude of your arbitrage profit at t = 15?
d) Repeat question b, but this time for 1 unit of the zero coupon bond bought or sold at t = 0, and either borrowing or lending $7,000 at a rate of r0,3 = 5%.
e) What is the magnitude of the arbitrage profit at t = 15 from part d?