Problem : On March 1, 2023 (= Year 0), you are interested in purchasing 6-month zero-coupon Treasuries with the proceeds of a sale of equipment to take place in 6 months (= Year 0.5). You want to lock in the price of the Treasuries today through a forward contract. The market price of 6-month T-bills is P_0.5 and the price of 1-year T-bills is P1. Denote the face value of the T-bills by F. To compute the no-arbitrage price, consider two alternative investment strategies for 1-year investment horizon as follows: (i) Buy $100 million worth of 1-year T-bills at price P1. (ii) Buy $100 million worth of 6-month T-bills at price P_0.5 today, and enter into a forward contract by which you will use the proceeds from the 6-month bill in Year 0.5 to buy new 6-month T-bills.

a) How much would you earn at the end of Year 1 by strategy (i)?

b) How much would you earn at the end of Year 1 by strategy (ii)?

c) To prevent arbitrage opportunities between (i) and (ii), what should be the forward price Pfwd? Accordingly, what is the implied (semi-annually compounded) forward rate f0.5, 1 that you can lock in today for the period from Year 0.5 to 1?

d) Now suppose that todays price of 6-month T-bills is $97.728, and the price of 1-year bills is $95.713. Assume that the face value of the T-bills is $100. Suppose a bank quoted a forward price (for the period from Year 0.5 to Year 1) of $97.80. Would there be an arbitrage opportunity? If so, give details (positions taken in different assets, cash flows at all times) of a strategy that would take advantage of the opportunity.