Looking at the spot rates {r1,r2,…,rt,…}, Mr Future decides to trade on existing discount bonds

Looking at the spot rates {r1,r2,…,rt,…}, Mr Future decides to trade on existing discount bonds {B1,B2,…,Bt,…} in order to lock in the rate between year t−1 and year t, which is given by the forward rate ft.

(a) If Mr Future wants to invest $X in t − 1 years from today for one year, describe the trading strategy (i.e., how he can trade on discount bonds TODAY) and characterize the cash flow table. If your answer is correct, the rate of return from your cash flow table should be equal to ft. [Requirement: In describing your trading strategy, you have to be specific about the position (whether being long or short), the number of securities being purchased or sold, and the timing of each transaction.]

(b) Mr Future thinks that trading on existing discount bonds is too much effort, instead, he wants to sign a forward contract with a bank which allows him to open a one-year saving account of $X in t − 1 years. The saving rate quoted by the bank, denoted by st, is greater than ft, i.e., st > ft. Is there an arbitrage opportunity? If yes, what is your strategy; and for every $1 saved with the bank, how much can you earn from this strategy?

(c) If st

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