Consider the following three securities: TIGHT, EASE and NEUTRAL. TIGHT pays $100 if the Fed raises interest rates at the next meeting. EASE pays $100 if the Fed lowers interest rates at the next meeting. NEUTRAL pays $100 if the Fed does not change interest rates (neither increases nor decreases rates) at the next meeting. Suppose that TIGHT is currently trading at $63, EASE is currently trading at $4 and NEUTRAL is trading at a price of $24.
(a) If you buy 1 share of TIGHT, 1 share of EASE and 1 share of NEUTRAL, what is the payoff you guarantee on the Fed's meeting day?
(b) According to the No Arbitrage Condition, what must be the price of a $100 face value zero-coupon bond that matures on the Fed meeting day?
(c) Suppose that this zero-coupon bond is trading at $96. How would you set up a transaction to earn a riskless arbitrage profit? Assume no trading costs.
(d) Suppose that shorting TIGHT, EASE, and NEUTRAL is costless, but shorting the zero-coupon bond costs $10 per $100 face value. Can you still make an arbitrage profit?
