Consider the following two securities: RAIN and SUN. RAIN pays $100 if it rains on NYU graduation day. SUN pays $100 if there is no rain. Suppose that RAIN is trading at a price of $27 and SUN is trading at a price of $70.

1. (a)If you buy 1 share of RAIN and 1 share of SUN, what is the payoff on NYU graduation day?
2. (b)According to the No Arbitrage Condition, what must be the price of a $100 face value zero-coupon bond that matures on NYU graduation day?
3. (c)Suppose that this zero-coupon bond is trading at $99. How would you set up a transaction to earn a riskless arbitrage profit? Assume no trading costs.
4. (d)Suppose that trading zero-coupon bonds is costless, but shorting RAIN and SUN each cost $1 per $100 face value. Can you still make an arbitrage profit?