Suppose that there are two securities RAIN and SUN. RAIN pays $100 in there is any rain during the next world cup soccer final. SUN pays $100 in there is no rain. Suppose that the world cup soccer final is 1 year from today (although this is not true), and suppose that RAIN is trading at a price of $23 and SUN is trading at a price of $70.
a) If you buy 1 share of RAIN and 1 share of SUN, what is your payoff after 1 year, depending on the weather?
b) What does the No-Arbitrage Condition imply about the price of a 1-year zero-coupon bond? (Assume no trading costs.)
c) Suppose that a 1-year zero-coupon bond is trading at $90. Show how you would set up a transaction to earn a riskless arbitrage profit. (Assume no trading costs.)
d) Suppose that trading zero-coupon bonds is costless, but trading RAIN and SUN each cost $2 per $100 face value. Can you still make an arbitrage profit?