Suppose that there are two securities, RAIN and SUN. RAIN pays $100 if there is

Question

Suppose that there are two securities, RAIN and SUN. RAIN pays $100 if there is any rain on the day of the soccer world cup final, $0 otherwise. SUN pays $100 if there is no rain, $0 otherwise. Suppose the soccer world cup final is 1 year from today, and suppose that RAIN is trading at a price of $23 and SUN is trading at a price of $70.

(c) Suppose that a 1-year zero coupon bond with face value $100 is trading at $90. Show how you would set up a transaction to earn a risk less 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?

Explanation / Answer

c) We should buy the 1 year zero coupon bond for 90 and sell SUN for 70 and MOON for 23 earning a profit of 70 + 23 - 90 = $3. This means at the end of 1 year only on of sun/moon is true and we have to pay 100 which we get from the bond.

d) No, we cant make profit as transaction cost on sun + moon = 2 + 2 = 4 > 3. ( 3 is the profit in the part c )   

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