Part 1: Arbitrage and the Law of One Price Assume for this problem that markets are frictionless (i.e. no transactions costs and no short-selling constraints). Its a week before the OSU-Michigan game and you find a market that sells two securities:

OSU Security which pays $1 next week if OSU wins and $0 otherwise; currently trading at $0.70

UM Security which pays $1 next week if Michigan wins and $0 otherwise; currently trading at $0.25

1. What is the risk-free rate if there is no arbitrage? (Do not worry about expressing this as an annualized percentage.) Hint: What is the payoff to the risk-free security of OSU wins? What is its payoff if Michigan wins? Can you use the information given above to construct this security?

2. Suppose that the risk-free rate is 2% for a week. (i.e. $1 invested today pays off $1.02 in a week.) What strategy would you use to take advantage of this situation?

3. What would you expect to happen if OSU = $0.70, UM = $0.25, and r = 2%? In particular, would you expect prices to change? If so, how would they change? If not, why not?