Assume for this problem that markets are frictionless (i.e. no transactions costs and no short-selling constraints). It’s a week before the UConn – South Carolina game and you find a market that sells two securities: @UConn security which pays $1 next week if UConn wins and $0 otherwise; currently trading at $1.90 @South Carolina security which pays $1 next week if South Carolina wins and $0 otherwise; currently trading at $1. 

a. Can you use the information given above to construct a risk-free security? 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 UConn wins? What is its payoff if South Carolina wins? 

b. Suppose that the risk-free rate is 1% for a week. (i.e. $1 invested today pays off $1.01 in a week.) What strategy would you use to take advantage of this situation?