Please show all formulas and calculations.
Assume for this problem that markets are frictionless (i.e. no transactions costs and no short-selling constraints). It’s a week before the Cubs-White Sox game and you find a market that sells two securities:
• CBS Security which pays $1 next week if Cubs win and $0 otherwise; currently trading at $0.75
• WS Security which pays $1 next week if White Sox win and $0 otherwise; currently trading at $0.20
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 if Cubs wins? What is its payoff if White Sox win? 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 CBS = $0.75, WS = $0.20, and r = 2%? In particular, would you expect prices to change? If so, how would they change? If not, why not?