2. (15 points)

A futures contract is written on a stock. The maturity of the contract is 6 months. The stock price is $50 today and the risk-free rate is 10% per year with continuous compounding.

1. What should the futures price for this contract be?

2. Suppose that the futures price for this contract quoted by Trader A is $56.56, is the futures contract under-valued or over-valued? Explain your answer.

What arbitrage opportunity does this create? Use the following table to show your positions (in the futures contract, the underlying asset and cash account) on date t (today) and the expiration day T. Assume that the stock price on the expiration day T is $60.

Action	Cash Flow at t	Cash Flow at T
1: (hint: long or short the stock?)
2: (hint: long or short the forward contract ?)
3: (hint: borrow or lend?)
Total

3. Does your answer (e.g., the arbitrage profit) in (2) change if the stock price on the expiration day is $40 instead of $60? Explain your answer.