25. A common stock trades today at S0 50, and the risk-free rate is 5% on...

25. A common stock trades today at S0 ¼ 50, and the risk-free rate is 5% on a semiannual basis.

(a) What is the forward price of this stock for delivery in 6 months?

(b) Replicate a long position in this forward contract with a portfolio of stock and T-bills, giving details on the initial position as well as the trade resolution in 6 months.

(c) If the market traded long and short 6-month forwards on this stock with a price of 53, develop an arbitrage to take advantage of this mispricing, giving details on the initial position as well as the trade resolution in 6 months.

(d) If an investor goes long the forward in part (a), how much does the investor make or lose at 3 months’ time when the contract is o¤set in the market if the stock price has risen to 52, and the 3-month risk-free rate is at 4:50% (semiannual)?