15. A common stock trades today at S0 15, and the risk free rate is 6%...

15. A common stock trades today at S0 ¼ 15, and the risk free rate is 6% on a semiannual basis.

(a) What is the forward price of this stock for delivery in one year?

(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 trade resolution in 1 year.

(c) If the market traded long and short 1-year forwards on this stock with a price of 15:10, develop an arbitrage to take advantage of this mispricing, giving details on the initial position as well as trade resolution in 1 year. (Hint: Go long the forward if this price is low, and short if this price is high. O¤set the risk with replication.)

(d) If an investor goes short the forward in part (a), what is the investor’s gain or loss at 3 months’ time when the contract is ‘‘o¤set’’ in the market (i.e., liquidated for the then market value) if the stock price has fallen to 13:50, and the 9-month risk-free rate is 7:50% (semiannual)?
Assignment Exercises