Motivated from what you learned in class, you decide to take a long position in a one-year forward contract on a stock whose price you expect to increase in the future. The current price of the stock is $100 per share. The interest rate is 10% continuously compounded and the stock pays dividends of $3 in 4 months and 8 months from now. A) What is the value of the long forward position at time? What is the forwand price at time?
Six months later, the price of the stock is S110 per share. You decide now to take a second long position, in a six-months forward contract on the stock (Thus, both contracts have the same delivery date).
B) What is the forward price of your second contract att 1/2?
C) What is the value at timet-1/2 of the long position you made at timet 0?
Four months later, you need to sell your long positions in the two forward contracts.
D) If the current price of the stock is $120 per share, how much money will you receive from selling your long positions?
E) How much money did you invest in total? Did you take advantage of an arbitrage opportunity?
F) Compute the minimum price of the stock such that you receive $20 from selling your long positions.