You want to buy a stock that is currently selling for $45. You forecast that in one year, the stock’s price will be either $104 or $8, with equal probabilities. There is a one-year call option on the stock available with an exercise price of $80. You are able to borrow at a rate of 6.50%. You would like to hedge your stock position using the call option.
a. What will be the call’s value if the stock price is $104 in one year? What will be the call’s value if the stock price is $8 in one year? (Round your answers to the nearest dollar.)
b. What is the hedge ratio you should use? (Round your answer to 4 decimal places.)
c. Assume that you can purchase fractional shares of stock. How many shares of stock would you buy? (Round your answer to 4 decimal places.)