Question

You want to buy a stock that is currently selling for $50. You forecast that in one year, the stock's price will be either $106 or $12, 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.

Call value at $106 $ ____
Call value at $12 $ ____

a. What will be the call's value if the stock price is $106 in one year?

b. What will be the call's value if the stock price is $12 in one year? Round your answers to the nearest dollar.) Call value at $106 Call value at $12 b. What is the hedge ratio you should use? (Round your answer to 4 decimal places.) Hedge ratio __

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.)
Shares ___

Answer 1

a. The call's value if the stock price is $106 in one year is $26, and b. The call's value if the stock price is $12 in one year is $0. c. The hedge ratio that should be used is 0.4643, and d. The number of shares of stock to buy is 46.43.

Step-by-step explanation:

a. The call's value if the stock price is $106 in one year can be calculated using the formula: Call value = Max(Stock price - Exercise price, 0). In this case, the stock price is $106 and the exercise price is $80. Therefore, the call value will be $106 - $80 = $26.

b. The call's value if the stock price is $12 in one year can also be calculated using the same formula. In this case, the stock price is $12 and the exercise price is $80. Therefore, the call value will be $12 - $80 = $0 (since the result is negative, it is rounded to $0).

c. The hedge ratio can be calculated by dividing the change in option value by the change in stock value. Since the option value increases by $26 when the stock price increases by $56 ($106 - $50), the hedge ratio will be 26/56 = 0.4643 (rounded to 4 decimal places).

d. To calculate the number of shares of stock to buy, multiply the hedge ratio by the number of shares required to cover the call option. Since one call option represents 100 shares of stock, the number of shares to buy will be 0.4643 * 100 = 46.43 (rounded to 4 decimal places).