The current price of a non-dividend-paying stock is $40.Over the next year it is expected to rise to $42 or fall to $37.An investor buys one-year put options with a strike price of $41.Which of the following is necessary to hedge the position?
A) Buy 0.2 shares for each option purchased
B) Sell 0.2 shares for each option purchased
C) Buy 0.8 shares for each option purchased
D) Sell 0.8 shares for each option purchased

Question

Quizplus · Accepted Answer

The payoff from the put option is zero if there is an up movement and 4 if there is a down movement.Suppose that the investor buys one put option and buys F1F1F1S1F1F1F10 shares.If there is an up movement the value of the portfolio is F1F1F1S1F1F1F10×42.If there is a down movement it is worth F1F1F1S1F1F1F10×37+4.These are equal when 37F1F1F1S1F1F1F10+4=42F1F1F1S1F1F1F10 or F1F1F1S1F1F1F10=0.8.The investor should therefore buy 0.8 shares for each option purchased.

The Current Price of a Non-Dividend-Paying Stock Is $40