You own 2,000 shares of ABC stock that is currently priced at $27 a share. Given this price, the option delta for a $25 call option on this stock is .718. How many $25 call options do you need to hedge against a -$1 change in the price of the stock?

Question

Quizplus · Accepted Answer

To hedge against a -$1 change in the price of the stock, we need to calculate the total delta we have to hedge, which is:
Total delta = number of shares x delta per share
Total delta = 2,000 x 0.718
Total delta = 1,436
Since the delta of a call option is positive, we need to buy put options to hedge against a price drop. To calculate the number of put options we need, we divide the total delta we need to hedge by the delta per option, which is:
Number of put options = total delta / delta per option
Number of put options = 1,436 / 0.517
Number of put options = 2,786
Therefore, we need to write 2,786 $25 put options to hedge against a -$1 change in the price of the stock. The closest answer choice is D.

You Own 2,000 Shares of ABC Stock That Is Currently