You are managing a stock portfolio with a value of $100 million. The portfolio is unique in that the beta is-0.10. The S&P 500 is currently trading at 1,108. The delta of a call option on the index with a strike price of 1,150 has a delta of 0.52. How can you hedge your portfolio using call options?
A) Buy 174 contracts
B) Sell 167 contracts
C) Buy 156 contracts
D) Sell 174 contracts
E) Buy 167 contracts

Question

Quizplus · Accepted Answer

To hedge the portfolio, you would need to buy call options on the S&P 500 with a delta of 0.52. Since the beta of the portfolio is -0.10, you would need to buy options on the opposite side of the market to achieve a delta-neutral portfolio.

First, calculate the number of shares of the index needed to achieve a delta of -0.10:

Shares = -0.10 * $100,000,000 / 1,108 = -9,027

Since options have a delta of 0.52, the number of option contracts needed would be:

Contracts = -9,027 / (0.52 * 100) = -174

Since you want to buy options to hedge the portfolio, the best choice is A) Buy 174 contracts.

You Are Managing a Stock Portfolio with a Value of $100