You are managing a stock portfolio with a value of $50,000,000 and a beta of 1.15. The S&P 500 index is trading at 1,120. If the delta of the options is-0.48, how can you hedge your portfolio using put options?
A) buy 1,070 contracts
B) sell 1,130 contracts
C) sell 1,070 contracts
D) sell 1,095 contracts
E) buy 1,130 contracts

Question

Quizplus · Accepted Answer

To hedge a $50,000,000 portfolio with a beta of 1.15 using put options with a delta of -0.48, you need to calculate the number of contracts required to achieve a neutral position. The formula to calculate the number of contracts is: (Portfolio Value * Portfolio Beta) / (Option Delta * S&P 500 Index Value * 100). Plugging in the values: ($50,000,000 * 1.15) / (-0.48 * 1,120 * 100) = 1,070.09 contracts. Since you can't buy a fraction of a contract, you round to the nearest whole number, which is 1,070 contracts. Therefore, you would buy 1,070 put option contracts to hedge the portfolio.

You Are Managing a Stock Portfolio with a Value of $50,000,000