Laura has an equity portfolio valued at $11.2 million that has a beta of 1.32.She has decided to hedge this portfolio using SPX call option contracts.The S&P 500 index is currently 1402.The option delta is .582.How many option contracts must Laura write to effectively hedge her portfolio?
A)37 contracts
B)42 contracts
C)175 contracts
D)181 contracts
E)191 contracts

Question

Quizplus · Accepted Answer

First, we need to calculate the market value of the underlying S&P 500 index for Laura's portfolio:

Market value of Laura's equity portfolio = $11.2 million
Beta of the portfolio = 1.32
Current level of the S&P 500 index = 1402

Market value of the underlying S&P 500 index = $11.2 million / 1.32 = $8,484,848.48

Next, we need to calculate the number of option contracts required to hedge Laura's portfolio:

Delta of each option contract = 0.582
One option contract represents 100 shares of the underlying index.

Number of option contracts required = (Market value of portfolio / Current level of underlying index) / Delta of one option contract
= ($11.2 million / 1402) / 0.582 / 100
= 181.24

Since we cannot trade in fractional contracts, Laura will need to write 181 SPX call option contracts to effectively hedge her portfolio.

Therefore, the answer is D) 181 contracts.

Laura Has an Equity Portfolio Valued at $11