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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 with a $100 multiplier. The call option delta is .582. What is the appropriate strategy for Laura to effectively hedge her portfolio? What is the appropriate strategy for Laura if she decides to use put contracts on the same index with the same expiration?

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Answer:

Explanation:

Put Delta = call delta - 1 = 0.582 - 1 = -0.418

No of Options = (-11.2 million / (-0.418 × 1402)) × 1.32 = 25,227 options

No of Contracts = 25,227 / 100 = 252 contracts

The appropriate strategy for Laura if she decides to use put contracts on the same index with the same expiration is 252.

First step is to calculate the put delta

Put delta=Call delta - 1

Put delta= 0.582 - 1

Put delta= -0.418

Second step is to calculate the number of options

Number of Options=(Equity portfolio÷(Put delta× Index)× beta

Number of Options = [-$11.2 million×(-0.418 × 1402)] × 1.32

Number of Options= 25,227

Third step is to calculate the put contracts

Put contract=Number of Options/Multiplier

Put contracts=25,227 / 100

Put contracts=252.27

Put contracts=252 (Approximately)

The appropriate strategy for Laura if she decides to use put contracts on the same index with the same expiration is 252.

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