A portfolio manager in charge of a portfolio worth $8 million is concerned that

Question

A portfolio manager in charge of a portfolio worth $8 million is concerned that the market might decline rapidly during the next six months and would like to use options on the S&P 100 to provide protection against the portfolio falling below $7 million. The S&P 100 index is currently valued at 400 and each contract is on 100 times the index.

1. If the portfolio has a beta of 1, how many put option contracts should be purchased?

2. If the portfolio has a beta of 1, what should the strike price of the put options be?

3. If the portfolio has a beta of 0.5, how many put options should be purchased?

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Explanation / Answer

1)

Value of one put option contract = 400 x100

                                                                = 40,000

Beta = 1

No. of contracts needed = lowest Value of portfolio x beta / value of one contract

                                                = 7,000,000 x 1/ 40,000

                                                = 175 contracts.

2)

Strike price of the put option would be equal to the spot value of the index that is 400.

3)

No. of contracts needed = lowest Value of portfolio x beta / value of one contract

                                                = 7,000,000 x 0.50/ 40,000

                                                = 87.5 contracts.

There are 100 options in each contract. Therefore, total no. of put options required are:

No. of put options required = 87.50 x 100

                                                       = 8750

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