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?

Explanation / Answer

If the portfolio has a beta of 1

= put option contract to be purchased

= 1x($8,000,000/400x100) = 200 contracts

If the portfolio has a beta of 1

= Strike price of put option would be

= 7,000,000/100x200

= $350

If the portfolio has a beta of 0.5

0.5 x (8,000,000/400 x 100) = 100 contracts
1 contract = 100 options

= 100 x 100 = 10000 put options should be purchased

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