You are managing a pension fund with a value of $380 million and a beta of 1.70.

Question

You are managing a pension fund with a value of $380 million and a beta of 1.70. You are concerned about a market decline and wish to hedge the portfolio. You have decided to use SPX calls. How many contracts do you need if the delta of the call option is .68 and the S&P Index is currently at 1,250? (Negative values should be indicated by a minus sign.)

You are managing a pension fund with a value of $380 million and a beta of 1.70. You are concerned about a market decline and wish to hedge the portfolio. You have decided to use SPX calls. How many contracts do you need if the delta of the call option is .68 and the S&P Index is currently at 1,250? (Negative values should be indicated by a minus sign.)

Explanation / Answer

Number of option contracts = -[(Portfolio beta × Portfolio value) / (Option delta × Option contract value)]

Number of option contracts = -[(1.70 × $380,000,000) / (0.68 × 1,250 × $100)]

Number of option contracts = -7,600 (contracts to write)

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