You have a stock market portfolio with a beta of 0.9 that is currently worth $696 million. You wish to hedge against a decline using index options. Suppose you decide to use SPX calls. Calculate the number of contracts needed if the call option you pick has a delta of 0.5, and the S&P 500 Index is at 1,160. (Writing options should be indicated by a minus sign. Round your answer to the nearest whole number.)

Call contracts

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You have a stock market portfolio with a beta of 0.75 that is currently worth $319 million. You wish to hedge against a decline using index options. Suppose you decide to use SPX calls. Calculate the number of contracts needed if the call option you pick has a delta of 0.6, and the S&P 500 Index is at 1,160. (Writing options should be indicated by a minus sign. Round your answer to the nearest whole number.) Call contracts -3,437.5 + 0.1% Explanation You can either buy put options or sell call options. In either case, gains or losses on your stock portfolio will be offset by gains or losses on your option contracts. To calculate the number of contracts needed to hedge a $319 million portfolio with a beta of 0.75 using an option contract value of $116,000 (100 times the index) and a delta of 0.6, we use the formula from the chapter: Portfolio beta * Portfolio value Number of option contracts Option delta x Option contract value Filling in the numbers, we need to write (0.75 $319M)/(0.6 * $116,000 = -3,437.5 call contracts