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S&P 500 Index Puts

On August 3, 2010, the S&P 500 index cost $1,121.45. The prices of various puts on this index are listed in Table 18.1 These puts are for strikes listed in the table's first column for expiration at the end of the month and centered on $1,000. The intent here is to show a ±20 percent range of puts prices around the current spot price for the index. To fix ideas, any strike below the current spot price ($1,121.45) is said to be out of the money (OTM) while any strike above spot is in the money. The OTM prices are of interest to us since we want to hedge downside risk.

Table 18.1 August 3, 2010, S&P 500 Puts.

Take, for example, the center strike of $1,000, which provides the option to sell the index on the strike date for $1,000. A decline in the index to this level would constitute a 10.83 percent drop in the value of the index (see the column labeled Implied Move). The asking price of the index on August 3 for this contract was $1.30 per share and the bid price was $1.20. (Note that we pay the ask price if we want the contract.) The contract, itself, is for 100 shares of the S&P 500 (each share currently worth $1,121.45).

The portfolio we want to insure is a large pension fund that has current market value equal to $49 billion and the public equity allocation in that fund is $22.8 billion. Suppose we wanted to hedge 50 percent of the public equity exposure to ...