# Calculate Contracts to Hedge

## Calculating Index Contracts to Hedge a Portfolio

Stock prices tend to move in tandem in response to the overall stock market as measured by the S&P 500 Index (SPX). The 500 stocks that comprise the S&P 500 Index represent almost 85% of the stock market value in the United States. Therefore, the index is an excellent reflection of the overall stock market. If an investor owns a portfolio of stocks and is concerned about a near-term downward move in the overall market, purchasing the appropriate SPX put options could be a desirable alternative to hedging each stock individually.

Determining the number of contracts to use to hedge a portfolio is a fairly simple process using the following formula:

Each SPX option represents \$100 times the strike price. For instance, if an SPX put with a strike price of 1250 is utilized, it would represent \$125,000 of market value (1250 x \$100). So, an investor with a stock portfolio valued at \$500,000 would purchase 4 SPX 1250 puts (\$500,000 / \$125,000) to hedge the portfolio.

For example, consider an investor who has a diversified stock portfolio valued at \$500,000 and is concerned about a market correction of 10% over the next 30 days. With the S&P 500 Index quoted at 1250, a correction of 10% would result in the S&P 500 trading at 1125.00. The investor could choose to purchase four 30-day SPX 1250 puts quoted at 25.00 (\$2500 per contract) that would have a total cost of \$10,000 or 2% of the value of the portfolio.

SPX % Gain Portfolio \$
Gain / Loss
Hedging Cost 1250 SPX
Put Value
Total Portfolio %
Gain / Loss
1375.00 +10% \$50,000 \$10,000 \$0 \$40,000 +8%
1312.50 +5% \$25,000 \$10,000 \$0 \$15,000 +3%
1250.00 +0% \$0 \$10,000 \$0 \$10,000 -2%
1187.50 -5% \$25,000 \$10,000 \$25,000 \$10,000 -2%
1125.00 -10% \$50,000 \$10,000 \$50,000 \$10,000 -2%

The previous table shows the dollar and percent results of this strategy based on the S&P 500 index at a few levels upon option expiration. Because at-the-money SPX option contracts are used for hedging, the maximum potential loss is equal to the 2% cost of hedging. 2% of performance is sacrificed on the upside if an unanticipated market rally occurs. A payout comparison between a hedged and un-hedged portfolio appears in the payout diagram below.

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