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 nearterm 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 30day 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 atthemoney 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 unhedged portfolio appears in the payout diagram below.


