Portfolio Hedging using Index Options
An alternative to selling index futures to hedge a portfolio is to sell index calls while simultaneously buying an equal number of index puts. Doing so will lock in the value of the portfolio to guard against any adverse market movements. This strategy is also known as a protective index collar.
The idea behind the index collar is to finance the purchase of the protective index puts using the premium collected from selling the index calls. However, as a result of selling the index calls, in the event that the fund manager's expectation of a falling market is wrong, his portfolio will not benefit from the rising market.
Implementation
To hedge a portfolio with index options, we need to first select an index with a high correlation to the portfolio we wish to protect. For instance, if the portfolio consist of mainly technology stocks, the Nasdaq Composite Index might be a good fit and if the portfolio is made up of mainly blue chip companies, then the Dow Jones Industrial Index could be used.
After determining the index to use, we calculate how many put and call contracts to buy and sell to fully hedge the portfolio using the following formula.
No. Index Options Required = Value of Holding / (Index Level x Contract Multiplier)
Example
A fund manager oversees a well diversified portfolio consisting of fifty large cap U.S. stocks with a combined value of $10,000,000 in October. Worried by news about surging oil prices, the fund manager decides to hedge his holding by purchasing slightly out-of-the-money S&P 500 index puts while selling an equal number of slightly out-of-the-money S&P 500 index calls expiring in two months' time. The current level of the S&P 500 is 1500 and the DEC 1475 SPX put contract costs $20 each while the DEC 1525 SPX call contract is quoted at $25 each.
The SPX options has a contract multiplier of $100, and so the number of contracts needed to fully protect his holding is: $10000000/(1500 x $100) = 66.67 or 67 contracts. A total of 67 put options need to be purchased and 67 call options need to be written.
- Total cost of the put options is: 67 x $20 x $100 = $134,000.
- Total premium collected for selling the call options is: 67 x $25 x $100 = $167,000.
- Net premium received is: $167,000 - $134,000 = $33,000.
| S&P 500 Index | Call Option Value | Put Option Value | Net Premium Received | Unhedged Portfolio | Hedged Portfolio |
| 1200 | $0 | $1,842,500 | $33,000 | $8,000,000 | $9,875,000 |
| 1300 | $0 | $1,172,500 | $33,000 | $8,666,666 | $9,872,166 |
| 1400 | $0 | $502,500 | $33,000 | $9,333,333 | $9,868,833 |
| 1500 | $0 | $0 | $33,000 | $10,000,000 | $10,033,000 |
| 1600 | -$502,500 | $0 | $33,000 | $10,666,666 | $10,197,166 |
| 1700 | -$1,172,500 | $0 | $33,000 | $11,333,333 | $10,193,833 |
As can be seen from the table above, should the market retreat, as represented by the declining S&P 500 index, the value of the put options rise and almost fully offset the losses taken by the portfolio. Conversely, should the market appreciate, the rise in his holding's value is capped by the rise in the value of the call options sold short. Hence, once the index collar in entered, the fund manager has effectively locked in the value of his portfolio.
Note: The example does not include transaction costs in the calculations and also assumes full correlation (beta of 1.0) between the portfolio and the S&P 500 index.
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