# Portfolio Insurance using Index Puts

Index put options are often used to insure a portfolio against adverse market movements. Through the use of index puts, fund managers concerned about declining markets do not need to liquidate their holdings and this confers two advantages: 1) faster execution and 2) greatly reduced transaction costs.

Furthermore, in the event that the fund manager's expectation of a falling market is wrong, his portfolio can continue to participate and appreciate in the rising market.

## Implementation

To insure a portfolio with index puts, 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 contracts to buy to fully protect the portfolio using the following formula.

No. Index Puts Required = Value of Holding / (Index Level x Contract Multiplier)

## Example

A fund manager oversees a well diversified portfolio consisting of thirty large cap U.S. stocks with a combined value of \$10,000,000. Worried by news about a possible outbreak of war in the middle east, the fund manager decides to insure his holding by purchasing slightly out-of-the-money S&P 500 index put expiring in two months' time in December. The current level of the S&P 500 is 1500 and the DEC 1475 SPX put contract costs \$20 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. Total cost of the options is: 67 x \$20 x \$100 = \$134,000.

 S&P 500 Index Portfolio Value Put Option Value Insured Portfolio 1200 \$8,000,000 \$1,842,500 \$9,842,000 1300 \$8,666,666 \$1,038,500 \$9,705,166 1400 \$9,333,333 \$368,500 \$9,701,833 1500 \$10,000,000 -\$134,000 \$9,866,000 1600 \$10,666,666 -\$134,000 \$10,532,666 1700 \$11,333,333 -\$134,000 \$11,199,333

As can be seen from the table above, should the market retreat, the value of the put options rise and almost fully offset the losses taken by the portfolio. In case the fund manager is wrong about the market, his holding will continue to appreciate along with the market's rise. The only downside is if the market stayed flat, there will be a loss equals to the premium paid for the put insurance.

Note: The example above assumes full correlation with beta of 1.0 between the portfolio and the index and transaction costs are not included in the calculations.

## Index Collars

The fund manager can alternatively finance the purchase of the index put options by simultaneously selling index call options. This strategy is also known as the index collar.

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