Many times it is in an investor’s best interest to lock in recent gains or to protect a portfolio of stocks from a decline beyond a certain price. One way to do this would be to purchase a put option contract on each of your various holdings. However, if the portfolio consists of diversified stocks, then it is probably not cost-effective to insure each and every position in this manner.

As an alternative, ?using index options? is a solution to hedge the risk in the portfolio. Depending on the stocks the choice of index could be Bank Nifty, Midcap or even the benchmark Nifty. Next in order to decide the number of contracts of a particular index required to hedge, calculating beta ( ?) of the portfolio is the key. This may sound like an obscure technical term, but beta simply measures the amount of variance in a portfolio in relation to the market. If using the S&P CNX Nifty as a proxy for the market, then ? would indicate how much the portfolio moves when the Nifty changes by 1%. For example, if the portfolio changes by 2% whenever the Nifty moves up 1%, then the portfolio has a ? of 2.0. If the portfolio changes by 0.5%, then ? = 0.5.

The next step is finding the risk-free rate. As the name implies, this is the rate of interest that can be obtained without incurring any risk. For the short-term T-bill rate is appropriate. The last step is dividend yield (dividends paid / value of portfolio).

Now consider the following example: Suppose you own a Rs 1 million portfolio and wish to insure this portfolio against a decline of greater than -6% during the next three months. In other words, you want to put a hedge in place to make certain that your portfolio does not fall below Rs 940,000. To make the calculations fairly simple, let’s assume that the Nifty index is currently trading at 1,000. Let’s also assume that your portfolio is volatile and has ? = 2.0. Finally, let’s assume that the risk-free rate is 4% and the dividend yields on both your portfolio and the Nifty are also 4%. The assumed return of the Nifty is 12% per year. In this example, if you want to employ Nifty put options as a hedging tool, then here’s how to calculate how many contracts you need to purchase:

In three month’s time you expect a 3% return (assuming 12% pa) and a 1% dividend (assuming a 4% annual yield) for a total return of 4%.

Excess return of Nifty: The excess return of any asset is the amount it returns over the risk-free rate. In this case, the risk-free rate would be 1% (assuming a 4% annual rate) in three months. The excess return is therefore 3%.

Total return of portfolio in three months: For this example we stated that the ? of the portfolio is 2, which implies that if the market returns 3%, then your portfolio will double that amount by returning 6%. The expected dividend is still 1% during the next three months, so the total expected return will be 7%.

Excess return of portfolio: The expected excess return is 7% and the risk-free rate is 1%, so the excess return here will be 6%. This is the return you expect in three month’s time.

From the chart we can see that the portfolio will perform twice as well, or twice as poorly, as the market. In this example, you do not want to let your portfolio fall below Rs 940,000 in the next three months. Using the table, you can see that buying Nifty puts with a strike price of 970 will accomplish this. To find the optimal number of put option contracts to purchase, use this formula: 2 * {portfolio value / [(100 x current strike price) / ?]} = number of put contracts

In this example, where the portfolio value equals Rs 1,000,000 and the current strike price is 1,000, the calculation would yield 40 put contracts. This means you should buy 40 Nifty 970 put contracts that expire in 3 months to insure your portfolio against a decline below Rs 940,000.

To see that this is correct, suppose the Nifty finishes at 940 when the options expire in three months. This implies from the chart that your portfolio would be worth just Rs 880,000. However, the Nifty 970 put contract will expire ?in the money? and will be worth Rs 30 (970 – 940) at expiration. In this scenario, your 40 options contracts (each contract is for 50 options) will now carry a value of Rs 60,000. When you add that figure to the Rs 880,000 that your portfolio is now worth, this equals exactly Rs 940,000?pre-decided acceptable loss.

Portfolio hedging is an important technique to learn. Although the calculation of ? must be correct to ensure an exact result, most investors find that even a reasonable approximation will deliver a satisfactory hedge. This technique is especially helpful when an investor has experienced an extended period of gains and feels this increase might not be sustainable in the future.

?The writer is a derivatives analyst