**DELTA NEUTRAL STRATEGIES**

**Can you briefly summarise what is Delta? **

We have discussed Delta in our previous articles. Delta indicates the responsiveness of the option price to the price of the underlying. It varies between 0 (no responsiveness) to 1 (100% responsiveness). For example, if Satyam is quoted at Rs 240 and the 240 Strike Call Option carries a Delta of 0.52, it means that if Satyam were to move up by Re 1, to Rs 241, the Option price will move up by Rs 0.52. If it were Rs 17 now, it would become Rs 17.52.

We have also discussed that In The Money Options have higher Deltas and are hence more responsive to underlying price changes, while Out of the Money Options have lower Deltas and do not respond actively. If you buy Out of the Money Options, it may well happen that your prediction about the directional movement of the underlying was right, but you still did not make significant gains due to low Deltas.

**What is Delta Neutral? **

Skilled players in the derivatives market might not be interested in predicting directional movements on the underlying. They might be interested in reviewing volatility closely and profiting on volatility predictions. Remember volatility does not depend on direction, it merely depends on the fluctuation level (up or down).

Thus, delta neutral players compare the historical volatility of the scrip with the implied volatility of the option price at the moment. If they believe that a particular call option is underpriced (for example, historical volatility is 41% while the option is priced at 51%), they will sell the option to gain advantage of the higher price.

But the moment they sell the option, they are caught in the framework of price prediction of the underlying in the sense that if the underlying moves up, the call option price will also move up. They however are not concerned in understanding or predicting the underlying price movement.

They will therefore take up an opposite position in the underlying. The objective is to neutralize the movement in the price of the underlying with the movement in the price of the option itself, so that they gain based on volatility alone and not on price movement.

**How will they decide the volume of the underlying to trade? **

This is based on delta of the option at that point in time. For example, if a Satyam 240 call option with 20 days to expire and Satyam itself quoting at Rs 240 is priced at Rs 12, the implied volatility is 51% (you can derive this from a Black Scholes calculator). The historical volatility is say 41%. Thus, the option is expensive and hence you sell the option.

You will look up the Delta of the option, which happens to be 0.54. One contract of Satyam is 1,200 Units. You have a positive Delta which means that with Satyam going up the price of the Call will move up (Rs 0.54 for every upward movement of Re 1.00 in Satyam) and will move down correspondingly.

You do not want to bet on this directional movement. You will therefore buy Satyam futures to the tune of 1,200 x 0.54 i.e. 648 Futures. This will neutralize the impact in such a manner that whether Satyam moves up or down, the changes in Futures price will offset the changes in the Option price.

For example, if Satyam moves up to Rs 245 tomorrow, you will find that the Option price has moved up to Rs 14.54. In case you wonder why, the background is with a Delta of 0.54, the Option price should go up by Rs 2.70 (0.54 x Rs 5 upward movement in Satyam). As one day has passed, the time factor will impact Option prices downward – say by Rs 0.16. Thus, the net Option price will tend to go up by Rs 14.54 (derived from the Black Scholes calculator).

You will have lost Rs 3,048 on the Call. You will find that you have gained Rs 3,240 on the Futures, thus generating a net gain of Rs 152.

**What is the next step? **

The next step is to look for and define re-hedging techniques.

**What is re-hedging? **

The act of buying futures in the above example is hedging your option sale position with the help of Delta. This Delta is however not static. When the Delta changes, your hedge position of 648 Futures might no longer be valid.

For example, on the next day, the Delta has changed to 0.61 (as per Black Scholes Calculator). Thus, you need a hedge position of 1,200 x 0.61 = 732 Futures. You already have bought 648 Futures. You should now buy the balance 84 Futures.

This new position will now help you to balance your gains and losses.

Thus on the third day, if Satyam moves down to say Rs 241, your position will be as under:

The Option price will be Rs 11.90. As you sold at Rs 12, your net gain is Rs 120 (i.e. Rs 0.10 on 1,200 Units). On Futures, you bought 648 Futures at Rs 240 and another 84 Futures at Rs 245. The current price is Rs 241. Thus you make a profit of Re 1.00 on 648 Futures and a loss of Rs 4 each on 84 Futures. The net profit will be 312 on Futures. The total profit will be Rs 422.

**How long will this go on? **

This process of re-hedging can go on upto the expiry day, unless you believe you have generated a decent profit and want to now exit.

You will generate a net profit on this strategy if the volatility of the Option on an implied basis reduces in the period before expiry and moves towards the historical volatility level of 41%. That is your expectation too.

The payoff profiles of the two positions are provided in these graphs. The payoff of the Call is first provided.

The payoff of the futures position appears like this:

The directional movements as you can observe are opposite and in effect attempt to cancel out each other.

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