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LAST fortnight, we saw how to estimate the value of delta using a thumb rule. To recapitulate, deltas measure the sensitivity of an option position with respect to the underlying.

Normally, delta values will range between +1 and - 1. A long call option will have a delta between 0 and +1 while a long put option will have a delta of 0 and - 1. An approximate method to estimate the value of delta is that an ATM option will have a delta of 0.50 and as the underlying moves in-the-money, the delta will increase by 0.1 for every strike and decrease by 0.1 for every strike if the stock moves out of money.

In reality, most of the investors will not have single legged option positions. They are likely to have multi-legged options or options in combination with positions in stock or in the futures.

How to estimate the value of such combination positions?

Option deltas are cumulative. That is, for an investor having multiple positions, the position delta is the sum of the individual deltas. Consider an investor having a Bull Call Spread position on Satyam Computers. The current market price is Rs 162 and an ATM call will have a strike price of Rs 160.

** A Bull Call Spread will be constructed with a long call position with lower strike price (say Rs 160) and a short call position with a higher strike price (say Rs 165).

** The long call position will have a delta of 0.50 while the short call position which is one strike in-the-money will have a delta of - 0.60

** If the stock moves up to Rs 165 (one strike in-the-money), the long call will go from ATM to one strike ITM and the short call will go from one call ITM to ATM.

** The effect of the price change on the option position will be as follows; the long call will increase in value by Rs 3 (0.60*5) while the short call will decline in value by Rs 2.50 (.5*5).

** The net spread position will hence increase by Rs 0.50. Similarly, the impact of the movement of the underlying price on the combination positions can be estimated for other strategies like straddle, strangle, strip, strap etc.

The deltas can also be understood from the viewpoint of a hedge ratio. Delta measures the hedge ratio because it measures how many option contracts are needed to hedge a long position or short position in the underlying. Taking the above example, if an investor has a short position in the futures market and is also long on a call option, which is at-the-money.

The combined delta of the position will be -0.5, the futures position having a delta of - 1 and the long call having a delta of +0.50. To arrive at a delta neutral position, the investor should buy two ATM call options along with shorting in the futures market. This will mean that if there is an increase of Re. 1 in the underlying, then the two call options together will lead to a gain of Re. 1 while the futures will lead to a loss of Re. 1.

By changing the ratio of calls to the number of positions in the underlying, we can turn this position delta either positive or negative. If the investor is bullish on the stock, he can buy three call options along with a short on futures (combined delta of +0.50) and if bearish, buy one call option along with one short position on the futures (combined delta of - 0.50).

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