Trading Strategy – OPTION GREEKS – DELTA IN DETAIL

OPTION GREEKS – DELTA IN DETAIL

Can we first revise the concept of Delta again?

Yes – Delta measures the sensitivity of the Option price to the change in the price of the underlying. For example, if Satyam is currently quoting at Rs 219 and the Satyam 220 Call carries a Delta of 0.50, this implies that for every Re 1.00 rise in the price of Satyam, the price of the 220 Call will rise by Rs 0.50. A similar movement is indicated in the case of a fall in the price too.

How is Delta useful?

It is useful in several ways. In the first place, when you have bought several calls and puts as well as sold several calls and puts (on the same underlying), you may not even realize whether an upward movement is good for you or a downward movement. The Delta quickly measures your position in terms of the underlying stock and tells you what move you will gain from. Let me explain with an example. We assume that you are trading in Satyam options alone. Satyam is currently trading at Rs 219 and there are 23 working days to expiry.

Strike Position Delta Volume Portfolio Delta
220 Call Buy 0.51 2,400 1,224
230 Call Buy 0.37 1,200 444
220 Put Buy -0.49 3,600 -1,764
Total -96

In the above table, Delta is derived from the Black Scholes calculator. As you can see from the above table, puts carry negative deltas. The implication is that if the price of Satyam goes up, the price of the Put option will move downwards.

Portfolio Delta is worked out by multiplying the delta of each option with the volume. The total Portfolio Delta is -96. This indicates that your portfolio will lose Rs 96 for every Re 1.00 upward move in Satyam and it will gain Rs 96 for every downward move of Re 1.00 in Satyam.

Does the Delta change?

The Delta certainly changes and quite rapidly at times. It primarily depends on the movement in the underlying (Satyam in our example). It also depends to a smaller extent on the number of days to expiry and the volatility in the market.

For example if Satyam moves down from Rs 219 to Rs 215 on the same day (i.e. with 23 days to expiry), the above table will appear as under:

Strike Position Delta Volume Portfolio Delta
220 Call Buy 0.45 2,400 1,080
230 Call Buy 0.32 1,200 384
220 Put Buy -0.55 3,600 -1,980
Total -516

As you can now see, a small movement of Rs 4 in Satyam (from Rs 219 to Rs 215) has changed your portfolio Delta from -96 to -516. 

What is the implication of this change in Delta?

If Satyam now moves down to Rs 214 (by Re 1.00), you will gain Rs 516 and if Satyam now moves up to Rs 216 (by Re 1.00), you will lose Rs 516.

Your portfolio is now far more sensitive to Satyam movements than it was some time ago when Satyam was quoting at Rs 219.

Is this good or bad?

If you are expecting a downward move, it is very good. But if you are expecting an upward move, you should change your option portfolio quickly as your actions are not in consonance with your view.

What is the Delta of the share itself?

The Delta of the share itself is 1. Similarly the Delta of Stock Futures is 1. This means if the price of the share goes up (or the price of the Stock Futures go up) by Re 1.00, you will gain Re 1.00 if you are a buyer and lose Re 1.00 if you are a seller.

This Delta is so commonsensical that it need not be elaborately explained. Option deltas are less than 1 as the Option prices do not move up equally with movements in prices of the underlying.

If I do not want Delta of a certain level what should I do?

Let me explain the direction of various Deltas in the following table first:

Derivative Delta
Futures Buy Positive
Futures Sell Negative
Calls Buy Positive
Calls Sell Negative
Puts Buy Negative
Puts Sell Positive

Thus if your position has a negative Delta (to continue from the previous example, you have a portfolio Delta of -516), you will lose if Satyam moves up. You believe that Satyam will move up and hence this negative Delta needs to be neutralized. You could take the following actions:

  • Buy a Call
  • Sell a Put
  • Buy Futures

All of these actions will generate positive Delta and may convert your position from negative to positive. 

Why do you say ‘may’ convert? Why not ‘will’ convert?

Your current Delta is -516. We will have to see the Delta of the derivative you will be using and recalculate the Portfolio Delta after taking the action. The following table will explain the implications:

Action Strike Delta Volume Positive Delta Generated Portfolio Delta
Buy Call 220 0.45 1,200 540 +24
Buy Call 230 0.32 1,200 384 -132
Sell Put 220 -.55 1,200 660 +144
Buy Futures Not Applicable 1.00 1,200 1,200 +684

As you can now see, each Option carries a different Delta while Futures carry a Delta of 1. The minimum lot size on Satyam is 1,200 Units. Thus, each action will generate a different quantum of positive Delta which may or may not convert your position to a positive Delta.

How important it is to track Delta?

Tracking Delta is extremely important especially if you are taking combination positions. By combination positions, I mean if you are buying as well as selling options or futures or alternatively you are buying both calls and puts (or selling both calls and puts).

Unless you track Delta you will not be able to understand your profit potential at various price levels of the underlying which is a basic requirement for trading in derivatives. In the cash market, you know your profits automatically. For example, if you buy Infosys at Rs 4,300 you know that if it moves to Rs 4,500 you will make a profit of Rs 200. However, with options that is not so.

How frequently should I track Delta?

If you are an active trader taking various positions continuously during the day, it is important to track Delta continuously. With each new position or with each move in the price of the underlying your Delta will change.

If you are not very active and trade say less than 2 trades a week, you should track Delta at least at the end of the day.

How does passage of time affect Delta?

The maximum possible Delta value for a Call is 1.00 while the minimum possible value is 0. For a Put, the maximum possible value is 0, while the minimum possible value is -1.

As time passes, different options react differently. Out of the money Options tend towards zero, while In the Money Options tend towards 1 in case of Calls (or -1 in case of Puts).

The following table explains the position better (Satyam at Rs 219 currently and remains at the same level):

ITM Call Days to Expiry Delta OTM Put Days to Expiry Delta
210 Call 23 0.65 210 Put 23 -0.35
13 0.69 13 -0.31
3 0.83 3 -0.17
1 0.95 1 -0.05
0 1.00 0 0.00

 

OTM Call Days to Expiry Delta ITM Put Days to Expiry Delta
230 Call 23 0.37 230 Put 23 -0.63
13 0.32 13 -0.68
3 0.14 3 -0.86
1 0.03 1 -0.97
0 0.00 0 -1.00

 

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