Secrets of Option Greeks Delta in option trading strategies

Add up the Deltas

The Delta has an interesting ability, it can be summed up!

Let me explain, we will revisit the Futures contract. We know if there is a change of 1 point in the spot value of the underlying, then it means Futures changes by the same amount.

For example, when Nifty Spot moves from 24,850 to 24,870, we see that Nifty Futures also shifts from 24,865 to 24,885 (with an existing value of 24,865 when Nifty Spot was at 24,850). Therefore, if we assign a delta value to this Futures, it would be 1 as every 1 point move in the underlying brings an equivalent change in the Futures.

Assuming I buy 1 ATM option with a delta of 0.5, it is equivalent to possessing a half futures contract. Consequently, with 2 such ATM contracts, the total delta is equal to possessing 1 futures contract. Thus, the deltas of two or more option contracts can be combined to determine the overall delta of the position.

We can use a few examples to gain more knowledge on this subject.

Case 1—The Nifty spot is currently at 24,350 and a trader has 3 distinct Call options.

Observations:

A positive sign next to the number 1 in the Position Delta column indicates a long position

The delta for the joint position is a positive one, that being +1.25, indicating both the underlying and combined positions will progress similarly

For every 1-point shift in Nifty, the total position changes by 1.25 points

If Nifty increases by 80 points, it is estimated that the total position will climb by an amount equal to 100 points, which is a 25 per cent increase

In case 2, with the Nifty spot at 24,350, the trader has a mixed position consisting of both call and put options.

Observations:

The overall delta for the combined positions is +0.25; this indicates that the underlying and the entire position will move in the same direction

The integration of Deep ITM PE has resulted in a decrease in the overall delta of the position, rendering the combined position less exposed to any changes in the market direction

For every 1-point movement in Nifty, the combined position experiences a change of 0.25 points

If Nifty shifts by 80 points, the cumulative position should increase/decrease by 20 points, which is equivalent to 0.25 times the magnitude of Nifty’s movement

It is crucial to remember that the deltas of calls and puts can be combined, as long as they refer to the same underlying asset

Case 3—Nifty being at 24,350, the trader has a combination of Call and Put options. He has 2 lots of Put options.

Observations:

The combined positions have a negative delta, indicating that the underlying and this option would move in opposite directions

The inclusion of 2 Deep ITM PE has made the entire position delta-negative, meaning it is now inclined to follow market trends

For every fluctuation in Nifty, the combined position is affected by a variance of 0.75 points

If Nifty rises or falls by 80, then the position will shift by a corresponding 80 × (-0.75) = -60 points

In Case 4, when the Nifty spot is at 24,350, the trader holds both Call options and Put options with the same strike price and underlying asset.

Observations:

The 24,350 CE (ATM) option has a delta of +0.5, indicating a positive relationship with the underlying asset

On the other hand, the 24,350 PE (ATM) option has a delta of -0.5, indicating a negative relationship with the underlying asset

When these options are combined, their overall delta becomes neutral, with a value of 0

This means that any changes in the underlying asset will not have an impact on the combined position. For instance, if the Nifty experiences a 150-point movement, the options positions in this case will remain unchanged, resulting in a change of 0 points

Positions like this, with a combined delta of 0, are commonly referred to as “Delta Neutral” positions

Delta Neutral positions will not be affected by any alterations in the market trend. They are effectively shielded from movements in the market

Delta neutral positions may be influenced by factors such as Volatility and Time; this issue will be addressed later

In Case 5, the Nifty spot is at 24,350, and the trader has sold a Call Option.

Observations:

The ‘-1’ in the Position Delta column signifies a ‘short’ position

It is evident that a short call option results in a negative delta, indicating an inverse relationship between the option price and the underlying asset’s movement. This aligns with the understanding that an increase in the spot value would result in a loss for the call option seller

Similarly, when you short a put option, the delta becomes positive. This implies that the option price and the underlying asset move in the same direction. Consequently, an increase in the spot value would result in a gain for the put option seller

-1 × (-0.5) = +0.5

Let’s consider a scenario where the trader has a long position of 5 lots of deep in-the-money (ITM) options. We know that the total delta of such a position would be +5 × +1 = +5. This means that for every 1 point change in the underlying asset, the combined position would change by 5 points in the same direction.

It’s important to note that the same effect can be achieved by shorting 5 deep ITM put options. In this case, the calculation would be -5 × -1 = +5. The -5 indicates 5 short positions, and -1 represents the delta of the deep ITM put options.

This case study should have given you insight into the process of summing up the deltas of individual positions to determine the total delta. This technique can be very helpful when managing multiple options simultaneously and determining their combined directional effect.

I strongly advise you to always consider the change in each position when evaluating your overall position, as this will give you an idea of the risk and leverage associated with it.

Here’s something to note:

Delta of ATM option = 0.5

When you have 2 ATM options, the total delta of the position would be 1.

For every point movement of the underlying, the overall position changes by one due to the delta value being one. This demonstrates how similar an option is compared to a Futures contract. However, it is important to note that these two instruments should not be seen as equivalents. The Futures contract is only impacted by market direction whereas options can be affected by a variety of variables beyond just price direction.

If you want to explore the margin perspective, consider an options contract rather than a futures contract. Be aware of its implications first, and we’ll discuss this further later on.

For those exploring equity investment opportunities through a stock broker or consulting with a financial advisor, understanding delta aggregation proves essential when navigating the stock market. Whether evaluating trading calls or utilising a stock screener to identify opportunities, comprehending how to sum deltas across positions enables more sophisticated portfolio delta management and risk assessment.

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