Managing Risk in Options Trading: Exploring Delta, Gamma, and Position Sizing

Estimating Risk using Gamma

The idea of defining risk limits in trading is common among traders. Let us understand better with the help of this example. 

Suppose a trader has Rs. 300,000/- capital in his trading account and the Nifty Futures contract requires a margin of approximately Rs. 16,500/-. To protect himself from undue exposure and losses, the trader may decide not to hold more than 5 Nifty Futures contracts at any given point in time; this way he will be able to define his own risk limits easily and it works quite well with futures trading strategies.

But does this form of risk management apply to options trading? Let’s investigate whether it is the right approach.

Here is a situation –

• The quantity of trades conducted is equal to 10 lots. Please note that 10 lots of at-the-money (ATM) contracts, with each contract having a delta of 0.5, is equivalent to 5 futures contracts.

• Option = 8400 CE

• Spot = 8405

• Delta = 0.5

• Gamma = 0.005

• Position = Short

The trader is currently short 10 lots of Nifty 8400 Call Option, which falls within their predefined risk parameters. As we discussed previously in the Delta chapter, we can sum up the position’s deltas to get the overall delta. It is also important to note that a delta value of 1 is equivalent to one lot of underlying. Therefore, by keeping this in mind, we can figure out the net delta for this position.

• Delta = 0.5

• Number of lots = 10

• Position Delta = 5 i.e. (10 * 0.5)

From a delta perspective, the trader must not exceed trading 5 Futures lots. Additionally, it should be noted that because the trader is short on options, he is also short gamma.

This 5-point delta means that a shift of one point in the underlying causes the trader’s position to change by five.

Assuming Nifty moves 70 points against him and he still holds his position, the trader must think that holding 10 lots of options is within his risk appetite.

Here’s the behind the scenes: 

• Delta = 0.5

• Gamma = 0.005

• Change in underlying = 70 points

• Change in Delta = Gamma * change in underlying = 0.005 * 70 = 0.35

• New Delta = 0.85 i.e. (0.5 + 0.35) 

• New Position Delta = 0.85*10 = 8.5

Do you recognise the issue? A trader has set a risk limit of 5 lots, yet due to a high Gamma value, their position size has effectively grown to 8.5 lots. This can be a surprise for someone who isn’t familiar with this market behaviour, believing that their risk is still in check. In actuality, however, their exposure is larger than expected.

Since the delta is 8.5, it’s expected that this trader’s position will move 8.5 points for every 1-point difference in the underlying. Instead of being short on the call option, if they were long they would be glad as the market is moving in their favour. Furthermore, because of the ‘long gamma’, their position extends, resulting in a larger delta which means their rate of changing premium with each change in underlying accelerates.

If you found the material unclear, try reading it in small segments.

As the trader is short, they are short gamma. This means that when the market moves up whilst they are in a short position, their deltas will increase (due to gamma). These rapid increases in deltas add to the risk of trading options with a short position. This is the reason why options that are short (sold) can be highly risky, particularly when it comes to being short gamma.

There is no need to completely avoid shorting options. Instead, a skilled trader embraces the flexibility of having both short and long positions based on market conditions. However, it is crucial to have a solid understanding of the Greeks when engaging in short options trading, as they can have a substantial impact on your position.

It’s advisable to steer clear of trading option contracts with a high Gamma.

Another interesting question to ponder is what could be regarded as a ‘large gamma’.