Convexity in Options Trading: Risk, Reward & Strategy | 915

Stock trading is linear. It is relatively easy to understand. For example, if a trader buys a Reliance stock at the end of the day at ₹1,500. He has a 1:1 chance of making the same profit or incurring the same loss the next day. If the stock gaps up by 100 points, the trader makes a 100 points profits. If the stock gaps down by 100 points, the trader makes a 100-point loss. This shows that the stock has a linear payoff curve.

However, options trading is not linear. This nonlinear relationship between price movement and profit is called convexity. Understanding convexity is important for trading and for appreciating how options work.

What Is Convexity?

Convexity is the nonlinear pay-off structure of different options. It means that if the stock or the underlying moves in the direction, the profit on options can increase rapidly.

For example, if you buy a call option and the underlying index or stock moves up quickly, then the profit from the call option can increase rapidly as the underlying moves up. This acceleration or this sensitivity is called convexity. We can also say that convexity is similar to gamma, but conceptually, it means that:

• Small favourable moves may produce small gains
• Large favourable moves can produce disproportionately large gains.

As we can see, this convexity can be extremely favourable or unfavourable to option traders

Why Convexity Matters

Convexity is very important for traders, and it can introduce three critical differences:

• As an option buyer, the trader already knows what their maximum risk is
• When the trader starts trading, they have a risk-to-reward ratio in mind. However, if the underlying moves very quickly, the risk-to-reward ratio can increase non-linearly, which can favour the option buyer. 
• It is important to note that speed, volatility, and time are key factors in option buying. If either of them is missing, the convexity might not play out in favour of the option buyer.

The other way to look at this is that in stocks, just being right in the direction is enough. But in options, the trader must be right about the direction, timing and the volatility to make profits

The Psychological Difference

Convexity also has a strong impact on the trader's psychology. As a stock trader, they are only worried about the direction. So the only question they ask is the direction it will move in.

However, trading options is not easy. Option traders think in multi dimension. Here are some of the questions that the option trader will have to answer before taking a trade: “How far can it move? How fast? And how is volatility priced?”

Let us understand with an example. Assume that a stock, ABC, will have its earnings announced soon. A stock trader will be able to take a bullish entry if you feels that these earnings are going to be strong.

On the other hand, an options trader will have to look at many aspects due to the convexity of options. They will have to check whether the expected move is already priced in the implied volatility. They will also have to check whether the skew is favourable.

And finally, they will have to look at the probability distribution of the outcomes.

Options trading is probability-weighted, not opinion-based.

Convexity and Risk Management

Apart from psychological factors, convexity also creates many symmetric risk profiles. For option buyers, here are the benefits from convexity: 

• The traders have a limited downside
• Theoretically, they have a very high upside
• They benefit from volatility expansion

On the other hand, option sellers experience negative convexity:

• They have limited profit potential
• If risk management is poorly done, they can potentially have large losses
• One of the major reasons for losses is due to volatility expansion

Given the above reasons, short option traders should focus on tail risk rather than win rate. It is very much possible that a strategy with 85% accuracy but negative convexity can still boost the account during extreme moves. Stock traders rarely face that same nonlinear tail exposure unless they use leverage.

Convexity During Market Shocks

Convexity is extremely important, especially during extreme events. For example, during COVID, when the markets crashed, long options (put options) can multiply significantly very quickly. On the other hand, put option writers incurred massive losses during the same period. This is due to the non-linear acceleration arising from the convexity of options. Stock traders also experienced losses during this time, but their losses were minimal. That is why professional options traders obsess over position sizing, volatility regimes, and tail exposure.

Conclusion

Convexity in options is why option traders consider more than just the direction. Convexity is further amplified by the speed, magnitude, and volatility of the move. It also encompasses time decay and the probability of profit. That is why experienced options traders often sound different. They speak in probabilities and distributions, not predictions.