Day2.Why is the profit speed of at-the-money options the fastest?

Hello

Welcome to Tiger Academy - 「Options Greeks Column」episode 2.

In our previous episode, we discussed the delta value of options. We learned that deep in-the-money options have a delta value close to 1, at-the-money options have a delta value of 0.5, and we concluded that the more in-the-money an option is, the higher its delta value. So, if we have a relatively clear prediction of future stock prices, how should we choose the strike price of an option to maximize profit quickly?

Many investors might think that choosing in-the-money options with a higher delta value is the way to go. This way, you can maximize the price movement of the option based on stock price changes and, in turn, maximize your profits.

However, this answer is incorrect because options have another crucial parameter—the gamma value.

Today, we'll learn how to enhance the speed of profit generation through gamma value.

1. What is the gamma value of an option?

The so-called gamma value measures the change in the delta value caused by a change in the underlying asset. As we discussed in the previous lesson, changes in the price of an option result from the influence of delta. However, the delta value is not a constant but continuously changes with the price of the option. This is why option returns are nonlinear. In many cases, when the underlying asset's price experiences favorable changes, options can help us make money more quickly.

Gamma value can be understood as the acceleration of an option's delta.

For example, if Tesla's stock price is currently around $260.53, and a call option with a strike price of $260 that expires on October 20, 2023, has a delta value of 0.537 and a gamma value of 0.014.

The meaning of this parameter is as follows: When Tesla's stock price increases from $260.53 to $261.53, this call option will first increase by $0.537 due to the effect of delta.

Furthermore, due to the presence of the gamma value, the delta value of this call option will increase by 0.014. So, after the price increase, the theoretical new delta value is 0.551 (0.537 + 0.014). If, on top of this, the stock price increases by another $1 (going from $261.53 to $262.53), then theoretically, the option price will increase by $0.551, not the previous $0.537, with the extra $0.014 being the acceleration generated by gamma. This acceleration is the root cause of options being able to make money faster.

Therefore, we can conclude that, without considering other parameters, the greater the gamma value of an option, the faster the option's profit potential. So, what type of options have the highest gamma value?

2. Why at-the-money options have the fastest profit potential

The answer is at-the-money options because they have the highest gamma value, whereas deep in-the-money and deep out-of-the-money options have the smallest gamma values (approaching 0). To understand this, let's revisit the previous article, "Day 1: Quantitative Trading for Beginners- How Option Delta Values Are Used"

We learned that delta, to some extent, reflects the probability of profit at the time of option exercise. A larger delta value indicates a higher probability of profit at expiration. Deep in-the-money options have a delta value close to 1, meaning a near 100% probability of profit at expiration. Deep out-of-the-money options have a delta value close to 0, indicating a near 0% probability of profit at expiration. At-the-money options have a delta value of 0.5, signifying a 50% probability of profit at expiration.

So, since gamma measures the change in delta values, on this level, gamma gauges the impact on the probability of profit at expiration for an option.

For deep in-the-money and deep out-of-the-money options, the probability of profit at expiration is essentially confirmed, and there is little suspense. Therefore, gamma is smaller. At-the-money options, on the other hand, have a probability of profit at expiration that is just around 50%, sitting at the critical point, with the greatest room for imagination and the highest susceptibility to changes in the probability of profit. Therefore, they have the highest gamma value.

From a gamma perspective, at-the-money options have the fastest profit potential and acceleration. At this point, many readers may wonder: Why isn't it the options with the highest delta value that have the fastest profit potential?

The reason is simple: profit potential is measured in terms of returns, not absolute amounts. Although deep in-the-money options have a high delta value, they are also more expensive, requiring a larger investment. For instance, at the same expiration date, a deep in-the-money option with a price of $10 and a delta value of 1, and an at-the-money option with a price of $2 and a delta value of 0.5. When the underlying stock price changes by $1, the deep in-the-money option's price increases by $1, yielding a 10% return, while the at-the-money option's price increases by $0.5, resulting in a 25% return.

At-the-money options are less expensive because they only contain time value and have a greater potential to increase their return rates. Additionally, at-the-money options have a higher gamma value, which accelerates price increases when the underlying asset's price experiences favorable changes, making them the fastest in terms of both profit potential and acceleration.

Of course, since at-the-money options primarily consist of time value, they are more exposed to time decay risk. How to manage this risk will be discussed in the next article when we introduce the theta coefficient. For those interested in options investing, there's a free introductory course on options available for you to learn.

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See you in the next episode!~