When trading options, a trader is constantly faced with the choice between the gamma and theta. In simple words, if a trader has bought options, the gamma will be positive and the price for positive gamma will be theta. Conversely, if a trader has sold options, the trader will receive theta for negative gamma. Therefore, traders with positive gamma want to see high volatility in the price of the underlying asset until the option is exercised. While traders with a short option position hope that the underlying asset will not move.
Gamma trading involves a delta hedge. The difference between a long and short gamma-hedge is that the positive gamma results in a gain in hedging, while a negative gamma always means a loss in hedging. You can learn more about the difference between the long and short gamma in this article. The reverse side for any gamma position is theta.
When hedging the delta from the short gamma position, the trader will always fix the losses (hedging is performed only to prevent even greater losses). But the trader hopes that the total amount of losses from this hedge will be less than the profit from receiving theta over time. On the other hand, a trader with a long gamma pays theta over time and tries to cover the cost of theta by hedging delta. A positive gamma always implies a profitable hedge of the delta.
Main principle when trading gamma
One of the important variables with respect to the gamma and theta is the implied volatility of the options. Implied volatility can also be considered the price of options, since the higher the implied volatility the more expensive the value of options. Read The relationship between Vega and implied volatility.
Now let us assume that options are traded with implied volatility of 25%. For this level of volatility to be “fair”, the realized volatility of the price of the underlying asset before an option is exercised must be about 25% in annual terms.
However, let us assume that instead of 25%, the price of the underlying asset showed a realized volatility of 50%. In this case, these options would be too cheap: you can buy them and generate a higher return on the delta hedge than what you will pay in theta. The theta of these options would be lower than the income from delta hedging. Delta hedging is at the heart of most strategies for trading the gamma. Trader has to determine whether he can earn more from delta hedging (due to the high gamma) in order to cover the cost of a theta?
Relationship between gamma and theta
Note that the implied volatility of options with the same expiry time on the same underlying asset but with different strikes vary considerably. Typically, the implied volatility of OTM put options is different from the implied volatility of OTM call options. A graph of the relationship between implied volatility and strikes is known as a volatility curve, volatility smile or volatility skew. Options with different strikes have different implied volatility.
For stock indices (such as the S&P 500) OTM put options have higher implied volatility than ATM or OTM call options. This is due to the fact that stocks usually fall sharply and grow slowly. Thus, in terms of trading the gamma some of the options will have a relatively cheap gamma, due to the difference in implied volatility.
Example of a gamma/theta ratio
Let's consider ATM option with an implied volatility of 20%, which has a gamma and a theta equal to $4 and $8 respectively. If a trader buys 100 options, the gamma will be $400 and the theta will be $800 a day. Now let's assume that there are OTM put options that expire at the same time. They trade with 25% implied volatility, and have $2 gamma and $6 theta.
Note that OTM puts have a lower gamma and theta than ATM options, which is to be expected. To buy $400 gamma through OTM put options, you must buy 200 options. But OTM puts have a higher relative theta. When buying 200 put options, the trader will pay $1,200 per day ($6 gamma x 200 options).
The conclusion is that OTM puts have a more expensive gamma than ATM options, i.e. theta of OTM puts is higher for the same gamma. Of course, there are other risks (e.g. Vega, Vomma and Volatility skew), but if we look at option strategies from the perspective of trading the gamma, in this example ATM options provide a more attractive opportunity than OTM put options.
One simple way to estimate the cost of a gamma is using a gamma/theta ratio. By observing this ratio over time, trader can set an acceptable gamma/theta ratio for a specific asset. In the above example, the gamma/theta ratio for the ATM option is $400/$800 = 0.5. For OTM put options, the gamma/theta ratio was only 0.33. The higher the coefficient, the more attractive the gamma becomes. And vice versa, the lower the ratio, the more expensive the gamma becomes. A high coefficient means that you can buy a lot of gamma at a low price. Therefore, with experience, a trader will be able to choose suitable strikes for profitable gamma trading in different circumstances.
Gamma/theta ratio is also worth tracking for the entire option portfolio. In some assets with very steep volatility skew you can see really profitable gamma trading opportunities.
Sometimes you can build a risk reversal position with a positive gamma and receive theta. This is possible if the trader buys options with high implied volatility and sells options with low implied volatility. For example, stock index options provide an opportunity to have a positive gamma and receive theta by buying a risk reversal strategy. However, there are good reasons to explain this relationship between the gamma and theta for stock index options.
However, any trader should understand that buying the gamma is always accompanied by a negative theta, that is, for the opportunity to hedge the delta with profit, the trader must pay theta, and vice versa.