Gamma trading and option time decay

By , CEO of Volcube.

In options trading, there is a never-ending duel fought between gamma and theta. In very simple terms, if you own options, you own gamma which you pay for via theta. In contrast, if you are short options, you will hope to collect theta in exchange for the risk of being short gamma. Again, in simplified terms, the owners of gamma want to see plenty of volatility in the underlying product. Whereas the short option players hope the underlying will never move again!

Gamma trading involves scalping the underlying product via gamma hedges. The difference between long and short gamma hedging is that long gamma hedges are always locking-in some kind of revenue, whereas short gamma hedges always lock in some kind of loss. You can learn more about the difference between long and short gamma in this article.  The flip-side to any gamma position is the theta position. So whilst any gamma hedges that the short gamma player will make will be losing hedges (and are only executed to prevent even bigger losses occurring), he hopes that the total loss from these hedges is outweighed by the gain from the decay in the option value. The long gamma player is fighting against time decay, hoping his gamma hedges make more than enough revenue to cover the theta bill.

The basic idea behind any gamma trading strategy

One important variable in the gamma/theta trade-off is the implied volatility of the options in question. Remember that implied volatility can also be viewed as the price of the options. The higher the implied volatility, the more expensive the options will be in dollar terms (due to vega). Now suppose that the options are trading with an implied volatility of 25%. For this vol level to be a ‘fair’ price for the options, the realized volatility in the underlying would have to be around 25% in annualized terms, during the option’s life. Suppose that instead, the underlying product moved around with an annualized volatility of 50%. In that case, these options were too cheap; they could be bought and by gamma hedging efficiently, a profit could be realized. The theta decay of these options is unlikely to outweigh the profits that can be made from gamma hedging. This basic principle underlies most gamma trading strategies. The trader must believe he can gamma hedge to capture a realized volatility that is significantly different from that priced into the options.

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The importance of gamma/theta ratios

Take a look at the implied volatility levels of options with the same expiration on the same underlying, but with different strikes, and you are likely to see that they vary significantly. It is not unusual for an out-of-the-money put option to trade with a significantly higher implied volatility level than say an out-of-the-money call option on the same product, expiring on the same date. This is known variously as the volatility curve or smile or skew. (The names have slightly varied meanings; you can learn more in this article). Now, the effect of this is that options on the same product with the same expiration are priced differently in volatility terms. So from a gamma trading perspective, some of these options will be relatively cheaper than others, even though they are struck on the same underlying.

An example of gamma/theta ratios

Consider an at-the-money option trading at 25% implied vol which has 5 gamma and 10 theta. Assume then, that if I buy 100 lots of the options, I will have 500 gamma and be paying $1,000 per night for the privilege.  Now suppose there are some out-of-the-money puts, expiring at the same time and struck on the same underlying. These are trading at 30% implied vol, have 2 gamma and 5 theta. Notice that they have lower gamma and theta than the at-the-money options, as we would expect. To own 500 gamma via the puts, I need to buy 250 lots (250 * 2 gamma). But these puts have a higher relative theta. 250 lots of these puts will cost $1250 per night (250 * 5) to own. The conclusion is that these puts are a more expensive way to own gamma than the at-the-money options. Sure, there are other risks to consider (such as vega risk and skew risk) but when viewed as a straight gamma trading-play, owning the puts is less efficient than owning the at-the-monies. And flipping things round, shorting the puts in order to be short gamma and collect theta, is done more efficiently via the puts.

One easy way to view this is via the position gamma/theta ratio. By monitoring this ratio over time, a trader can acquire a feel for what could be a good or bad ratio in the light of the market conditions. In the example above, owning the at-the-money options led to a gamma-theta ratio for the portfolio of 0.5 (500 gamma/$1000 of theta). For the puts, the gamma/theta ratio was only 0.4. The higher the ratio, the more attractive owning gamma becomes. And vice versa the lower the ratio, the happy one would be to short gamma. A high ratio means lots of gamma at low cost. A low ratio means not much gamma, but reasonably high theta. So it should be obvious which position you would rather have on under which circumstances.

The ratio of the portfolio is worth tracking. For some products with very steep skews, it can be possible to generate truly awful/fantastic ratios (such as paying theta to be short gamma or collecting theta to be long gamma). This could occur when the portfolio is long very high vol options and short low vol options. For example, in equity index options, owning puts and being short calls is notorious for causing undesirable gamma/theta ratios. There are other reasons why a trader may still want to hold such a position in spite of the inefficient gamma/theta trade-off (and why shorting index puts is not a ‘free money gamma trade’!).  But any trader is still well served by knowing the gamma he owns or is short relative to the theta decay he is paying or collecting. Forewarned is forearmed, as they say!

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