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Understanding the “Greeks,” Part 4: Theta

Understanding the “Greeks,” Part 4: Theta
March 06
19:35 2012

The analysis of options includes four important risk metrics, which are identified by the Greek letters delta, gamma, vega, and theta. (Based on that, it should not be difficult to imagine why these four metrics are collectively nicknamed the “Greeks.”) Here we’ll examine what the fourth Greek, theta, measures. (This discussion will require an understanding of the fundamental workings of options, so if you do not have a good grasp of those concepts, please first review some of our material on options basics.)

It is important to recognize that all of the Greeks are derived from mathematical models. They are not “hard” numbers like an option’s price, bid/ask spread, volume, or open interest. For that reason, the Greek measures are only as good as the model that underlies them—something you should carefully consider before relying heavily on a particular set of Greeks to develop a trading strategy. This is also why you will see different conventions for representing the value of any given Greek.

Theta is in some sense the stepchild of the Greeks, perhaps because it measures something that is utterly unavoidable: the time decay of an option. Time decay is the loss of value an option experiences over its lifespan as expiration approaches. In other words, if all else were to remain the same, the option value would slowly evaporate as time passed.

Option traders generally don’t like things they can’t affect, which is why they focus on what they can affect. For that reason, advanced option strategies are mostly built around delta, gamma, vega, or some combination thereof. As a bit of Wall Street wisdom puts it, “Delta beats theta.” In other words, the point of trading is to pick an option that will produce a price change in the underlying that negates the loss due to time decay and generates a profit to boot.

Theta, which is represented as the dollar value of the option price lost each day, is always negative. The value increases for at-the-money options as the expiration date approaches; it decreases for options that are in-the-money or out-of-the-money. Once again, we are dealing here with issues of predictability, since the risk premium built into the option price is less for in-the-money and out-of-the-money contracts the closer the contract is to expiring.

However, theta may also be high in the case of an out-of-the-money option that has a high level of implied volatility. Also, for contracts that are deeply in-the-money, theta also tends to accelerate as expiration draws near, because the only way to attract buyers for what is increasingly a “sure thing” is to discount the premium.

Considering the example of Amazon that we examined in Parts 1 through 3, with the stock price at $182.50, the March $115 strike price option carried (on February 20) a premium of $68.60. Excluding any commissions, the stock would have to reach $183.60 just for the trader to break even, so theta has increased to ‒0.24 ($24.00 per day in value lost) compared to ‒0.17 for the April $115 option and only ‒0.02 for the July $115 option.

Blackcard

We all know that time marches on—and relentlessly so at that—so pity poor theta, tasked with not only reminding us that time is passing but also putting a hard number on just what is being lost on a daily basis. However, theta does serve as a useful reminder to option traders that they are working against the clock, hoping that the underlying stock price moves far enough and quickly enough to ensure that “delta beats theta.”

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