Theta: Time Waits for No Trader

Almost everything that goes into an option’s price moves in two directions. In the short term, stock prices move up and down. So does volatility. Over longer periods, even dividends and interest rates change. But one thing doesn’t change: time marches on at a steady rate, and always in the same direction, one day at a time. Like our mortal selves, each flip of the calendar, from one day to the next, takes an option one day closer to its expiration date. 

Yes, time passes, and that’s why options have time decay — also known as theta — to the detriment of option buyers and the benefit of option sellers. Theta is a theoretical metric (a “greek”) that represents how much an option’s price loses, or decays, as one day passes to the next. And because of time’s reliability, many option traders rely on theta. 

But why do options prices decay in the first place? Keep in mind that an option’s price has two components: intrinsic and extrinsic value. Intrinsic value is affected only by where the stock price is relative to an option’s strike price. It’s either zero for out-of-the-money (OTM) options, or the difference between the stock price and the strike price for in-the-money (ITM) options. Extrinsic value (also called time value) is an option’s value over and above its intrinsic value. Thus, the price of an OTM option represents 100% extrinsic value.  

The extrinsic value of an option is essentially the market’s opinion of how likely it is to be ITM at expiration, and by how much. All else being equal, an OTM option that the market thinks is more likely to end up ITM will have a higher price—more extrinsic value—than an OTM option the market thinks is less likely to go ITM.

The Cone of Uncertainty

Time gives stocks the opportunity to move up or down. All else being equal, the more time is left until expiration, the more likely it is a stock may move up or down by a larger amount from its current price. That means a longer-term OTM option has a greater likelihood of turning into an ITM option. The less time is available, the less likely it is the stock may move significantly. See Figure 1.

So, in theory, an option with less time—fewer days to expiration—has a lower extrinsic value than an option with more days to expiration. Thus, theta measures how much each day reduces an option’s extrinsic value. 

Let’s look at a theoretical example of the impact of theta on options pricing (Figure 2). Say the SPX was at 2738 at the end of November 2018. The 2700 put with 90 days to expiration was valued at $73.33. Roll the calendar ahead a month. Assume the SPX is still at 2738. With volatility unchanged, the value drops to $62.01. Note that it dropped $11.32 over the month, although nothing changed except the passage of time.

Now roll the calendar ahead another month. Keep all else unchanged, and the value drops by $22.06, from $62.01 to $39.95. 

One month after that, in our example, the option has expired worthless, having lost the remaining $39.95. Notice, though, that over each 30-day period, theta was higher—first $11.32, then $22.06, then $39.95. Theta isn’t linear. It increases as the option approaches expiration. 

In this example, at 90 days out, the daily theta was $0.47. So, when the calendar was rolled from 90 days left to 89 days left, the theoretical value went from $73.33 to $72.86. At 60 days out, theta was $0.56, and with 30 days to go, theta was $0.78. If you’re designing time-sensitive options strategies, it’s important to remember that theta isn’t linear.

More to the point, how can one single day have such different impacts on options with different days to expiration? Although time is a constant in and of itself, as a percentage of time before expiration, it continues to grow as expiration nears. One day is 0.55% of 180 days, 1.67% of 60 days, 3.33% of 30 days, and 6.67% of 15 days. If an option is expiring the following day, it will lose 100% of its remaining extrinsic value over the next 24 hours.  

That’s why the theta of an option increases as time to expiration decreases. And it’s why a trader who’s short an option profits as time passes, all else being equal. 

But all things aren’t always equal. And theta is impacted by volatility. 

It’s All in the Vol

Volatility and an option’s extrinsic value are related. In theory, when volatility goes up, an option’s extrinsic value rises. That suggests theta has a bigger impact on an option when volatility is higher—because it has to erode more extrinsic value by expiration.  

For example, if SPX is at 2738, and vol is at 21%, then the theta of the 2700 put with 60 days to expiration would be $0.65 per day. If vol was at 30%, then the theta of that same put would be $1.01.  

Theta is often also highest for ATM options because extrinsic value is highest for ATM options, and moves lower for options that are further OTM. In effect, theta has to whittle down more extrinsic value for ATM options than it does for OTM options. 

As a trader looking to make money from theta, you want to analyze it in a dollar amount. To do that, multiply the option’s theoretical theta by the option’s multiplier (typically $100 for U.S. equity and index options, but varies with options on futures), and then by the number of contracts you plan to trade. Conveniently, the thinkorswim platform from TD Ameritrade does this for you. To see the total theta of your positions—positive and negative—look at the Position Statement section under the Monitor tab. 

Yet, as we’ve seen, theta is a moving target. As time, stock price, and volatility change, so does theta. So if you want to maintain a certain level of theta for a particular strategy, or even your entire portfolio, monitor your positions closely to make sure you stay within target parameters. Otherwise, it might be time to tweak, roll, or close out positions. 

And if you typically beta-weight your portfolio, there’s no need to do so with theta as you would with, say, your delta or vega exposure. Unlike those greeks, for which you might want to normalize to a benchmark such as the S&P 500, theta is just what it is. Time passes for that high-flying tech name at the same rate as for SPX or anything else.

So much of trading, as with life, is in flux—up one minute and down the next, with the occasional sharp turn sideways. Yet time marches on. This is your options position, and it’s decaying. One. Day. At. A. Time.