Theta refers to time decay and is the amount a theoretical option’s price will change for a corresponding one-unit (day) change in the number of days to expiration of the option contract.
Each moment that passes melts away some of the option’s value. Not only does the premium melt away, but it does so at an accelerated rate as expiration approaches. This is particularly true of at-the-money options. If the option is either very in- or out-of-the-money, its options tend to decay in a more linear fashion.
Because the price of the option erodes over time, theta takes the form of a negative number. However, its sign actually depends on what side of the trade you are on. Theta is enemy number one for the option buyer, and a friend to the option seller. Mathematically, this is represented by a negative number when buying options and a positive number when selling them.
If we focus on at-the-money (ATM) options, there’s a quick and easy way to calculate and therefore estimate how fast an option’s time premium may decay. At-the-money options work best in this example because their prices only consist of time value, not intrinsic value (the value by which an option is in-the-money). This simplifies the calculations a bit.
At-the-money options move at the square root of time. This means if a one-month ATM option is trading for $1, then a two-month ATM option would be trading for 1 x sqrt of 2 or $1.41. A three-month ATM option would be trading for 1 x sqrt of 3 or $1.73.
If you work backwards and assume the underlying stock price and other variables have not changed, the three-month ATM option’s time value would lose 32 cents after one month passes. It’d lose another 41 cents after two months, and in the final month after three months have passed, the option would lose the entire dollar. It’s pretty obvious from this example that not only do options decay, but they decay at an accelerated rate as expiration approaches.
If we plot these points graphically you can see the accelerated curve of decay.
Since the time decay of ATM options accelerates as expiration nears, it makes sense that theta is a larger number for near-term options than for longer-term options. Consider XYZ trading at $100, the 100 call trading at $1.15 with an implied volatility of 20%, and seven days until expiration. The one-day theta for this option is -.085 or a negative 8.5 cents. If no other variables change except one day of time passing, this contract will trade for around $1.15 – .085, or $1.065.
What if this same contract had 180 days until expiration? The rate of theta here would be much slower than the seven-day option, about -.025 or negative 2.5 cents.
Time decay and volatility: an interesting relationship
If volatility increases, theta will become a larger negative number for both near- and longer-term options. As volatility decreases, theta usually becomes a smaller negative number.Put in plainer terms, a higher-volatility option tends to lose more value due to time decay than a lower-volatility option. If you’re drawn to buying higher-volatility options for the action they bring, keep in mind that you’re also fighting time decay a bit harder with these contracts.
On the flipside, you may be more drawn to selling these high-volatility options because of the more rapid rate of decay they have over lower-volatility options. (Remember: time decay is the option seller’s friend and the option buyer’s foe.)
In either case, the rate of time decay is only one piece of the puzzle when analyzing opportunities. You’ll need to consider a variety of factors at once when deciding what, when and how to trade.
Considering time decay’s effect on your whole portfolio
It’s not only useful to look at theta on individual options; you should also consider net theta across your entire portfolio. If you are net long options in your account, your portfolio would likely have a negative theta. In other words, each day that passes your portfolio would suffer a bit from time decay. If you are net short options in your account, your portfolio would have positive theta, which means your account value may benefit with each day that passes.
Ally calculates both your individual positions and your net portfolio theta automatically.
At that point, this sample account would theoretically lose $1,579.93 in one day from time decay alone. Keep in mind that many other factors beyond simple time decay would also affect your ultimate gains or losses: price swings on the underlying, changes in volatility, or a change in carry costs.
Comment on this article