Greeks: Theta

Option Greeks: Theta Risk and Reward
Published originally at

By John Summa, CTA, PhD, Founder of

ime value decay, the so-called “silent killer” of option buyers, can wipe a smile off the face of any determined trader once its insidious nature becomes fully felt. Buyers, by definition, have only limited risk in their strategies together with the potential for unlimited gains. While this might look good on paper, in practice it often turns out to be death by a thousand cuts.

In other words, it is true you can only lose what you pay for an option. It is also true that there is no limit to how many times you can lose. And as any lottery player knows well, a little money spent each week can add up after a year (or lifetime) of not hitting the jackpot. For option buyers, therefore, the pain of slowly eroding your trading capital sours the experience.

Now, to be fair, sellers are likely to experience lots of small wins, while getting lulled into a false sense of success, only to suddenly find their profits (and possibly worse) obliterated in one ugly move against them.

Returning to time value decay as a risk variable, it is measured in the form of the (non-constant) rate of its decay, known as Theta. Theta values are always negative for options because options are always losing time value with each tick of the clock until expiration is reached. In fact, it is a fact of life that all options, no matter what strikes or what markets, will always have zero time value at expiration. Theta will have wiped out all time value (also known as extrinsic value) leaving the option with no value or some degree of intrinsic value. Intrinsic value will represent to what extent the option expired in the money. (For more, see The Importance of Time Value.)


Figure 7: IBM options Theta values. Values taken on Dec. 29, 2007 with IBM at 110.09. Source: OptionVue 5 Options Analysis Software.

As you can see from a look at
Figure 7, the rate of decay decreases in the more distant contract months. The yellow highlights the calls that are at the money and the violet the at-the-money puts. The January 110 calls, for example, have a Theta value of -7.58, meaning this option is losing $7.58 in time value each day. This rate of decay decreases for each back month 110 call with a Theta of -2.57. If we think of time value on these 110 calls as if it represented just one July option, clearly the rate of loss of time value would be accelerating as the July call gets nearer to expiration (i.e., the rate of decay is much faster on the option near to expiration than with a lot of time remaining on it). Nevertheless, the amount of time premium on the back months is greater.

Therefore, if a trader desires less time premium risk and a back month option is chosen, the trade-off is that more premium is at risk from Delta and Vega risk. In other words, you can slow down the rate of decay by choosing an options contract with more time on it, but you add more risk in exchange due to the higher price (subject to more loss from a wrong-way price move) and from an adverse change in implied volatility (since higher premium is associated with higher Vega risk). In Part VIII of this tutorial more about the interaction of Greeks is discussed and analyzed.

The common options strategies have position Theta signs that are easy to categorize, since a selling or net selling strategy will always have a positive position Theta while a buying or net buying strategy will always have a negative position Theta, as seen in Figure 8.

Figure 8: Position Theta signs for common options strategies. The position Thetas in this table represent standard strategy setups.



Interpreting Theta (both position and non-position Theta) is straightforward. Looking at Theta horizontally across time and vertically along strike price chains for different months, it is shown that key differences in Thetas inside a matrix of strike prices depend on time to expiration and distance away from the money. The highest Thetas are found at the money and closest to expiration. Finally, position Theta for popular strategies is presented in table format.

Go to Part 6 – Options Greeks: Gamma Risk and Reward