Options Forum: Thinking About Theta
Steve:
Could you explain the proper time to sell options? I read one options adviser, who sells things early despite the fact they have a loss but are still in the money. I think they would recover if given time. Is there a magic formula, given time decay?
Thanks,
 J.M.
Even though many option strategies are based on pricing models, which contain some mindboggling equations, there is not, as far as I know, any magic involved (though I suppose the occasional ability of options to make money mysteriously disappear right before your eyes suggests some measure of magical power).
So, while there is no definite answer as to the "right" time to sell or close out an existing long option position (and I won't try to interpret another person's advice), understanding how time decay, or theta, is calculated and its effect on an option's price can help make more informed decisions.
Here, courtesy of James Hosker, vice president of Derivative Research at Lehman Brothers, is an equation for the theta of a long put:

While this may be comprehensible to "mathemagicians" such as Hosker, who did his best to explain it, it still makes my eyes glaze over. Just as you don't need to know how to build an engine to drive a car, I'm not so interested in how theta was created as I am in trusting its accuracy, reliability and practical applications to help me arrive at a profitable destination.
Like all the other
greeks that are used to describe, and hopefully forecast, optionpricing behavior, calculating theta, which measures the expected change in an option's value with respect to a change in the time remaining until expiration, is a function of the usual inputs, such as the underlying stock price, time remaining until expiration, implied volatility, the riskfree interest rates and expected dividends. (These components are represented by the symbols in the equation above.)
Fascinating, right? OK, maybe not, but these items are important because they're the variables that we plug into our
options calculator. (All hail the options calculator, and show your appreciation for all the tools, software and electronictrading access that allows us ordinary investors to play with the same levers that were once the privileged domain of those wizards of options known as specialists and market makers).
Here are some basic concepts about theta that should be considered in establishing, adjusting or exiting an option position.
An option's theta is sloped, meaning that the rate of time decay accelerates as expiration approaches. For example, if a theta is 10, and 0.01 of a year passes, the predicted decay in the option's price is about 10 cents.
Theta is highest for atthemoney options and decreases as the strike moves further into the money or further out of the money. This is because atthemoney options have the highest time value, and inthemoney options are mostly composed of intrinsic value, while outofthemoney options have a larger implied volatility component. This is because the time component of an option's value is a squareroot function, hence the slope.
Theta is higher when implied volatility is lower. This is because a high implied volatility suggests that the underlying stock is likely to have a significant change in price  this has the effect of expanding the time remaining in the life of the option. The more time passes, the higher the probability of a change in price.
These concepts can be helpful in determining what strategy is best for a given environment or set of assumptions. For example, with a short time frame and low volatility, selling vertical spreads, or net credit positions, will take better advantage of theta or time decay than buying spreads or establishing debit positions.
Steven Smith writes regularly for TheStreet.com. In keeping with TSC's editorial policy, he doesn't own or short individual stocks. He also doesn't invest in hedge funds or other private investment partnerships. He was a seatholding member of the Chicago Board of Trade (CBOT) and the Chicago Board Options Exchange (CBOE) from May 1989 to August 1995. During that sixyear period, he traded multiple markets for his own personal account and acted as an executing broker for thirdparty accounts. He invites you to send your feedback to
steve.smith@thestreet.com.