Option Investor
Trader's Corner

The Option Trader's BFF

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What's both the best friend and worst enemy of the option trader? Theta, better known as time decay.

Imagine that at the close of trading November 23, with Citigroup trading at $31.70, you bought 10 contracts of DEC 32.50 calls. If you were adept at getting between the $1.39 bid and the $1.44 ask, you might have paid about $1.42, or $1420 without commissions.

Imagine that Citigroup opened near that $31.70 level Monday morning, November 26, and nothing else changed other than the passage of time. (You'll have to be good at using your imagination here.) One calculator returned a new theoretical value of $1.32 for that DEC 32.50 call on Monday morning. Your 10 contracts would then theoretically have been worth $1320, and you would have lost $100 plus commissions for the purchase and sale of the call contracts. Thats seven percent of your purchase price, excluding commissions.

Of course, anyone tuning into CBNC this week knows that a whole lot happened with Citigroup early in the week. Almost every input into an option's price changed Monday and Tuesday, including the passage of time. No opportunity occurred to test the theory of how theta would have impacted the option's price if nothing else had changed. C hit $31.70 again a couple of times but traveled quickly through that value each time. CBOE's "Options Report with Doctor J" on November 27 even featured Citigroup, noting a collapse in options volatility.

By Tuesday, C had closed at $30.32. That DEC 32.50 call showed a bid/ask spread of only $0.73/0.75. A $1.38 drop in price and a collapse in volatility contributed to that option's loss in value, but so did theta.
The decay due to theta accelerates as option expiration approaches. Not all option traders understand how that acceleration can impact their trades. Imagine that by Friday, December 14, the Friday before option expiration week, C has magically returned to that same $31.70 value and volatility has plumped up again, so that all factors but theta have remained as they were on November 23. One calculator returns a value of $0.61 for the DEC 32.50 calls. If you decided to try the trade again and purchased 10 contracts that Friday before opex, youd theoretically pay $610.00 plus commissions.

Good deal, right? Those options are cheap. However, by the Monday of option expiration week, they're cheaper. A lot cheaper. Your options would theoretically be worth only $0.41. You would have lost $200 ($610.00 - $410.00) plus two commissions. That's almost 33 percent of your purchase price, excluding commissions, far more than the seven percent that would have been lost during a single weekend earlier in the option expiration cycle.
 
All traders buying options should be aware that of the way theta changes as expiration approaches. The closer option expiration approaches, the bigger the move that is needed to overcome the action of time decay.

Theta or time decay is clearly the enemy of the option buyer. One former financial writer explained theta as the price we options traders pay for being able to trade both directions, using either calls or puts. Some would call that a misguided statement, however. As an options trader, theta can be your best friend. If you're selling options, your strategies often benefit from time decay. If you've sold or written options, you've taken in a credit and you want to keep some or all of that credit, depending on the type of trade you initiated. One way to keep it is to have the option's value decrease through time decay. Think of theta as the enemy of the options buyer and the friend of the options seller or options writer.

Theta is expressed as a negative number for both long calls and long puts, because the value of both calls and puts is lowered by time decay. Theta tells how much the options price can be expected to decline each day due to the time decay alone.

For example, on November 23, theta for the DEC 32.50 call was -0.03. Three days of decay from Friday until Monday would theoretically cost the call buyer about $9.00 per contract ($0.03 change/day x 3 days x 100 multiplier/per contract). Theoretically, on Friday, December 14, theta will be -0.035 if C has again returned to $31.70, its price at the close on November 23, and if all other pricing inputs have also magically returned to their previous levels. Three days of decay from that Friday until the following Monday would theoretically cost the options trader $10.50 ($0.035 decay/day x 3 days x 100 multiplier/contract) per contract, although the theoretical value calculator returned a greater $20.00/contract loss.

Either way, the absolute value of theta has grown (absolute value of 0.03 on November 23 and theoretically 0.035 on December 14) as options expiration approaches. Moreover, since the options value has already suffered from time decay, the projected percentage loss over the weekend is much greater for that Friday just before opex week. With only 8 days until the expiration (equity options expire Saturday, December 22), three days of decay over the weekend represent a heftier proportion of the option's value.

Think of it this way: theta relates to the "time value" of an option. That time value plumps up options prices, but it seeps and then pours away as option expiration approaches, reaching zero at expiration.
That time value isn't pouring away when options still have weeks or months before expiration, however. Those options aren't going to suffer much time decay from a single days passing. The absolute value of theta should be small for those options. On November 23, C's JUN 08 32.50 calls had a theta of only -0.01 and an absolute value for theta of only 0.01.

Whether buying or selling options, traders should factor in the effect of theta on their positions. Options buyers must expect a big move in a short time if theyre buying about-to-expire options. A big move is needed to overcome the effect of time decay. Options sellers often like to sell in the last weeks or days before options expiration, when theta or time decay wreaks the most havoc on the values of the options theyve sold or written.

Not all options are created equally when it concerns theta or time decay. Calls and puts with the same expiration and strikes dont always have equal thetas. On November 23, for example, C's DEC 32.50 call's theta was -0.03, as mentioned earlier. C's DEC 32.50 put's theta was also -0.03, but move out to the DEC 45 or DEC 20 strikes, and you'll find differences. In both cases, theta for the calls was 0.00 and for the puts, -0.01.
Theta also varies with volatility of the underlying. On November 23, for example, DuPont (DD) traded at $44.69. Its DEC 45 calls featured a theta of -0.027, with DD's options having a then-current implied volatility of 26.13. JP Morgan (JPM) traded at $41.95. Its DEC 42.50 calls featured a theta of -0.042. Both options were less than a dollar out of the money, but JPM's options had a higher implied volatility of 45.56. If you're regularly trading the options of particularly volatile stocks, you should understand how volatility impacts theta.

In his book, OPTIONS AS A STRATEGIC INVESTMENT, Lawrence G. McMillan included a graph of the way theta varied with price of the underlying and option price for three securities with varying volatilities. The follow graph recreates his to the best of my ability with a rudimentary graphing program:

Theta Comparisons for Three Hypothetical Securities of Varying Volatilities, Each Valued @ $50.00

The absolute value of theta is always higher for options on a high-volatility stock. Those options are the expensive ones with high extrinsic values.

To summarize, theta is negative for both calls and puts when options are bought. That means that they'll lose value as time moves forward. When options are bought, the option buyer wants movement in the underlying or an expansion of volatility to overcome that time decay. When options are sold, theta is positive, meaning that that the option seller benefits from the passage of time. Those options that were sold are losing value, and the option seller gets to keep some or all of the credit collected when the options were sold or written. Theta can be but isn't always the same for calls and puts at the same strike. It changes over time, with time decay accelerating as option expiration approaches. The absolute value of theta for options on volatile stocks will be higher than the absolute value of theta for less volatile stocks.

This article opened by saying that theta was both the best friend and the worst enemy of the options trader. Vega can be described that way, too. My next Traders Corner article will discuss vega.

One note: I recently bought a new computer. In the process of setting it up and uploading my articles, some problems with some punctuation marks have appeared. I'm sorting through those problems which relate to my computer's attempt to auto format everything, but rest assured that I haven't forgotten how to use an apostrophe when writing a contraction or indicating possession. The process of uploading my articles is just erasing them.
 

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