In this back-to-basics series TradeKing’s Brian Overby explains options for beginners. Today’s post reviews theta, the options "Greek" that measures the effect of time decay on your position.

It's been a while since I blogged in this back-to-basics series, so let's quickly recap a few things about the "Greeks". First, what the heck are they? “Greeks” refer to a set of calculations with mostly Greek-sounding names like delta, theta, vega, gamma and rho. The Greeks help you measure the impact of certain variables – like interest rates, time passing, and so on – that will likely affect the price of your options contract.

First I introduced delta, probably THE most discussed Greek. Delta measures the amount an option's price is expected to move based on a $1 change in the underlying stock. We also discussed how delta is dynamic: it moves not only as the underlying stock moves, but as expiration approaches.

Next we moved on gamma, closely related to delta. Officially speaking, Gamma is defined as the amount a theoretical option's delta will change for a corresponding one-point change in the price of the underlying security. There's a more intuitive definition, though: If you look at delta as the "speed" of your option position, gamma is the "acceleration".

Today's post will define another Greek, theta, which measures the effect of time decay on your options position. As you'll see, gamma and theta have a symbiotic relationship: with explosive gamma-acceleration comes similarly accelerated time decay.

(Note: even though the Greeks represent the consensus of the marketplace as to how the option will react to changes in certain variables associated with the pricing of an option contract. There is no guarantee that these forecasts will be correct.)

Theta: enemy for options buyers, friend to options sellers

Theta is the option buyer's #1 enemy - but on the other hand, it's also the option seller's best friend.

Theta is defined as the amount a theoretical option's price will change for a corresponding one-unit (in this case, 1-day) change in the days to expiration of the option contract. To the option buyer, the passage of time is similar to the effects of the hot Florida sun's rays on an ice-cream cone. Each hour that passes causes some of the long option's value to "melt away". Not only does the premium "melt away", but it does so at an accelerated rate as expiration approaches. 

If we focus on at-the-money (ATM) options and ignore the effects of interest rates and dividends for a minute, you can do a quick and dirty calculation for how fast an option will decay: Options move at the square root of time. That is, if a one-month ATM option is trading for $1, then a two-month option would be trading for 1 x sqrt of 2 or 1.41 and a three-month option would be trading for 1 x sqrt of 3 or 1.73:

Let's work backwards and say the underlying does not move at all and none of the other variables change. If all of that is true, the 3-month option's time value will lose 32 cents as soon as it drops to 2 month. It loses another 41 cents in month 2, and in the final month 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 call see the accelerated curvature of the graph:

Keep in mind: this large rate of decay is mainly true with ATM options. If the option is way ITM or OTM, the options will decay in a more linear fashion, largely because these options will have a much lower time value.

Theta is a larger number for near-term options than for longer-term options. For example, consider XYZ trading at 100 and the 100 call, trading at 1.15, with an implied volatility of 20% and 7 days remaining to expiration. The one-day theta for this option would be -.085 or a negative 8 1/2 cents. This means if nothing else in the marketplace changes except one day of time passing, this contact will trade for around 1.15 -0.085, or $1.065 in absolute terms.

What about if the same option contact had not 7 but 180 days remaining to expiration? The call would be worth $7, and the theta would be -.025 or negative 2 ½ cents - a much slower rate of decay than the 7-day option.

Now that we've set the stage, my next post will dig deeper into theta itself and how you can use it to factor in time decay risk to your trading.

Regards,
Brian Overby
TradeKing's Options Guy
www.tradeking.com

[image: melting ice-cream by sarboo on Flickr]

Options involve risk and are not suitable for all investors. Please read Characteristics and Risks of Standardized Options available at http://www.tradeking.com/ODD.

Any strategies discussed or securities mentioned, are strictly for illustrative and educational purposes only and are not to be construed as an endorsement, recommendation, or solicitation to buy or sell securities.

Supporting documentation for any claims made in this post will be supplied upon request. Send a private message to All-Stars using the link below the profile image.

TradeKing provides self-directed investors with discount brokerage services, and does not make recommendations or offer investment, financial, legal or tax advice.

(c) TradeKing, Member FINRA, SIPC. http://www.tradeking.com