Options Decay and the Dispensation of Decision

Largely we live in a country and culture where choices can be multiplied to the highest sum.  One where we find strange pleasure in our relentless attempt to pat the brim of the thinkable:  Four restaurants on every block, 100+ television channels chocked-full of drivel, and gazing upon the myriad of half-price hotels in Orlando that the world doth possess.

I love coffee but, it pains me to spend 25 cents an ounce when I can equally consume my fill for .0625 cents an ounce.  On the other hand, I will shell out to be comfortable.  Recently, I took a brief trip to Shanghai and paid $232 an hour for the 28-hour round-trip flight when I could’ve disbursed $54 anhour and arrived at the same time.  For me, a justifiable price differential so as to stretch out and ward off any chance of some worn-out old man breathing sour wine and garlic into my face.

Options are similar in that there is a cost/benefit associated with them.  At the end of the day, every option position is a trade-off between market movement and time decay.  If price movement in the underlying contract will benefit the trader, the passage of time will hurt and vice-versa.  Sadly, you can’t have it both ways.  You either want the market to move, or sit still.

What is (theta) time decay?

Theta, otherwise known as time decay, is an approximation that measures how quickly time value disappears from an option with the passing of one day without movement in either the underlying asset or implied volatility. Specifically, theta is used to approximate how much an option’s extrinsic value is carved away by the passage of time.

Theta causes an option with more time to expiration to hold additional extrinsic value as compared with an option with fewer days remaining to expiry. Thus, it should make sense that long options contain negative theta, whereas short options have positive theta. If options, by their very nature, continuously lose extrinsic value, a long option will lose money in part due to theta, whereas a short option will make money in part due to theta. An option’s rate of decay (theta) is mathematically sloped, insinuating that option theta will accelerate as expiration draws near.

Example of the Cost/Benefit of Theta

John Doe has been consistently successful at running his fifth-generation Midwestern trucking company straight into the pavement. And today is no different in that even a recent 40% drop in petroleum prices have done nothing to stave off his creditors as he recently learned that one of his employees/cousins was skimming funds.

John Doe was in a severe, short-term cash crunch and one thing he knew was he needed to quickly hedge his fuel risk exposure – even a fractional uptick in prices would put his company over the cliff.  While driving his rig along the left-hand lane, John performed some back of the napkin calculations and figured he needed the United States Gasoline Fund ETF(ticker: UGA – reference: $37.70) to trade below $42.50 for John to remain solvent.  On one hand, he could buy 10,000 shares of UGA @ $37.70 – costing him an astounding $377,000. Alternatively, he could buy 100 December $40 calls at $1 – costing him $10,000 and in effect, provide him the right to buy shares at $40 if UGA should actually climb to that value or higher.

As a third choice, John could purchase 100 December $42 calls at 30 cents – setting him back $3,000 and providing him with the right to buy 10,000 shares of UGA stock should it climb above $42 by expiration.  John realized these call contracts were a fast wasting asset however, and was looking to make a snap-decision with the cost/benefit in mind.

From a simplicity standpoint, tying up $377,000 to buy 10,000 shares of UGA makes the most sense. However, John doesn’t have the funds and, he smartly realizes that purchasing $377,000 worth of underlying exposes him to $377,000 of potential downside risk.  Choice number two, he could buy the December $40 calls for $1 spending $10,000 but giving him a firm purchase price of $41 ($40 strike price + $1 premium paid) if UGA should rally.  Choice three allows him to spend only $3,000 for the right to buy UGA stock at a $42.30 ($42 strike price + 30 cent premium paid).

Choice two (December $40 calls) has a daily “theta” of eight cents – i.e. if UGA doesn’t move the option will lose eight cents per day.  Choice two has a daily “theta” of three cents – i.e. if UGA doesn’t move the option will lose tree cents per day.  However, with that benefit is a cost trade-off.  There’s no free lunch.  John needs to quickly decide whether he pays and perhaps loses $10,000 to potentially purchase UGA at $41.00 or spend $3,000 to purchase the same at $42.30.  There’s no right or wrong – simply cost vs. benefit.

Synopsis of Options Theta

• A long (purchased) option position loses value with the passage of time and hence it will always have a negative theta whereas a short (sold) option position will always have a positive theta.
• Theta vs. Strike price location: At-the-money options have greater thetas than either in-the-money or out-of-the-money options.  This makes sense as at-the-money options have the highest extrinsic value, so they have MORE extrinsic value to lose over time than an in-the-money or out-of-the-money option.
• Theta vs. Volatility: As we decrease (increase) our implied volatility assumption, the theta of an option will increase (decrease) accordingly.
• Theta vs. Time-to-expiry: For at-the-money options, the theta increase as expiration approaches.  The theta of a short-term at-the-money option will always be greater than the theta of a longer-term at-the-money option.  For in-the-money and out-of-the money options, the theta of short-term options will be lesser than the theta of a longer-term option.