#### theta

About fifteen years ago, my first stock broker told me a story that happened to him almost twenty five years earlier. I can’t remember all the details, so it can’t be verified. He swore it was true, and if you can’t trust your stock broker who can you trust?

To make this point, I’d like to share the story the best I can remember. It takes place when my broker started in business, in the early 1960’s. He had some clients wanting to buy stock in a company he had never traded before, but the name was familiar. In doing research about the company, he discovered a new company had bought the “corporate shell” of an older, out of business company. (It is a long and difficult process to turn a company into a publicly traded company. Many times it is easier to merge into the “shell” of an abandoned company, and fill it with your own “slug.”)

This “new” stock hadn’t traded for years, maybe even decades, but now had volume and an increasing price. Why was this company familiar?

My broker told of being at his childhood home and realizing the reason for the stock’s familiarity. He remembered, his parents had lost a fair amount of money in the “old” company years earlier. All that was left of the monumental loss was the reminder his father had framed and hung on the wall… the stock certificate.

The story goes, he took the certificate off the wall, sold it to his client. Giving his widowed mother the money and earning a large commission from his satisfied client. If I remember the story correctly, the new company went the way of the old, it once more became a shell.

The moral of the story; If you own a stock long enough it may come back from the dead.

With an option, there is no after life, no reincarnation! One funeral is all it gets. If your option dies, you don’t get a certificate to hang on your wall. All you have left is the trade confirmation from your broker and the memory of the money in your account.

Options are a fixed time investment. After expiration, they cease to exist. When buying options, you need to be right, and right on time. Stock prices go up, they go down and they stay the same, but time always passes.

The nice thing about time, it’s consistent. Time’s passage is an integral part of an option’s price.

Time Value and Time Decay:

Option prices can have two elements, Intrinsic value and Time value. Intrinsic value is equity, a “down payment on the stock.” Time value is potential.

If an option has time remaining, the stock has the capability to move. Consider time value as possible movement value. At expiration, there is no time, there is no potential. The “Greek” term Theta measures the time value decay of an option.

The Laws of option pricing are constant. The Laws regarding time value include; “The At the Money Option ALWAYS has the highest time value.” “Time value drops the further In or Out of the Money the option moves.” “Time value decays at its square root.”

**Time Passes**

Beginning traders go broke taking big losses. Novice traders fall victim to attrition through multiple small losses. Advance traders falter taking small profits. Where are you on the evolutionary chain of traders?

The ability to pick market direction reigns as the most important factor for success for all option traders. Understanding option pricing helps traders magnify gains, and avoid losses.

Many new option traders dig themselves such a deep hole they can’t climb out. At least, can’t climb out fast enough. Stock prices go up, they go down, they may end up where they started, but time always passes. Sometimes, there just isn’t enough time.

Have you heard the joke, “Convicts are the number one buyers of options, nothing makes time fly like owning an option.” If you break a Law of option pricing, you don’t go to the jail house, you go to the poor house!

What does all this mean?

An option’s rate of erosion shouldn’t surprise or scare anyone. Option buyers can calculate time’s expense before buying. This is done with the Greek called **Theta**. Option sellers can predetermine maximum returns. Traders can know the cost of carrying option positions, both long and short. Hedged position traders can profit from the continual and constant passage of time.

**Time’s Effect on Option Pricing:**

Time value and time decay ranks as one of the easiest components of option pricing to understand. The time value of an option includes everything but the intrinsic value. Time costs money! More time, more money. Less time, less money. It’s that simple.

But options can’t be simple, they have to have some complexity. Time passes rhythmically with the tick of a clock, but time value erodes at a different tempo. Time value decays at its square root.

The square of a number is the product of a number multiplied by itself. 1 x 1 = 1, 2 x 2 = 4, 3 x 3 = 9, etc. The square root is the other side of the equation. It’s the equal divisor. The square root of 1 is 1, the square root of 4 is 2, the square root of 9 is 3, etc.

The Laws of option pricing dictate time value is highest for the At the Money (ATM) option. Not sometime or most of the time but always. Time value drops as the strike prices move In and/or Out of the Money (ITM, OTM). Strike prices Deep In and/or Out of the Money (DITM, DOTM) have the lowest time value. Not sometime or most of the time but always.

To better understand time value and its rate of decay, one should think in price units and time units. Price units include dollars and cents; In the case of options, dollars and fractions of dollars. Time units can be days, weeks or months. You can even use hours, minutes or seconds. We won’t discuss an option’s blink of an eye decay rate, but we could mathematically figure it out.

A Hypothetical Example of At the Money (ATM) Call options, (All other option pricing components being constant):

One Time Period = The Square Root of One Price Unit

Two Time Periods = The Square Root of Two Price Units

Three Time Periods = The Square Root of Three Price Units

Four Time Periods = The Square Root of Four Price Units

Insert the time period of your choice, months, weeks, days. Insert the price unit of your choice dollars or fractions of dollars. For our example, lets make it months and dollars.

1 Month = $ 1.00 (Square Root of 1 = 1)

2 Months = $ 1.41 (Square Root of 2 = 1.41)

3 Months = $ 1.73 (Square Root of 3 = 1.73)

4 Months = $ 2.00 (Square Root of 4 = 2)

We could extrapolate, the nine month option would cost only $ 3.00 (Square Root of 9 = 3), the 16 month option’s price would be $ 4.00 (Square Root of 16 = 4).

We could replace months with weeks and dollars with fractions, such as 1/2. Therefore if the one week option were priced at $ .50, the four week option should be $ 1.00, the 16 week option would be $ 2.00.

If we assume four weeks per month, the consistency of the pricing of time becomes evident. We can see the one month option and the four week option are both priced at $ 1.00. $ 2.00 buys the four month option and/or the16 week option. Continuing the math, the 16 month/64 week (LEAP) option would be priced at $ 4.00.

Both equations provide an equal answer:

16 Time Periods = The Square Root of 16 Price Units.

16 Months = The Square Root of 16 Dollars.

16 Months = 4 Dollars.

64 Time Periods = The Square Root of 64 Price Units.

64 Weeks = The Square Root of 64 ½ Dollars.

64 weeks = 8 x .50. = 4 Dollars.

Stock prices go up, they go down, they may end up where they started, but time always passes. The passage of time can be a profitable journey.

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