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Friday, April 5, 2013

Standard Deviations for Dummies (and me)


I always think I know things when I really just have a vague-ish idea of it.  Standard Deviation is one of those.  Yeah, yeah, I know that sounds stupid.  But think about it.  I'm not a mathematician, I'm not even a thoroughly seasoned option trader.  My education has major  holes in it, (no mathematical or statistical)  so I lean on the internet.  Do You?  It makes my  head hurt.


I read things on the internet, like:

In options trading, standard deviation refers to a range of possible stock prices.  It can be useful to an options trader who would like to estimate how likely it is that a stock price will rise above or fall below a specific price level..

Well, that's somebody's definition.  Does that mean that I  now "get" it?  I don't think so.


Or should we delve into  tech speak?

A standard deviation is a measure of the dispersion of a set of data from its mean. The more spread apart the data, the higher the deviation. Standard deviation is calculated as the square root of variance. 

1.      A specific numerical value for the annual standard deviation can be calculated using the implied volatility of the options  using the formula: :underlying price X implied volatility

2.      This standard deviation can be adjusted for the specific time period under consideration by multiplying the value derived above by the square root of the number of days divided by the square root of 365

Question: Huh? Do I need to do this math in order to trade?   
Answer:  No.  But you do want to understand what it is you’re doing when you use the standard deviations and probabilities that others provide you, right?

Options Playbook has good  explanations of options, and this is how they show the danged formula:

And here’s a square root calculator for you, if you’re the kind of geek who wants to do this!
 Square Root Calculator


Well, thank heaven for Tasty Trade, because I FINALLY found some definitions that make sense to ME.


The volatility of an option is by definition equal to a 1 standard deviation expected move. So, if we sell a put: 1 standard deviation below the current stock price, it has a 84% probability of expiring out of the money.

Now isn't that more helpful???  THIS GIVES YOU A MECHANICAL MEANS OF DECIDING ON YOUR STRIKE PRICE/PROBABILITIES, given that you pick the right strategy...

and furthermore, check out these probabilities:

There are chart studies on Think or Swim (and other platforms) which actually draw standard deviation lines for you, so this math is done for you automatically.


Here's some more info I picked up and want to pass on for those of you who want a little more explanation.

Let’s consider the price of an underlying asset (be it a stock, index, future, whatever).  Let’s call that  price “the mean”.  Prices higher and lower than the mean might be considered “data values” or “data points.  The prices of any given underlying can be considered to be distributed on a classic bell shaped curve. 

Plus / minus one standard deviation from the mean will include 68% of the individual price points, two standard deviations will include 95%, and three standard deviations will include 99.7%

These derived values are immensely important for the options trader because they give definitive metrics against which the probability of a successful trade can be gauged. An essential point of understanding is that the derived standard deviation gives no information whatsoever on the direction of a potential move.  It merely determines the probability of the occurrence of a move of a specific magnitude.

(It is important to note that no trade can be established with 100% probability of success; even boundaries of profitability allowing for a three standard deviation move have a small but finite probability of moving outside the predicted range. A corollary of this observation is that the trader must NEVER “bet the farm” on any single trade regardless of the calculated probability of success. Black swans do exist and have a nasty habit of appearing at the most inopportune imes.)

The higher the volatility, the bigger the standard deviation.
The further the future date is, the bigger the standard deviation.
The larger the stock price, the bigger the standard deviation.

Usually you need a table of standard deviations (SD) to calculate exactly. However, option-traders use the following approximations:
• Plus or minus 1 SD of the mean includes 68.3% (approximately 2/3) of all possible results.
• Plus or minus 2 SD of the mean includes 95.4% (around 19/20) of all possible results.
• Plus or minus 3 SD of the mean includes 99.7% (roughly 369/370) of all possible results.

In other words, we can expect a result that ends further away from the mean in:
• 1 SD in 1 out of 3 occurrences
• 2 SD in 1 out of 20 occurrences
• 3 SD in 1 out of 370 occurrences 

Remember, that most charts allow you to put on Standard Deviations as an Indicator,  and Think or Swim give the Probability %'s right on the Option Chain, so there's no math needed once you truly
understand what you're looking for.

Tasty Trade has many "Market Measures" regarding Standard Deviation, plus many Iron Condor videos showing that 1 Standard Deviation (which is what Tom Sosnoff uses to trade) is not always the best choice, that 2 SD's have a higher success with Iron Condors.  But I'll do another blog post about that later.

From Tasty Trade: Liz & Jenny's video on STandard Deviation (a normal distribution curve)


A nice article about Tom Sosnoff:

Interview on Daily Finance

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