WHAT IS A STANDARD DEVIATION and WHY DO I CARE?
I always think I know things when I really just have a vagueish 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.
FROM BAD
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.
TO WORSE
FROM BAD
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.
TO WORSE
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


to THE BEAUTIFUL
Well, thank heaven for Tasty Trade, because I FINALLY found some definitions that make sense to ME.
STANDARD DEVIATION
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.
Well, thank heaven for Tasty Trade, because I FINALLY found some definitions that make sense to ME.
STANDARD DEVIATION
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.
SOMETIMES A PICTURE IS WORTH 1,000
WORDS?
Here's some more info I picked up and want to pass on for those of you who want a little more explanation.
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, optiontraders 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. 
STANDARD DEVIATION DEFINITION.
A nice article about Tom Sosnoff:
Touch Options
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