# Key Concepts 1. Probabilities & Statistics

Options involve risk and are not suitable for all investors. Please read Characteristics and Risks of Standardized Options before deciding to invest in options.

## Standard Deviation

In statistics, standard deviation is a unit of measurement that quantifies certain outcomes relative to the average outcome.

Before diving into how it applies to options trading, it’s important to understand the probabilities associated with certain multiples of standard deviations:
- 1 standard deviation encompasses approximately 68.2% of outcomes in a distribution of occurrences
- 2 standard deviations encompasses approximately 95.4% of outcomes in a distribution of occurrences
- 3 standard deviations encompasses approximately 99.7% of outcomes in a distribution of occurrences

The standard deviation of a particular stock can be quantified by examining the implied volatility of the stock’s options. The implied volatility of a stock is synonymous with a one standard deviation range in that stock.

For example, if a \$100 stock is trading with a 20% implied volatility, the standard deviation ranges are:
- Between \$80 and \$120 for 1 standard deviation
- Between \$60 and \$140 for 2 standard deviations
- Between \$40 and \$160 for 3 standard deviations

From this, we can conclude that market participants are pricing in a:
- 68% probability of the stock closing between \$80 and \$120 a year from now
- 95% probability of the stock closing between \$60 and \$140 a year from now
- 99.7% probability of the stock closing between \$40 and \$160 a year from now

How do we capture all of this with options trading? We just need to remember a few probabilities in our strike prices:
- Strikes with a probability of 16% ITM / 84% OTM capture a 1 standard deviation range for an OTM option
- Strikes with a probability of 2.5% ITM / 97.5% OTM capture a 2 standard deviation range for an OTM option

It’s important to note these values are just for one side. For a strangle where we’re selling an OTM put and an OTM call together, we look for 16% ITM probabilities on either side, which gives us that 68% probability of the stock closing within that range (16 + 16 = 32. 100-32 = 68%). One cool thing about standard deviation & implied volatility is that when IV is high, we can obtain these probabilities using much wider strikes. Implied volatility is high, which means there is a larger implied range the stock can move. That directly translates to higher probabilities of being ITM for further out strikes. That’s the power of high implied volatility!

As we can see, understanding what implied volatility is telling you about a stock’s expected future movements is very valuable!