# How will Standard Deviation help in trading

Option Premium sellers often sell options one Standard Deviation away from the market price. In this way there is a high probability of profit. The Options sold may expire worthless or you take profits now buy buying them back.

Standard Deviation is a statistical term that measures the amount of variability or dispersion around an average. It is a number used to tell how measurements for a group are spread out from the average (mean), or expected value.

A low standard deviation means that most of the numbers are very close to the average. A high standard deviation means that the numbers are spread out.

### Understanding Standard Deviation

The Greek symbol for Standard Deviation is sigma. SD is the most common measure of statistical dispersion, measuring how widely spread the values in a data set are. If the data points are all close to the mean, then SD is close to zero. If many data points are far from the mean, then the SD is far from zero.

Generally speaking, dispersion is the difference between the actual value and the average value. The larger this dispersion or variability is, the higher the standard deviation. The smaller this dispersion or variability is, the lower the standard deviation. Chartists can use the standard deviation to measure expected risk and determine the significance of certain price movements. Standard deviation is also a measure of volatility.

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With selling options we want to know how likely it is when we can keep the credit or when we bought options how likely it is to make some money with an option (strategy).

### How Volatility relates to SD

Say it other way, A standard deviation is a unit of measure for volatility, and measures how tightly data is bunched around a mean, or average. SD is a statistical term that measures the amount of variability or dispersion around an average.

Some stocks like Coca Cola don’t range too much up or down from the current price. Other stock like APPLE can vary hugely. SD tells you about the potential percentage move a stock might make by a certain date. You can say that for a $100 stock, SD is either 10%, or $10. In the option trading world, this may be defined as how tightly stock or index prices are bunched around the current price.

The SD is based mainly on an estimate of future stock or index volatility, a future date, and the current stock or index price. It also incorporates interest rates, but to a lesser extent.

- The higher the volatility, the bigger SD.
- The further the future date is, the bigger SD.
- The larger the stock price, the bigger the SD.

You may use historical volatility, but in my opinion implied volatility is a better estimate of future volatility. **Here is how you can calculate 1 SD:**

1 standard deviation = stock price * volatility * square root of days to expiration/365.

Let’s take an example. With SPY trading at 142.00, and March expiration 53 days away, and a volatility of 11.6%, what is the 1 SD range for the SPY at March’07 expiration? **142.00 * .116 * square root (53/365) = 6.27**

The above means 68% of the time, the index will be 142+/-6.27 by Mar’07 expiration. This assumes that stock and index price returns are normally distributed. One SD covers the same percentage number of occurrences regardless of the size of SD. That is, the $100 stock with a $10 standard deviation will be between $90 and $110 68% of the time. And a $20 stock with at $3 standard deviation will be between $17 and $23 68% of the time.

For your information,

+1/-1 standard deviation covers 68% of occurrences,

+2/-2 standard deviations cover 95% of occurrences, and

+3/-3 standard deviations cover 99% of occurrences.

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If you don’t want to calculate the standard deviation for each trade you can also look at the delta of the option. There are platform who show the delta of the option very easily like Think Or Swim or Dough is showing SD in a graphical way.

**Conclusion**

When you want to enter a trade with a 68% probability of success you choose options with strikes at 1 SD away of the current price. If you choose to sell option premium with strikes at 2 standard deviation away from the market price you know that the options expire worthless 95% of the time. In this way you can keep the credit you received. So, by choosing the right strikes you can determine the risk you take.