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Standard deviation definition and tutorial

A well-understood measure of absolute volatility that shouldn't be used in isolation.
  1. Define - Define standard deviation.
  2. Context - Use standard deviation in a sentence.
  3. Video - See the video.
  4. Script - Read the transcript.
  5. Quiz - Test your knowledge.
by Paul Alan Davis, CFA, June 28, 2016
Updated: December 22, 2018
When investors and non-investors alike use the term 'volatility' they're probably referring to standard deviation. Let's see more.

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Standard Deviation for Investment Modeling

Intermediate

Standard deviation is a measure of dispersion within a set of data. It is likely the best-understood measure of risk in Finance. It is used for statistical estimation and the calculation of probabilities. Standard deviation is the square-root of variance. It is interpretable because the units match the original data, where variance is in units-squared.

Synonym: volatility

In a Sentence

Doc:  Please understand how to calculate standard deviation  by hand.
Leo:  May we have a phone in that hand?

Video

This video can be accessed in a new window or App , at the YouTube Channel or from below.

Standard deviation definition for investment modeling (4:16)

Video Script

The script includes two sections where we visualize and demonstrate the concept of standard deviation.

Visualize

We're sitting right here in Excel and this is a snippet from our boot camp course.

This is one depiction of standard deviation, from a discussion on portfolio theory. Think about each dot here as a portfolio. Each has a return and a risk measure. Risk is on the x-axis and return is on the y-axis.

Risk here can be interpreted as either variance or standard deviation. As you will see shortly, they are both related. You go seven steps with the exact same calculation, until the final step.

Demonstrate

Let's walk through a calculation for two stocks, Microsoft and eBay.

We have six monthly observations of return for each stock from April to September 2003. Column F is the return on Microsoft, eBay is in column G.

Next we compute the average of each, here 2.38% for Microsoft and 3.98% for eBay. Then we move those over to columns H and I.

In column J we take the return minus this average which gives us 3.24%. That's 5.62% minus 2.38%. For eBay it is 8.91% minus 3.98% or 4.93%. Carry that formula down for all months. Next square these in columns L and M.

Next, using the =SUM function, add up the products for each stock to get 0.0062 for Microsoft and 0.0109 for eBay. Next divide by 6 observations to get the variance of 0.0010 and 0.0018.

Recall, with variance, the units are returns-squared and aren't interpretable. So to get standard deviation take the square root using the =SQRT function or take variance to the one-half power, as I have done here.

So the standard deviation for Microsoft was lower, at 3.20% per month, and it was 4.26% for eBay.

Of course you could ignore all of this and use the function =STDEV.P, but you wouldn't understand it as well when using the shortcut.

Quiz

Click box for answer.

Standard deviation measures the spread of a distribution around the mean and roughly three-quarters of observations fall within +/- 1 standard deviations? | True or False?

False. The first part is true, but roughly two-thirds of observations fall within +/- 1 standard deviations.

Questions or Comments?

Still unclear on standard deviation? Leave a question in the comments section on YouTube or check out the Quant 101 Series, specifically Four Essential Stock Risk Measures.

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What's Next?

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  • To see all terms in the Glossary, click Outline.
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