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Variance definition and tutorial

No need to interpret variance. That's what standard deviation is for.
  1. Define - Define Variance.
  2. Context - Use Variance in a sentence.
  3. Video - See the video.
  4. Script - Read the transcript.
  5. Quiz - Test your knowledge.
by Paul Alan Davis, CFA, June 27, 2016
Updated: December 22, 2018
Variance in the investment space is highly dependent on the timeframe selected when measuring it. Keep reading.

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Variance for Investment Modeling

Intermediate

Variance is one of the most commonly used, yet least understood risk measures in Finance. It applies to individual assets and portfolios. It is calculated by taking the sum of all squared differences between each observation and the average over the measurement period, then divide by the number of observations. Variance is not easily interpreted because the scale is in units squared, like returns squared. To interpret, it is commonly translated to standard deviation by taking the square root of variance.

Synonym: second central moment

In a Sentence

Doc:  Besides variance  what else could we use on the x-axis for MPT charts? And why?
Wes:  Standard deviation, because it's more interpretable and the relationship still holds.

Video

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

Variance definition for investment modeling (4:22)

Video Script

The script includes two sections where we visualize and demonstrate the calculation of demeaned returns.

Visualize

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

This is one depiction of variance, from a discussion on portfolio theory.

Think about each dot here as a stock or 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.

The key with variance is the calculation, so let's head there now.

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 Column G.

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

In column J we take the return minus the average which gives us 3.24%. That's 5.62% minus 2.38%, or 3.24%. 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 for Microsoft and 0.0018 for eBay. Recall, these are in units of returns squared so aren't interpretable. So it is common to use standard deviation, which is the square root of variance.

To get that, use the =SQRT() function or take the variance to the one-half power, as I have done here.

Quiz

Click box for answer.

If inputs are in decimal form, then variance is lower than standard deviation. | True or False?

True

Questions or Comments?

Still unclear on variance? 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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