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# Demeaned Returns Definition and Tutorial

Even seasoned experts don't remember how using demeaned returns simplifies the calculation of risk statistics.
1. Define - Define Demeaned Returns for investments.
2. Context - Use Demeaned Returns in a sentence.
3. Video - See the video for the concepts.
4. Script - Follow along with the transcript below.
5. Quiz - Test yourself. by Paul Alan Davis, CFA
Updated: February 17, 2021
Demeaned returns are helpful when programming because you can hand off the named range to another process to arrive at four important risk measures.

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## Demeaned Returns for Investment Modeling

Intermediate

Demeaned returns are the stream of returns over a measurement period after subtracting the mean return over the period. Demeaned returns are used for the calculation of variance, standard deviation, covariance and correlation. The length of the measurement period is thus an important input in the evaluation of risk.

Synonym: centered returns

For context, recall that nearly all risk measures, whether absolute (variance and standard deviation) or relative (covariance or correlation) all require determining how far from the average observations fall. That way the dispersion from this average can be summarized. For investment returns this process starts with subtracting, or demeaning, the returns.

### In a Sentence

Pat:  Why does Guy harp on the importance of demeaned returns?
Wes:  Knowing him, he's likely upset that nobody else remembers linear algebra and portfolio theory.

### Video

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

Demeaned returns definition for investment modeling (4:17)

### Video Script

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

#### Visualize

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

The best way to visualize demeaned returns is to walk thorugh the four primary risk measures.

First, let's look at the calculation of variance and standard deviation, and at the end of the video there is a link so you can see this in detail. The demeaned returns for two stocks Microsoft and eBay sit in columns J and K.

In the second table, for covariance and correlation, J and K are identical.

#### Demonstrate

Let's walk through a calculation for two stocks, Microsoft and eBay. We have six monthly returns 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 for each, here 2.38% for Microsoft and 3.98% for eBay. Then move those over to columns H and I. In column J take the return minus the 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 demeaned returns on each stock.

Next, in column L, multiply these together and follow through by adding the products, dividing by the number of observations to arrive at variance. Standard deviation is the square root of variance.

Again, in the second table, up to columns J and K, the calculations are the same. And because covariance and correlation refer to the co-movements between a pair of stocks, multiply them together this time. Follow through by adding the products, dividing by the number of observations to arrive at covariance. Then divide by the product of the two standard deviations to get correlation.

So, you can see the importance of demeaned returns. Once you have them you can quickly calculate four important risk measures.

Also, we used 6 periods here to keep it simple, but you can see how important the mean, in demeaned returns, is to the final calculations. This illustrates the importance of selecting a long enough period of say 30, 60 or more periods that you feel represent the data.

### Quiz

The demeaned returns for XYZ stock times demeaned returns for ABC stock is the first step in calculating variance. | True or False?

False, covariance.

Because the calculation of demeaned returns uses the average, it is subject to bias from outliers. | True or False?

True. An outlier has more impact on the mean than the median.

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

### Related Terms

Our trained humans found other terms in the category statistics for finance you may find helpful.

## What's Next?

• To see all terms in the Glossary, click Outline.
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/ factorpad.com / fin / glossary / demeaned-returns.html

demeaned returns
subtract mean
covariance calculation
variance calculation
standard deviation calculation
correlation calculation
stock standard deviation
portfolio standard deviation
stock returns
portfolio returns
portfolio statistics
portfolio math
stock variance
portfolio variance
return minus average

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