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
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.
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Variance definition for investment modeling (4:22)
The script includes two sections where we visualize and demonstrate the calculation of demeaned returns.
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.
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
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
or take the variance to the one-half power, as I have done here.
Click box for answer.
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