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Intermediate
Standard Deviation is a measure of dispersion within a set of data. It is likely the best-understood measure of risk in Finance for stock and investment volatility.
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
For context, while there are many measures of risk that capture risk of downside risk only (semi-deviation), risk relative to a benchmark (beta) or risk of loss relative to an asset's peak (drawdown), standard deviation is the most widely used and understood.
With respect to investments, the fact that much of Modern Portfolio Theory was built around variance as the main measure of risk, and given that standard deviation is its interpretable companion, it will likely continue as the main measure used by investment analysts.
The popular Sharpe Ratio measure utilizes standard deviation in the denominator and provides a return-per-unit-of-risk for a portfolio or individual investment.
Doc: Please understand how to calculate
standard deviation by hand.
Leo: May we have a phone in that hand?
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)
The script includes two sections where we visualize and demonstrate the concept of standard deviation.
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.
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.
Click box for answer.
False. The first part is true, but roughly two-thirds of observations fall within +/- 1 standard deviations.
True
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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