Download Standard Deviation - What is it and what you need to calculate it

Standard Deviation: What it is and What You Need to Calculate it
The Standard Deviation of monthly returns shows the degree to which the returns have fluctuated over a given
time period. When evaluating returns, the standard deviation is compared to the standard deviation on the
appropriate market index to determine how volatile the portfolio return is compared to the index return. A higher
standard deviation usually indicates a higher level of risk. The calculations are displayed and explained below.
Where:

Ri = return in the ith time period

MEAN(R) = average of all period returns in the study

n =number of periods in the study
Interpreting the formula:
1
Calculate the Mean by totaling all the observations (portfolio or asset class returns) and dividing by the
number of observations.
2
Take each observation (portfolio or asset class return), subtract the result from step 1, and then square that
number.
3
Total the results of step 2.
4
Divide the result of step 3 by the number of observations.
5
Take the square root of the result of step 4.
6
Multiply the result of step 5 by the square root of 12 to annualize it. This is the standard deviation.
DocumentID: spt010507
Last Updated: March 4, 2011
Information Needed for Standard Deviation Calculation

A minimum of 12 monthly or quarterly intervals for the portfolio or asset class.
Important
All intervals must be the same length. For example, 12 monthly intervals or 12 quarterly intervals, but
not 6 monthly intervals and 6 quarterly intervals. However, 6 quarterly intervals and 18 monthly can be
used. By combining the 18 monthly intervals to create 6 quarterly intervals, you have a total of 12
quarterly intervals.
On the Web
Need help troubleshooting this number? See Troubleshooting an Incorrect Standard Deviation.
Standard Deviation: What it is and What You Need to Calculate it
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