# How to Compute Portfolio Standard Deviations

by Josh Victor ; Updated July 27, 2017Portfolio standard deviation is an important part of understanding volatility and risk. It allows an investor to understand how vulnerable he is to risk, because the standard deviation implies the possibility of dramatic changes in prices. You can compute your own portfolio standard deviation using a few simple steps.

Calculate all your returns based on the calendar date. Analyze in parallel with the time frame that you would like to invest in. For example, if you are trying to calculate on a basis of the next 10 years, use at least the previous 10 years as your base for comparison.

Record all of your returns by period, which could be a year, quarter or month depending on your level of analysis. Neatly place all of the returns next to their periods. Calculate the average for all of these returns by adding up the return values and then dividing the sum by the number of periods taken. For example:

Three yearly returns = 8 percent, 10 percent, 12 percent Average return = Sum of yearly returns/number of years = 30/3 = 10 percent

Calculate the difference between the average return and the return for each of the three years. Square each of the three results. Find the sum of these three numbers. This operation is done in the following way:

Sum of square differences = (10-8)^2+(10-10)^2+(12-10)^2=8

Divide the sum of squared deviations by the number of periods minus one.

Sum of squares /(Periods - 1) 8/ (3-1) = 4

Take the square root of that answer to get your portfolio standard deviation.

Square root of 4 = 2

The standard deviation in this example is 2 percent, which is the typical amount that a year's returns will stray from the mean. This is pretty simple in the given example, but can become more complex with more numbers and volatility.

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