Standard Deviation

What is Standard Deviation?

In simple terms, Standard Deviation (SD) is a statistical measure representing the volatility or risk in an instrument. It tells you how much the fund's return can deviate from the historical mean return of the scheme. The higher the SD, higher will be the fluctuations in the returns.

If a fund has a 12 percent average rate of return and a standard deviation of 4 percent, its return will range from 8-16 percent.

How to Calculate Standard Deviation?

To find standard deviation on a mutual fund, add up the rates of return for the period you want to measure and divide by the total number of rate data points to find the average return. Further, take each individual data point and subtract your average to find the difference between reality and the average. Square each of these numbers and then add them up.

Divide the resulting sum by the total number of data points less one -- if you have 12 data points, you divide by 11. The standard deviation is the square root of that number.

Let's understand better with illustration-

1. Find the Standard Deviation of both stocks

Let's find the SD of two different Mutual Funds. First, we will calculate their average return for the last five years.

Mutual Fund A: (11.53% + 0.75% + 12.75% + 32.67% + 15.77%)/5 = 14.69%

Mutual Fund B: (4.13% + 3.86% + {-0.32%} + 11.27% + 21.63%)/5= 9.71%

2. Calculate the variance of each stock

Since Standard Deviation is the square root of variance, we must first find the variance of each investment.

Then, you divide the sum of the squares from the first step by the 1 less the number of years (∑/n-1).

Mutual Fund A: (11.53%-14.69%)² + (0.75%-14.69%)² + (12.75%-14.69%)² + (32.67%-14.69%)² + (15.77%-14.69%)²= 0.052/4=.013

Mutual Fund B: (4.13%-9.71%)² + (3.85%-9.71%)² + (-0.32%-9.71%)² + (11.27%-9.71%)² + (21.63%-9.71%)²= 0.032/4=.008

3. Find the Standard Deviation for each

Mutual Fund A: √.013= 11.4%

Mutual Fund B: √.008= 8.94%

4. Standard Deviation in Excel

Excel offers the following functions:

STDEV.P to calculate standard deviation based on the entire population

STDEV.S to estimate standard deviation based on the sample

Using the functions one can determine the SD of the fund.

Example of Standard Deviation in Mutual Funds