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# What is Standard Deviation of Return?

Standard Deviation (SD) is a technique of statistics that represents the risk or volatility in investment. It gives a fair picture of the fund's return. It tells how much data can deviate from the historical mean return of the investment.

The higher the Standard Deviation, the higher will be the ups and downs in the returns. For example, for a fund with a 15 percent average rate of return and an SD of 5 percent, the return will deviate in the range from 10-20 percent.

**Note** − In SD, the ends of volatility are determined by adding and subtracting the average return from two ends

It is easy to derive standard deviation on a mutual fund −

Just add up the return rates for a given period of measure and then divide the result by the grand total number of used, rate data points to find the average return.

Next, subtract your average individual data point from the average return to find the difference between reality and the average. Find the square root of each one of these numbers and then add them again.

Finally, divide the result by the total number of data points minus one – that is if you have 10 data points, you’ll divide by 9. The SD is the square root of that number.

## More about Standard Deviation

To calculate the norm of the returns to get the information about how dispersed the returns are, the SD is calculated as the square root of the variance of the returns. This shows the average return by which the returns over a particular period deviate from the average return.

The higher the value of the standard deviation of returns, the higher will be the volatility of returns. High volatility means that high risk was apparent during the investment period.

For a fund that has an average return of 7.5% and returns in its subperiods were 13%, 11%, 2%, 6%, 5%, 8%, the SD will be −

$$\mathrm{SD = \sigma =\sqrt{\frac{\sum_{\substack{i=1}}^{n}(Return − Avg.Daily\:\%\:Return)^2}{No.\:of\:Return \:Periods − 1}} }$$

$$\mathrm{\sqrt{\frac{(13 − 7.5)^2 + (11 − 7.5)^2 + (6 − 7.5)^2 + (5 − 7.5)^2 + (8 − 7.5)^2}{6 − 1}}}$$

$$\mathrm{\sqrt{\frac{81.66}{5}}= 4.04\%}$$

Standard Deviation indicates the dispersion of returns or how much the returns deviate relative to the average return, and the usual normal range of returns expected. So, with an average return of 7.5% and a SD of 4.04%, the expected range of returns will be between 3.46% (7.5% - 4.04%) and 11.54% (7.5% + 4.04%).

**Note** − SD informs us about the dispersion of returns or how much the returns deviate relative to the average return.

## Considerations

Standard deviation is a measure of the dispersion and/or variation in data. It tells us how to spread out the returns around their mean. To calculate SD, subtract each value in a data set from its mean, squaring the value, average all squared values, and finally take the square root of the average.

When studying the volatility of investment returns, investors are particularly interested in two uses of standard deviation −

Comparing the measure of the or dispersion, variation in data

Determining the future range returns for an investment

Therefore, although SD is a statistical tool, it has widespread use in financial management too.

**Note** − Standard deviation is a measure of the dispersion, and/or variation in data. It tells us how to spread out the returns around their mean.

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