# Using Standard Deviation With Mutual Funds

## Learn How to Use Standard Deviation With Mutual Funds

If you've done extensive research when analyzing mutual funds, you may have run across a statistical analysis term called standard deviation. The term many sound complex and perhaps beyond the comprehension of anyone other than a math major but using standard deviation with mutual funds can be simple and useful.

### Standard Deviation Definition - Mutual Funds

Standard deviation is a statistical measurement that shows how much variation there is from the arithmetic mean (simple average).

Investors describe standard deviation as the volatility of past mutual fund returns.

In simple terms, a greater standard deviation indicates higher volatility, which means the mutual fund's performance fluctuated high above the average but also significantly below it. Therefore many investors use the terms volatility and standard deviation interchangeably.

### Standard Deviation Example With Mutual Funds

If XYZ mutual fund has an average annual return (mean) of 8% and a **standard deviation** of 3%, then an investor may expect the return of the fund to be between 5% and 11% 68% of the time (one standard deviation from the mean -- 8% - 3% and 8% + 3%) and between 2% and 14% 95% of the time (two standard deviations from the mean -- 8% - 6% and 8% + 6%).

But keep in mind that standard deviation is most useful when analyzing the past performance of one mutual fund in isolation. Investors holding several mutual funds cannot take the average standard deviation of their portfolio in order to calculate their portfolio’s expected volatility.

In order to find the standard deviation of a multiple-asset portfolio, an investor would need to account for each fund’s correlation, as well as the standard deviation. In other words, volatility (standard deviation) of a portfolio is a function of how each fund in the portfolio moves in relation to each other fund in the portfolio.

### Should You Use Standard Deviation When Analyzing Mutual Funds?

Standard deviation of historical mutual fund performance is used by investors in an attempt to predict a range of returns for various mutual funds. Although its usefulness in measuring volatility of past performance can provide an indicator of future volatility, and can therefore help an investor prevent the mistake of buying a mutual fund that is too aggressive, the volatility of a single mutual fund is not necessarily a concern in portfolio construction.

In fact, funds that have had past periods of extreme volatility can be complimentary to other funds in the portfolio that help balance the fluctuations of the aggressive fund. If the long-term returns are high enough to justify the short-term fluctuations, and the investor understands and accepts the risk, volatile funds can provide a valuable purpose.

Here are links to the key statistical measures of mutual funds: Beta, R-squared, Alpha, Sharpe Ratio, Expense Ratio, and Tax Cost Ratio.