# How to Find the Risk of Portfolio Volatility Determining the risk of a portfolio of individual securities is not a matter of simple math. Brand X Pictures/Brand X Pictures/Getty Images

Volatility is a measurement of risk. An investor can use volatility calculations, such as standard deviation, to find and quantify the risk of a given investment. Determining the volatility and, therefore, the risk of a portfolio of securities is no more difficult when the securities have been conglomerated in a pool, such as a mutual fund. Determining the risk of a portfolio of individual securities, however, is difficult. For most individual investors, finding the risk of individual investments, then combining them in ways that reduce risk in principle, approximates the result of a portfolio risk calculation.

## Defining Volatility

Volatility is the relative rate of change in price of an equity. Relative volatility is generally accepted by economists as an indication of relative risk. Volatility is most usefully measured over some extended period. It's also useful to compare the volatility of a portfolio to a benchmark. Relatively high volatility of a portfolio that's less than the volatility of a benchmark suggests lower risk than low volatility of a portfolio that exceeds the benchmark's volatility.

## Standard Deviation

One means of finding risk is to calculate its standard deviation, a statistical measurement of volatility. It is often computed using 36 consecutive monthly returns. The resulting number expresses the extent to which individual monthly returns deviate from the average return over the 36-month period. Several calculators, including some available online, perform the calculation from your inputs and output the result. A portfolio with a standard deviation of less than 10 percent is considered low risk.

## Comparative Standard Deviation

Because the standard deviation isn't relative to a benchmark, it may be misleading. A comparison of the portfolio's standard deviation with the benchmark gives you a better understanding of its significance. Online and hand-held calculators provide this comparison and express it as a percentage above or below the benchmark. Alternatively, you can calculate standard deviations for both the portfolio and a benchmark, then divide the portfolio's standard deviation by the benchmark's.

## Portfolio Risk

Although calculating the standard deviation of a portfolio of individual securities is difficult, modern portfolio theory, a field of economics, indicates that, in general, the risk of a portfolio of securities will be lower than the risk of the individual securities within it, provided that the portfolio is diversified -- it has a variety of assets -- and that the securities have low or negative covariance -- that is, they have unrelated price movements. For instance, a two-security portfolio of one stock and one bond has greater diversity than its elements -- two elements, rather than one -- and low covariance, because bond prices and stock prices generally do not track one another. Because the securities' prices move independently, the odds are great that they will not move in the same direction at the same time, with the result that the portfolio's volatility, and hence its risk, is lessened.