# What Is Portfolio Volatility? i Hemera Technologies/AbleStock.com/Getty Images

Volatility is a formal measure of a stock's risks. The higher the volatility of a stock, the greater its up and down swings. The volatility of a portfolio of stocks, on the other hand, is a measure of how wildly the total value of all the stocks in that portfolio appreciates or declines. Understanding the concept of portfolio volatility can be the difference between a safe growth path for your money and many sleepless nights.

## Stock Risk

Say you're comparing stocks A and B, both of which have advanced an average of half a percent per month over the last two years. Does that mean both carry the same level of risk? Absolutely not. Stock A might have always advanced between 0.3 and 0.7 percent every month, never registering a monthly loss, for an average of half a percent return per month. B, on the other hand, might have advanced by more than 30 percent per month on several occasions, while losing more than 35 percent of its value several times as well, yet it might also register a half percent monthly return on average. The true measure of risk is how much returns tend to deviate from the average return.

## Standard Deviation

Statisticians calculate something called standard deviation to measure how stable a variable has been over time. Financial experts use standard deviation of a stock's past return as a measure of its risk. The formula for standard deviation is relatively detailed, and calculating the standard deviation of a stock's monthly return over several years is a laborious process. However, plugging the monthly returns into a spreadsheet application makes the calculation a breeze. When looking at standard deviation of a stock's past returns, keep in mind that the higher the figure, the more spread out the returns. This means the stock had many months of very good and very bad returns and is a high risk, high return investment.

## Correlation

If you have \$5,000 worth of stock A and \$5,000 of B, in your portfolio and they return 4 and 6 percent, respectively, this portfolio of stocks will have returned 5 percent, which is the average of 4 and 6 percent. However, if the standard deviation, of the stocks are 4 and 6 percent, you cannot average the stock's standard deviations to find the portfolio's standard deviation. Before you can combine the standard deviations of the stocks in your portfolio to arrive at the portfolio's standard deviation, you have to understand whether these stocks tend to move up and down together -- or in financial lingo, how correlated the stocks are. If both stocks are issued by oil firms, they will tend to go up and down together as oil prices fluctuate. Such stocks have a high correlation.

## Portfolio Risk

The main idea behind investing in a portfolio of stocks is to reduce risk. However, it is not only the number of shares in your portfolio but also their correlation to each other that determines the portfolio's total risk. High correlation results in high total risk, because the stocks in your portfolio will have a higher chance of declining all at once. Shares of firms in unrelated fields have low correlation. A portfolio of such stocks has lower total risk, which makes intuitive sense. After all, the stocks of oil drillers, automakers and food manufacturers are rarely hit all at once, save for a huge economic downturn in the country. With the use of a spreadsheet, you can also calculate the correlation between stocks in your portfolio and the resulting total risk.