# Investment and Standard Deviation

By: Hunkar Ozyasar Standard deviation is an invaluabe tool for risk analysis. Duncan Smith/Photodisc/Getty Images

Standard deviation is a statistical concept with wide-ranging applications in the world of finance. Whether you are investing in stocks, bonds or valuable metals, standard deviation will help you assess the possible outcomes and be better prepared for what may go wrong. Although the mathematical formula for standard deviation is somewhat complex, the basic idea is straightforward.

## Standard Deviation

Standard deviation measures how much a variable tends to vary. Variables that are stable with small and infrequent fluctuations have low standard deviation. Variables that move wildly, either up or down, have high standard deviation. For example, the number of umbrellas sold in a convenience store will depend on weather and exhibit a large standard deviation. The amount of milk sold, however, will likely vary less and be more stable from day to day. The standard deviation of milk sales will therefore be smaller than the standard deviation of umbrella sales.

## Mathematical Formula

Spreadsheet programs, such as Microsoft's Excel, will automatically calculate standard deviation with a few keystrokes. However, understanding the formulation helps you make intuitive sense of standard deviation. First, you average all the values of the variable at hand. Next, you subtract the average from each value and obtain the difference between individual observations and the average, also known as the mean. You then square these differences and add up the resulting squares. Finally, you divide this sum by the number of values and calculate the square root of the result, which equals the standard deviation. The greater the deviation of each value from the average, the higher the standard deviation.

## Applications to Investing

The standard deviation of profits from an investment is an excellent measure of the risks involved. The higher the standard variation of the daily gains in a stock, the more wildly it tends to swing and the higher the risk. The advantage of standard deviation is that it allows you to compare the risks in investment alternatives that are trading in different markets with vastly different prices. By using standard deviation, for example, you can assess whether a bond selling for \$1,200 is more or less risky than a stock trading at \$10. Even investments in different currencies can be compared by using their standard deviations.

## High vs Low Standard Deviations

Investors generally prefer investment vehicles with low historic standard deviations. Such instruments have a history of mild price swings and are therefore less likely to decline sharply and suddenly in the future. This does not mean, however, that all investors like instruments with low standard deviation. A trader may purposely seek volatile stocks that have recently been beaten down in hopes that they're due for a sharp upswing. High standard deviation implies big swings on the upside and the downside. Even prudent investors may rationally invest a small portion of their holdings in such financial assets, especially if they have recently realized significant profits and the losses would, at worst, merely wipe out some of the recent gains.