How is standard deviation used to determine risk?

In many sectors of the finance industry, risk measurement is a primary focus. While it can play a role in economics and accounting, the impact of accurate or faulty risk measurement is most clearly illustrated in the investment sector. Whether investing in stocks, options or mutual funds, knowing the probability that a security moves in an unexpected way can be the difference between a well-placed trade and bankruptcy. Traders and analysts use a number of metrics to assess the volatility and relative risk of potential investments, but the most common metric is standard deviation.

Standard deviation is a basic mathematical concept that carries a lot of weight. Simply put, standard deviation measures the average amount by which individual data points differ from the mean. It is calculated by first subtracting the mean from each value, and then squaring, summing and averaging the differences to produce the variance. While variance itself is a useful indicator of range and volatility, the squaring of the individual differences means they are no longer reported in the same unit of measurement as the original data set.

In the case of stock prices, the original data is in dollars and variance is in dollars squared, which is not a useful unit of measure. Standard deviation is simply the square root of the variance, bringing it back to the original unit of measure and making it much simpler to use and interpret.

In investing, standard deviation is used as an indicator of market volatility and therefore of risk. The more unpredictable the price action and the wider the range, the greater the risk. Range-bound securities, or those that do not stray far from their means, are not considered a great risk because it can be assumed with relative certainty that they continue to behave in the same way. A security that has a very large trading range and tends to spike, reverse suddenly or gap, is much riskier. However, risk is not necessarily bad. The riskier the security, the greater potential for payout as well as loss.

When using standard deviation to measure risk in the stock market, the underlying assumption is that the majority of price activity follows the pattern of a normal distribution. In a normal distribution, individual values fall within one standard deviation of the mean, above or below, 68 percent of the time. Values are within two standard deviations 95 percent of the time.

For example, in a stock with a mean price of $45 and a standard deviation of $5, it can be assumed with 95 percent certainty that the next closing price remains between $35 and $55. However, price plummets or spikes outside of this range 5 percent of the time. A stock with high volatility generally has a high standard deviation, while the deviation of a stable blue-chip stock is usually rather low.

The more volatile a security, the larger the variance and standard deviation. While investors can assume that price remains within two standard deviations of the mean 95 percent of the time, this can still be a very large range. As with anything else, the greater the number of possible outcomes, the greater the risk of choosing the wrong one.