How Is Standard Deviation Used to Determine Risk?

Risk measurement is a very big component of the finance industry. While it plays a role in economics and accounting, the impact of accurate or faulty risk measurement is most clearly illustrated in the investment sector.

Knowing the probability that a security—whether you invest in stocks, options, or mutual funds—moves in an unexpected way can mean the difference between a well-placed trade and a total loss. Traders and analysts use a number of metrics to assess the volatility and relative risk of potential investments, but one of the most common is standard deviation.

Read on to find out more about standard deviation, and how it helps determine risk in the investment industry.

Key Takeaways

• One of the most common methods of determining the risk an investment poses is standard deviation.
• Standard deviation helps determine market volatility or the spread of asset prices from their average price.
• When prices move wildly, the standard deviation is high, meaning an investment is more risky.
• Low standard deviation means prices are more stable, so investments come with less risk.

What Is Standard Deviation?

Standard deviation is a basic mathematical concept that measures market volatility or the average amount by which individual data points differ from the mean. Simply put, standard deviation helps determine the spread of asset prices from their average price.

When prices swing up or down significantly, the standard deviation is high, meaning there is high volatility. On the other hand, when there is a narrow spread between trading ranges, the standard deviation is low, meaning volatility is low.

While standard deviation is an important measure of investment risk, it is not the only one. Investors can use many other measures, such as beta or Sharpe ratio, to determine whether an asset is too risky for them or not risky enough.

Important

The higher the standard deviation, the riskier the investment.

Calculating Standard Deviation

Standard deviation is calculated by first subtracting the mean from each value, and then squaring, adding, and averaging the differences to produce the variance.

Variance is itself a useful indicator of range and volatility, but squaring the individual differences means that they can be reported as a standardized unit of measurement and not in the units found in the original data set. This allows for apples-to-apples comparisons across different objects of study.

For 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.

The formula is:

$begin{aligned} &text{Standard Deviation} = sqrt{ frac{sum_{i=1}^{n}left(x_i – overline{x}right)^2} {n-1} }\ &textbf{where:}\ &x_i = text{Value of the } i^{th} text{ point in the data set}\ &overline{x}= text{The mean value of the data set}\ &n = text{The number of data points in the data set} end{aligned}$

​Standard Deviation=n−1∑i=1n​(xi​−x)2​​where:xi​=Value of the ith point in the data setx=The mean value of the data setn=The number of data points in the data set​

Standard deviation is calculated as follows:

1. Calculate the mean of all data points. The mean is calculated by adding all the data points and dividing them by the number of data points.
2. Calculate the variance for each data point. The variance for each data point is calculated by subtracting the mean from the value of the data point.
3. Square the variance of each data point (from Step 2).
4. Sum of squared variance values (from Step 3).
5. Divide the sum of squared variance values (from Step 4) by the number of data points in the data set less 1.
6. Take the square root of the quotient (from Step 5).

Note

Because investors are most often concerned with only losses when prices fall as a measure of risk, the downside deviation is sometimes employed, which only looks at the negative half of the distribution.

Relating Standard Deviation to Risk

In investing, standard deviation is used as an indicator of market volatility and thus 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. That’s because it can be assumed—with relative certainty—that they continue to behave in the same way. A security with a very large trading range and a tendency to spike, reverse suddenly, or gap is much riskier, which can mean a larger loss.

But remember, risk is not necessarily a bad thing in the investment world. The riskier the security, the greater potential it has for payout.

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% of the time. Values are within two standard deviations 95% 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% certainty the next closing price remains between $35 and $55. However, price plummets or spikes outside of this range 5% 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 fairly low.

So what can we determine from this? The smaller the standard deviation, the less risky an investment will be, dollar-for-dollar. On the other hand, the larger the variance and standard deviation, the more volatile a security. While investors can assume price remains within two standard deviations of the mean 95% 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.

How Are Standard Deviation and Variance Related?

The standard deviation is the square root of the variance. By taking the square root, the units involved in the data drop out, effectively standardizing the spread between figures in a data set around its mean. As a result, you can better compare different types of data using different units in standard deviation terms.

What Does the Standard Deviation of an Investment Measure?

Standard deviation is used as a proxy for risk, as it measures the range of an investment’s performance. The greater the standard deviation, the greater the investment’s volatility.

How Is Standard Deviation Related to the Sharpe Ratio?

The Sharpe Ratio computes an investment’s risk-adjusted performance. It does this by dividing an investment’s excess returns by its standard deviation.

The Bottom Line

Standard deviation is a key metric for understanding the risk of an investment or portfolio. The higher the standard deviation, the greater the volatility, which also means more risk. Pairing standard deviation with other metrics can help you investment performance and market risk.