How Is Standard Deviation Used to Determine Risk?

Risk measurement is a very big component of many sectors 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 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 one of the most common metric 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, standard deviation is high, meaning an investment will be risky.
  • Low standard deviation means prices are calm, so investments come with low risk.

Standard Deviation

What Is Standard Deviation?

Standard deviation is a basic mathematical concept that measures volatility in the market 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. What can we determine by this? Volatile prices mean standard deviation is high, and it is low when prices are relatively calm and not subject to wild swings.

While standard deviation is an important measure of investment risk, it is not the only one. There are many other measures investors can use to determine whether an asset is too risky for them—or not risky enough.

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.

This is the formula for the sample standard deviation.
This is the formula for the sample standard deviation, which is used when data is drawn from a larger set. It takes the degrees of freedom into account, using what is known as Bessel's correction. public domain

The formula for the SD requires a few steps:

  1. First, take the square of the difference between each data point and the sample mean, finding the sum of those values.
  2. Next, divide that sum by the sample size minus one, which is the variance.
  3. Finally, take the square root of the variance to get the SD.

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.

The higher the standard deviation, the riskier the investment.

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.

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.

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.

What Is the Standard Deviation of the S&P 500 Index?

The standard deviation will depend on the time period you look at. As of Q1 2022, the 3-year standard deviation of the S&P 500 index is around 18. The 10-year standard deviation of the index is closer to 13.

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.

Article Sources
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  2. Marshall, Cara M. "Isolating the systematic and unsystematic components of a single stock’s (or portfolio’s) standard deviation." Applied Economics, Vol. 47, No. 1. 2015, Pages 1-11.

  3. Jaaman, Saiful Hafizeh HJ, Weng Hoe Lam, and Zaidi Isa. "Different downside risk approaches in portfolio optimisation." Journal of Quality Measurement and Analysis, Vol. 7, No. 1, 2011, Pages 77-84.

  4. Morningstar. "SPX: Risk."

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