 Standard deviation and variance are used as risk metrics for investors. iStock by Getty

# How Are Standard Deviation and Variance Used in Investing? Masterworks
November 4, 2022

Standard deviation and variance are both measures of data variability. When it comes to investing, it’s used to identify the risk level of an asset’s returns.

## What is Standard Deviation?

The term “standard deviation” (or standard error) is used in many areas of statistics and occasionally involves some complex math. In personal finance, standard deviation is a volatility metric.

In math terms, standard deviation measures the dispersion of a dataset relative to its mean (average) and is calculated as the square root of the variance.

If data points are more spread out, there is a high standard deviation, while condensed data points have a low standard deviation.

For investors, the standard deviation essentially shows how much investment returns tend to deviate from a particular set of historical data. That data is measured either against itself or as compared to an average or benchmark.

In a normal distribution, standard deviation tells you how far values are from the mean.

### Standard Deviation Formula

Standard deviation is calculated by taking the square root of variance, which ends up being a pretty complex calculation. = population of standard deviation = the size of the population = each value from the population = the population mean

Don’t worry, you won’t have to hand-calculate this formula. There are numerous online calculators investors can use for free. Excel can also calculate standard deviation by using the STDEV.S or STDEVA formula.

Standard deviation generally follows a statistical rule, known as the empirical rule of the 68-95-99.7 rule. For investing, this rule means that:

• 68% of the time: returns fall within one standard deviation.
• 95% of the time: returns fall within two standard deviations.
• 99.7% of the time: returns fall within three standard deviations.

It is graphically depicted as a bell curve’s width around the mean of a data set. The wider the curve’s width, the larger the standard deviation.

## How is Standard Deviation Used in Investing?

Standard deviation in investing works by measuring how often stock prices tend to stray from the average. Investors use it as a tool to measure market volatility and predict performance trends.

An asset with a standard deviation of zero would provide the same annual returns without varying. However, this will never happen in the real world. Every asset has a historical range of returns.

Volatility varies between asset classes. For example, an index mutual fund likely has a low standard deviation compared to its benchmark index because the fund’s goal is to track and mimic the index’s rate of return.

On the other hand, higher standard deviations are typically found for aggressive growth funds compared to a relative stock index because the fund’s purpose is to generate higher-than-average returns. They do so by making aggressive bets.

In simple terms, investors use standard deviation to measure risk. Lower standard deviation is not always preferable, it instead depends on the individual investor’s risk tolerance.

## Limitations of Standard Deviation

There are some limitations when it comes to standard deviation as a risk metric. At its core, it doesn’t actually measure how far a data point is from the mean. Instead, it compares the square of the differences, a subtle but important difference from the actual dispersion from the mean.

Outliers have a heavy impact on standard deviation, especially considering the difference from the mean is squared, resulting in an even larger quantity compared to other data points. Just be mindful that standard observation gives more weight to extreme values.

Lastly, standard deviation can be difficult to manually calculate. As opposed to other measurements of dispersion such as range (the highest value – the lowest value), standard deviation requires several complex steps and is more likely to have computational errors compared to simpler measurements.

## What is Variance?

The term variance refers to a statistical measurement of the spread between numbers in a data set. More specifically, variance measures how far each number in the set is from the mean (average), and thus from every other number in the set.

Variance is used by investors and financial analysts to determine volatility.

The square root of the variance is the standard deviation, which helps determine the consistency of an investment’s returns over a period of time.

## How is Variance Used in Investing?

Investors use variance to assess the risk or volatility associated with assets by comparing their performance within a portfolio to the mean. For instance, you can use the variance in your portfolio to measure the returns of your stocks and ensure proper diversification across assets with varying volatilities.

This is done by calculating the standard deviation of individual assets within your portfolio as well as the correlation of the securities you hold.

## Understanding Risk Metrics

Investment risk is the possibility that actual returns might differ from expected returns.

In fact, actual returns will almost always differ from expected returns, but understanding how likely that variance is and how much that variance may be is helpful to understanding risk levels.

These two metrics are commonly used by traders and investors to measure stability and volatility, which play a large role in generating positive returns.

Standard deviation is one of the key metrics that analysts, portfolio managers and financial advisors use to determine risk. When a number of data points are closer to the mean, the investment is less risky because returns have had less variability.

Securities valued close to their means are seen as less risky, as they are more likely to continue behaving that way. Securities with large trading ranges, tending to have high highs and low lows, are riskier.

## Bottom Line

Both standard deviation and variance are used by investors as measures of risk. Actively monitoring a portfolio’s standard deviations and making adjustments allows investors to tailor their investments to their personal risk tolerance.

While both metrics are used as fundamental risk measurements, remember that they are not guarantees of future performance. Masterworks is a fintech company democratizing the art market. Our investors are able to fractionally invest in \$1mn+ works of art by some of the world's most famous and sought-after artists.