# Semivariance: Meaning, Formulas, and Calculations

## What Is a Semivariance?

Semivariance is a measurement of data that can be used to estimate the potential downside risk of an investment portfolio. Semivariance is calculated by measuring the dispersion of all observations that fall below the mean or target value of a set of data. Semivariance is an average of the squared deviations of values that are less than the mean.

### Key Takeaways

• The semivariance formula can be used to measure a portfolio's downside risk.
• Semivariance only considers observations that are below the mean of a data set.
• Spreadsheet programs can be useful in calculating semivariance for your portfolio.

## Understanding Semivariance

### The Formula for Semivariance Is

﻿ \begin{aligned} &\text{Semivariance}=\frac1n\times\sum^n_{r_t<\text{Average}}(\text{Average}-r_t)^2\\ &\textbf{where:}\\ &n = \text{The total number of observations below the mean}\\ &r_t = \text{The observed value}\\ &\text{Average} = \text{The mean or target value of the dataset} \end{aligned}﻿

### What Does Semivariance Tell You?

Semivariance is similar to variance, but it only considers observations that are below the mean. Semivariance is a useful tool in portfolio or asset analysis because it provides a measure for downside risk.

While standard deviation and variance provide measures of volatility, semivariance only looks at the negative fluctuations of an asset. Semivariance can be used to calculate the average loss that a portfolio could incur because it neutralizes all values above the mean, or above an investor's target return.

For risk-averse investors, determining optimal portfolio allocations by minimizing semivariance could reduce the likelihood of a large decline in the portfolio's value.

To use a spreadsheet program to calculate semivariance:

• Create a column—for example, column A—that consists of all returns in the portfolio.
• Remove all returns above the mean from column A.
• In column B, subtract the returns remaining in column A from the mean.
• In column C, square the difference, find the sum, and divide the sum by the number of returns that fall below the mean.

Different spreadsheets may have different functionality and some have easier ways or shortcuts to do this calculation.

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