# Semivariance and Semideviation

Discover the significance of semivariance and semideviation in finance and investment risk management. Learn how these statistical measures offer insights into downside risk, aiding investors in making informed decisions.

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## What is Semivariance?

Semivariance is a statistical measure that focuses on the downside risk of an investment. Unlike variance, which takes into account all deviations from the mean, semivariance only considers the deviations that are below the mean. In other words, it measures the dispersion of returns below a certain threshold.

By focusing on the negative deviations, semivariance provides a more accurate representation of the downside risk associated with an investment. It helps investors understand the potential losses they may incur and allows them to make more informed decisions.

## Calculating Semivariance

To calculate semivariance, you first need to determine the threshold or target return. This can be a specific rate of return that you consider as the minimum acceptable return. Once you have the target return, you calculate the squared deviations of all returns that are below the target return. Finally, you take the average of these squared deviations to obtain the semivariance.

Mathematically, the formula for semivariance can be expressed as:

Semivariance = (1/n) * Σ(Ri - T)^2

Where:

• n is the number of observations

• Ri is the individual return

• T is the target return

## What is Semideviation?

Semideviation is another measure that focuses on the downside risk of an investment. However, unlike semivariance, which considers the dispersion of returns below a threshold, semideviation focuses on the dispersion of returns below the mean return.

By only considering the negative deviations from the mean, semideviation provides a clearer picture of the potential downside risk associated with an investment. It helps investors assess the volatility and stability of an investment by focusing on the negative fluctuations.

## Calculating Semideviation

Calculating semideviation is similar to calculating semivariance. You first need to determine the mean return of the investment. Then, you calculate the squared deviations of all returns that are below the mean. Finally, you take the square root of the average of these squared deviations to obtain the semideviation.

Mathematically, the formula for semideviation can be expressed as:

Semideviation = sqrt((1/n) * Σ(Ri - M)^2)

Where:

• n is the number of observations

• Ri is the individual return

• M is the mean return