Variance is a widely used metric for determining risk. Investors calculate the variance of an expected return to determine the relative risk of various investment scenarios. Project managers calculate variance to determine if a project is over budget or behind schedule. There are three commonly accepted ways of calculating variance.

## Variance Based on Historical Data

Calculate the average of the data set by dividing the sum of the data set by the number of data points. In this example, there are three data points: n1, n2 and n3:

avg = (n1 + n2 + n3) / (3)

Calculate the difference between each data point and the average of the data set:

diff 1 = (n1 - avg) diff 2 = (n2 - avg) diff 3 = (n3 - avg)

Square each difference and add up the squared differences:

[(n1 - avg) ^2] + [(n2 - avg)^2] + [(n3 - avg)^2]

Divide the sum of the squared differences by the number of data in the set minus 1:

[(n1 - avg) ^2] + [(n2 - avg)^2] + [(n3 - avg)^2] / (3-1)

## Variance Based on Variance-Covariance

Use Excel's Covariance function to calculate the covariance.

Calculate the risk that occurs 5 percent of the time by multiplying the standard deviation by 1.65.

Calculate the risk that occurs 5 percent of the time by multiplying the standard deviation by 1.65.

Calculate the risk that occurs 1 percent of the time by multiplying the standard deviation by 2.33.

## Variance Based on Monte Carlo Method

Select a statistical distribution to approximate the factors that affect your data set. For example, if you are calculating the risk variance of a proposed investment scenario, choose a distribution that matches observed performance of past investments.

Use a computer program to generate between 1,000 and 10,000 random numbers from the statistical distribution you selected.

Graph the generated data as a function of probability, and calculate the variance of the resulting distribution.

#### Tips

Computer programs are available to assist in the calculation of variance, covariance and Monte Carlo simulations.

#### Warnings

Always compare calculated statistics to actual data when possible to avoid overestimation or underestimation of variance.

#### References

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