How to Calculate Variance for Risk Management

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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 & Warnings

  • Computer programs are available to assist in the calculation of variance, covariance and Monte Carlo simulations.
  • Always compare calculated statistics to actual data when possible to avoid overestimation or underestimation of variance.

References

  • Photo Credit Thinkstock Images/Comstock/Getty Images
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