Coefficient of Variation: A Relative Measure of Risk

Standard deviation can be misleading in comparing the uncertainty of alternative projects, if they differ in size. The coefficient of variation (V) is a correct technique in such cases. It is calculated as follows:

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The coefficient of variation for projects X and Y are 0.516 (Rs 10,756.4 + Rs 20.848) and 2,06 (Rs 43,026 + Rs 20,848). The higher the coefficient, the more risky is the project. Project Y, therefore, is more risky than project X. Thus, we find that V is not providing any additional information. However, the real utility of V is apparent when we compare the projects having differing expected values. The following example Example demonstrates the point further.

EXAMPLE

A company is considering selecting one of the two mutually exclusive projects A and B. The relevant information required to evaluate the riskiness of the project is given below:

Coefficient of Variation: A Relative Measure of Risk

Coefficient of Variation: A Relative Measure of Risk

On the basis of standard deviation alone, project B would be labelled as a more risky project than A since B has larger standard deviation (32,000) than A (27,000). But on the basis of V, project B would be considered less risky than project A since it has V lower than that of A (0.64 vs 0.75).

We can, therefore, conclude that the coefficient of variation is a better measure of the uncertainty of cash now returns than the standard deviation. This is because the coefficient of variation adjusts for the size of the cash now, whereas the standard deviation does not.

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