Appendix 33

Coefficient In some instances, you might want to compare the dispersion of two different series. The variance and of Variation standard deviation are absolute measures of dispersion. That is, they can be influenced by the magnitude of the original numbers. To compare series with greatly different values, you need a relative measure of dispersion. A measure of relative dispersion is the coefficient of variation, which is defined as:

Coefficient of Variation (CV ) =

Standard Deviation of Returns Expected Rate of Return

A larger value indicates greater dispersion relative to the arithmetic mean of the series. For the previous example, the CV would be:

1 0.0400

It is possible to compare this value to a similar figure having a markedly different distribution. As an example, assume you wanted to compare this investment to another investment that had an average rate of return of 10 percent and a standard deviation of 9 percent. The standard deviations alone tell you that the second series has greater dispersion (9 percent versus 7.56 percent) and might be considered to have higher risk. In fact, the relative dispersion for this second investment is much less.

1 0.0400

2 0.1000

Considering the relative dispersion and the total distribution, most investors would probably prefer the second investment.

Problems 1. Your rate of return expectations for the common stock of Gray Disc Company during the next year are:

Gray Disc Co. | |

Possible Rate of Return |
Probability |

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