Coefficient of Variation

The coefficient of variation is used in comparing yield risk between corn, soybean, and wheat in the risk file above, and the coefficient of variation is a measure of relative risk. The coefficient of variation is calculated as the standard deviation divided by the average. That is, the coefficient of variation takes into account both the average and variability around the average of a data series. For example, suppose the 5-year average corn yield is 100 bushels and the 5-year average soybean yield is 30 bushels. Furthermore, the standard deviation (measure of variability around the mean over the 5-year period) for corn is 15 bushels and for soybean is 15 bushels. Which crop is more risky? Evaluating only the standard deviation indicates both crops are equally risky with a standard deviation of 15 bushels. This says that you would expect to yield 100 bushels of corn and 30 bushels of soybean in year six, but statistical inference states that there is some range around the expected yield. For corn you would infer that 68% of the time the expected corn yield in year six would lie in the range [85,115] (plus and minus one standard deviation from the average corn yield) and for soybean the range would be [15,45] (plus and minus one standard deviation from the average soybean yield). This is based on the yield information for the previous five years. However, accounting for both average yield and standard deviation (risk) indicates the coefficient of variation for corn is 0.15 (15 bushels divided by 100 bushels) and for soybean is 0.50 (15 bushels divided by 30bushels). This indicates, on a relative level, soybean yield is over three times more variable than corn yield for this example. The larger the coefficient of variation the greater the risk relative to the average. Most producers would prefer less yield risk (lower coefficient of variation) to more yield risk.