To decompose the revenue variability, a simple technique was used that allows an analog of the risk from price to be isolated as well as the risk from yield. First, from a series of related yields and prices through time, the price is held constant at its mean and the revenue variance calculated allowing the actual yield changes observed. Then, the yield is held constant and the revenue variability calculated allowing the actual price changes observed. If there were zero correlation, the sum of these would equal the total observed risk.2 The actual total risk, however, is less than the sum by the amount that must be attributed to the effect of the negative covariance. The process of first holding prices constant and using actual yields, and then holding yields constant but reflecting actual price changes, and then comparing the total component variance to the actual was done for each county in Illinois for corn from 1975 to 2011. The fractions of the total variance and impact of correlation were then calculated. The table below contains results for selected representative counties around the state, and the average across all counties.

Consider Adams County where the actual average revenue per acre for corn is \$832.77 and the standard deviation of revenue is 127 using the procedures outlined above. The share of the variability attributable to price risk is 58% and the share attributable to yield risk is 42%. The Covariance effect reduced the actual variance from the component variance by 60%. In other words, if the price and yield were completed independent and varied with no relationship to each other, the actual variance of revenue would have been 60% higher. Likewise, had the price and yield series been independent, the actual average revenue would have been \$845.59 implying that the covariance also reduced the average revenue by about \$12.82/acre.

Alexander County has the highest share of yield risk of any county in Illinois at 50% while the relatively lower yield risk counties such as Christian, DeKalb, and Sangamon represent low yield risk cases where price is the primary driver of revenue variability. Across the state, price risk represents about 66% of the cause of revenue variability and the natural hedge or negative correlation reduces the total risk by 47% compared to a case of independence.

Overall, the price risk is found to be generally more influential on revenue variability than yield risk, and the correlation effects result in nearly a halving of the total variability compared to complete independence. These results do help support anecdotes that crop insurance has become a price risk program as much as a yield risk program, but that interpretation also adds to its usefulness in managing crop revenue risk. Areas of the state with relatively risker production have larger shares of overall crop revenue risk from yields, but the price and correlation effects are still at least as important.

Notes

1The correlation is a standardized measure of the relative movement between two series ranging from negative one to positive one. A value of negative one indicates that the series move exactly oppositely in identical proportions. A value of positive one means that the series move in lockstep fashion. A value of zero indicates no relationship at all between the movements in the series. The covariance between two random variables likewise relates the paired movements in the same scale as the variables themselves. Correlation is calculated as the covariance divided by the product of the standard deviations.

2The actual calculations are slightly more extensive involving squared means and variances as well as the covariance between squared values of each series. Details of the numeric procedures are available upon request.