Using the semivariance to estimate safety-first rules

Extract: Given only knowledge of a finite mean, variance, and semivariance, it is shown that a Chebychev-type inequality based on the semivariance gives the smallest upper bound on the probability of being k standard deviations below the mean. Three examples are considered for agricultural yield and revenue data for the United States and the Philippines. Comparisons are made to upper bounds derived from both the standard Chebychev inequality and the standard Chebychev inequality and the assumption of symmetry.