Coefficient of variation
The ratio of standard deviation to mean, which measures the relative volatility of a loss and allows portfolios of different sizes to be compared.
The coefficient of variation divides a quantity's standard deviation by its mean. Being unitless, it allows the volatility of portfolios of very different sizes to be compared, which the standard deviation alone does not. In insurance, it measures what the law of large numbers has or has not done: a portfolio of many independent risks sees the coefficient of variation of its annual losses fall as the inverse of the square root of the number of risks, whereas a catastrophe layer, which almost never has a loss but loses in full when it does, keeps a very high coefficient whatever its size. It is used to calibrate safety loadings under the standard deviation principle, to judge the credibility of an experience, and to explain why two activities with the same expected loss call for neither the same price nor the same capital.
Hypothetical case: a 50 million euro layer has a 2 percent chance a year of a total loss, and nothing otherwise. Its expected loss is 1 million; its standard deviation is 50 million times the square root of 0.02 times 0.98, or 7 million. Its coefficient of variation is 7, while that of a large motor portfolio is counted in percent.
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