Downward Bias of Using High-Low Averages for Loss Development Factors

This paper extends previous research that studied the downward bias associated with high-low averages, which occurs when high-low averages are applied to data that exhibits a long-tailed property. The current study conducted a comprehensive review of insurance industry data when three-of-five averages are used to determine the age-to-age development factors in setting reserves. The downward bias was analyzed by line of business, premium size, development age, paid and incurred loss development methods, for one hundred and forty paid and incurred loss triangles from seventy insurance companies/groups compiled from the A.M. Best database. The study assumes that the age-to-age development factors are log normally distributed. The three-of- five average was selected as the representative high-low average because it is commonly used by property/ casualty actuaries. The results for this average can be generalized to other types of high-low averages. The results given in the paper are based on a bias formula for a large volume of data. Since the real-world loss development data is limited in volume, the study used large scale simulations to review the effect of limited volume data on the bias.