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

This paper studies the downward bias associated with high-low averages. The bias occurs when the high-low averages are applied to data that exhibits a long-tailed property. This research included a comprehensive review of insurance industry data when 3-of-5 averages are used to determine the age-to-age development factors in setting reserves; 140 paid and incurred loss triangles from 70 insurers were compiled from the AM Best Database (1 gB6) to analyze the downward bias by: l line of business l data size l development age l paid and incurred loss development methods. The study assumes the age-to-age development factors are lognormally distributed. The 3-of-5 average was selected as the representative high-low average because it is commonly used by property and casualty actuaries. Results for the 3-of-5 average can be generalized to other types of high-low averages. The study also used large-scale simulations to review the effect of limited volume of data on the downward bias.