Department of Finance

 

Date of this Version

1996

Document Type

Article

Citation

Journal of Actuarial Practice 4 (1996), pp. 142-158

Comments

Copyright 1996 Absalom Press

Abstract

Property and casualty actuaries frequently employ a technique of averaging (called high-low averages) that excludes the same amount of data at both ends. For example, (0 in selecting loss development factors, the middle three of the latest five years or the middle eight of latest 12 quarters sometimes are used, or (ii) in calculating average expense ratios, the largest expense ratios and the smallest expense ratios may be removed from the sample. Although highlow averages can reduce the impact of influential data on analyzed results, the averages will result in downward bias when they are applied to pricing or reserving data that exhibit a long-tailed property. We derive the bias for two commonly used distributions: lognormal and Pareto. An example is provided using chain-ladder reserving where loss development factors are assumed to be lognormally distributed.

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