Chain-Ladder Bias: Its Reason and Meaning

By Leigh Joseph Halliwell

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Over the past twenty years many actuaries have claimed and argued that the chain-ladder method of loss reserving is biased; nonetheless, the chain-ladder method remains the favorite tool of reserving actuaries. Nearly everyone who acknowledges this bias believes it to be upward. Although supporting these claims and beliefs, the author proposes herein to deal with two deeper issues. First, does something inherent in the chain-ladder method dispose it to bias? Is there a diagnostic whereby one can predict how the chain-ladder method will fare with a particular loss triangle? To resolve this issue basic regression theory will suffice, specifically, the much misunderstood concept of regression toward the mean. And second, what lessons can we learn from the phenomenon of bias; in particular, is there a difference between actuarial methods and statistical models? These two issues constitute the reason and meaning of chain-ladder bias.

KEYWORDS: Chain-ladder method, loss development, statistical model, stochastic regressor, regression toward mean, credibility

NOTE: Article updated April 1, 2008.


Halliwell, Leigh Joseph, "Chain-Ladder Bias: Its Reason and Meaning," Variance 1:2, 2007, pp. 214-247.

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Variance (ISSN 1940-6452) is a peer-reviewed journal published by the Casualty Actuarial Society to disseminate work of interest to casualty actuaries worldwide. The focus of Variance is original practical and theoretical research in casualty actuarial science. Significant survey or similar articles are also considered for publication. Membership in the Casualty Actuarial Society is not a prerequisite for submitting papers to the journal and submissions by non-CAS members is encouraged.