Motivation. Tail factors are used by actuaries to estimate the additional development that will occur after the eldest maturity in a given loss development triangle, or after the eldest credible link ratio. Over the years, many valuable contributions have been made to the CAS literature that describes various methods for calculating tail factors. The CAS Tail Factor Working Party prepared this paper on the methods currently used by actuaries to estimate loss development ‘tail’ or ‘completion’ factors. Standard terminology for discussing aspects of link ratios and tail development is communicated within the paper. Descriptions of the advantages and disadvantages of each method are included as well general indications of what types of entities (companies, rating bureaus, or consulting firms) typically use each method.
Method. An extensive survey of existing CAS literature was performed, along with surveys of methods currently in use by various rating bureaus, insurers, and consulting organizations. The methods identified by the Working Party are grouped into six basic categories: (1) “Bondy Methods”; (2) algebraic methods that focus on relationships between paid and incurred loss; (3) methods based on use of benchmark data; (4) curve-fitting methods; (5) methods based on remaining open counts; (6) methods based on peculiarities of the remaining open claims; and (7) the remaining unclassified methods.
Results. Comparisons of the results of several key tail factor methodologies to the actual post-ten year development for a number of long-tail lines using multiple realistic data sets are included, along with the advantages and vulnerabilities of each method.
Availability. A copy of the Working Party’s paper and companion Excel template can be found below under documents.
Keywords. Tail Factors; Completion Factors; Link Ratios; Age-to-Age Factors; Development Factors; Loss Reserving; Curve Fitting; Bondy Method; Benckmark; Loss Development.
