Newsletter-volume 4 - 2011 (Draft) - Actuarial Society of Hong Kong

This article was first published in the November 2011 issue of the Asia Insurance Review.Why Risk Margin?In a perfect world, Actuaries would be able todetermine best estimate reserves which willexactly be equal to the actual future lossesincurred by an insurer. Unfortunately, in reallife, things are not as simple. There are manyuncertainties and surprises which will causethe best estimate reserves to be higher orlower than the actual future losses incurred.For example, past and future claimfluctuations, future economic or environmentalconditions, errors in data or incorrectprojection models selection.A risk margin on top of the best estimatereserves provides for situations where theactual future losses may be higher than thebest estimate reserves. This extra comfortlevel helps maintain the financial soundness ofinsurers and to protect policyholders.Risk Margin DeterminationThere are numerous approaches to determinerisk margin. It may be determined as a fixedmonetary amount or a percentage of the bestestimate reserves. In slightly morecomplicated form, the reserving actuarycarries out an alternative set of reserveprojections using more conservativeassumptions, such as claim inflation, to arriveat a more conservative reserve estimate. Thedifference between this conservative reserveand the best estimate reserve represents therisk margin.Both approaches are simple to implement, butthey fail to describe the degree of prudencequantitatively represented by the risk margin.There is little statistical reasoning or basisbehind the choice of the risk marginassumptions.A number of methods have been suggested toestimate the risk margin with more solidstatistical basis.Two commonly used methods which can beeasily adapted in Asia are (1) the Mack methodand (2) bootstrapping. In addition, there arethe cost-of-capital method integrated in theSwiss Solvency Test and the to-beimplementedSolvency II framework in Europe.Mack methodThe Mack method is a natural extension of thechain ladder method commonly used forestimating best estimate reserves. The chainladder method involves using run-off claimsdata to estimate development factors (measureof the speed of reporting and settling claims),then using the development factor to project theultimate cost of claims. Subtracting the paidclaims from the projected ultimate cost ofclaims gives the claims reserves of theportfolio. Even without any changes in theclaims management process, claimsdevelopment would still fluctuate over time dueto randomness of claims occurrence, claimsseverity and the speed at which the claims arereported and settled. Therefore the estimationof development factor is inherently uncertain.In statistical term, a number representing themeasure of uncertainty is called the standarddeviation. The uncertainty in claimsdevelopment can naturally be used to infer thestandard deviation of the ultimate cost of claimsand the reserves.The risk margin may be decided as a certainmultiple of the standard deviation of thereserves (e.g. 0.5 times, 1 time, 1.5 times, etc).Furthermore, it can be assumed that thereserves follow a particular statisticaldistribution to infer a full distribution of thereserves to calculate the level of sufficiency atvarious levels of reserve. Typically, the range ofsufficiency level insurers is interested in forreserving purpose is between 75% to 90 %sufficiency. In this case, a normal distributionmay be assumed. For more extremescenarios, e.g. stress testing purpose, thismethod is not recommended.The Actuarial Society of Hong Kong, 2202 Tower Two, Lippo Centre, 89 Queensway, Hong KongTel (852) 2147 9420 Fax (852) 2147 2497 Website: www.actuaries.org.hkNote: Views expressed are not necessary those of The Actuarial Society of Hong Kong13