Measuring Loss Reserve Uncertainty

Motivation: For property casualty insurers, loss reserves are by far their largest liability. These are actuarial estimates of future loss payments resulting form accidents that have already occurred. In fact, the actual future loss payments may deviate - sometimes substantially - from the amount that was estimated. Senior managers, shareholders, rating agencies, and regulators all have an interest in knowing the magnitude of these potential deviations need more capital or reinsurance than other firms with smaller potential deviations. Actuarial journals provide several proposed procedures for measuring loss reserve uncertainty. But in practice they are rarely used, since they typically require specialized software and use statistically complex procedures that are unfamiliar to most actuaries. Moreover, in at least some cases, these procedures provide estimates of loss reserve uncertainty that depend on very strong assumptions that virtually assume the conclusions obtained.

Method: In this report I provide a simple method for measuring loss reserve uncertainty that is easily implemented with a spreadsheet model, that relies on data available for all US insurers and all lines of business, and that makes relatively few easily accepted assumptions.

Results: The method for estimating loss reserve uncertainty explained and demonstrated here has five important advantages. First, it is simple, and easy to implement. This report even provides the relevant Excel formulas for implementing crucial steps in the method. Second, it avoids severe statistical problems that affect numerous rival methods, as explained in detail. Third, the method is validated (rather than merely illustrated) by applying it to answers. Fourth, the measure of loss reserve uncertainty used here - the standard deviation of loss reserves as a percentage of the estimated reserve - is scalable, so that it can be applied to reserves estimated by other methods. Fifth, the resulting measure of loss reserve uncertainty can be directly compared across different lines of business in a single firm, or for the same line of business across different firms.

Conclusions: The method presented here appears to be the first instance of a method for estimating loss reserves and loss reserve uncertainty that is thoroughly validated by comparing its estimates to those of a simulation with known parameters. Its results can assist CEO's, CFO's, Chief Risk Officers, actuaries, rating agencies, regulators, and stock analysts in estimating the variability of loss reserves, in estimating a firm's capital adequacy, in forecasting the distribution of possible loss reserve payments during the next calendar year, and in determining whether current or past calendar year deviations from expected loss payments are sufficiently large to deserve special attention.

Availability: To obtain the model presented here, email: Bill.Panning@Willis.com .

Keywords: Loss reserve rncertainty, regression, reserving, Enterprise Risk Management.