Brainstorms
CASNET Poses Reserving Question

By Stephen W. Philbrick

Ruy Cardoso recently posted an apparently straight-forward question on CASNET. His question generated many responses that touched on a variety of actuarial topics. I will comment on some of these aspects. Readers interested in the unadulterated version can read the seventeen posts by clicking here.

Assume you wrote an aggregate excess policy with a one-year term on July 1. An actuarial analysis indicates that the expected losses for the whole year are 120, while the aggregate deductible is 100. The original premium paid for the contract is 20. What is the appropriate loss reserve at December 31?

Glenn Meyers pointed out that the expected losses on this contract are not 20. While 120 may be the best estimate of the aggregate losses, if we assume that there is some possibility losses could be less than 100 in some scenarios, then the expected losses excess of the deductible are more than 20.

Christopher Diamantoukos notes that this phenomenon occurs, not just on excess aggregate policies, but on any excess policy. The expected losses in excess of an attachment point are not, in general, equal to the expected losses less the attachment point.

I suspect that this issue is not adequately addressed in many reserving analyses. Nevertheless, this was not the main point Ruy Cardoso intended to address. So let us suppose that we can restate the problem such that the expected losses in excess of the deductible are 20. Now how do we establish the year-end reserves? Michael R. Lamb notes that when many of us first learned reserving we were taught to pretend that the policy is canceled at year-end and then examine the earned premium and the associated losses. This works well with policies covering individual claims but falls down with aggregate coverage. In fact, the entire concept of canceling an aggregate cover policy raises some interesting issues.

In particular, if a policy actually is terminated mid-term, how are losses determined? Some argued that policies do not typically carry language pro-rating the attachment point. Alan E. Wickman, a regulator, noted that he had rejected contracts that did not provide for pro-ration in the case of cancellation by the insurer. However, the calculations done by Glenn Meyers strongly suggest that proportional pro-ration is not the actuarially fair answer.

Other respondents tackled the difficult question of how to earn the premium under this contract. We are so used to uniform earning patterns that we sometimes forget that some policies have earning patterns distinctly different from a uniform pattern. One notable example is extended warranty coverage for new cars, where failure to appreciate the appropriate earning pattern has literally led to insolvency. Note that in some of these situations, the true loss reserve may be negligible, while the unearned premium reserve and the possible deficiency in the unearned premium reserve may well be the important balance sheet items. It isn’t clear to me how to establish an appropriate earning pattern for aggregate excess coverage. It seems likely that such a pattern would be weighted toward the end of the contract, but a revised earnings pattern would not address the liabilities if no premium deficiency reserve is established. Bjorn Palmgren of the Financial Supervisory Authority of Sweden noted that he would establish a premium reserve, comprising both an unearned premium reserve and a provision for unexpected risks. Michael Lamb specifically suggested that we "should also include premium reserves and rate adequacy in the scope of the actuarial opinion."

After this column was written and sent to the CAS Office, I received the Academy’s Property and Casualty Practice Note on Actuarial Opinions. On page two, it notes that the scope of the Opinion in 1998 will be expanded to include the reasonableness of unearned premium reserves for contracts of greater than thirteen months duration. Sounds like this issue is already getting a response.

As a member of the Committee of Online Services, I am heartened to see the CASNET used for such a spirited discussion. For those who would like to receive or contribute to this arena, visit our Information on CASNET page, or contact Mike Boa by e-mail at mboa@casact.org.