Paul J. Kneuer

Mr. Kneuer is Assistant Actuary in the Data Management and Control Department of Insurance Services Office, Inc. He is an Associate of the Casualty Actuarial Society and a Member of the American Academy of Actuaries. Mr. Kneuer received a B.S. in Mathematics from the University of Notre Dame in 1982.

Abstract

Various methods have been advanced for allocating policyholders' surplus to lines of insurance. While these methods could be powerful analytical tools, there are practical and theoretical problems that limit their usefulness. These problems are due to both the functions and nature of surplus and the nature of the decision-making processes that might use an allocation method. The author reviews some proposed allocation methods and develops practical considerations for an allocation method. None of the proposed allocation methods considered meet these criteria.

These criteria address only the practical concerns about allocation methods, not the theoretical ones. So even proposed allocation methods that meet these standards have theoretical hurdles to overcome. Alternative analytical approaches are proposed as replacements for allocation methods.

An understanding of how an insurer's surplus supports its various operations would be a valuable tool for making business decisions, such as evaluating performance, analyzing the capital structure of the firm, and recognizing opportunity costs. This understanding is generally absent.

Yet, casualty actuaries are familiar with the concept of allocation. For example, indicated rate level changes are often allocated to classes or territories. So, it is surprising that a familiar tool, the allocation of the amounts in financial accounts, has not been applied to solve an important problem addressing property-casualty insurers. Perhaps the explanation for this failure to associate surplus with the different operations of the insurer lies in the difficulty of the task. It may be an impossible task. However, if an allocation is to be useful we should first consider in detail the question of

WHY ALLOCATE SURPLUS?

The surplus of an insurer is a finite good. The limitations to surplus prevent the insurer from writing greater volumes of business, or larger risks, or business that has an expectation of higher profits. Thus surplus has a value beyond the insurer's liquidation value. That value is the opportunity to earn additional profits by writing more insurance.

Open-market pricing of coverage reflects this value and calls it "underwriting profit margin", "surplus charge", or "risk load". If the amount of surplus directly associated with insurance contracts were known, the calculation of prices that recognize the value of that surplus could be explicit, and perhaps more accurate, consistent and stable.

A second beneficiary of an allocation of surplus would be insurer management. Since the use of surplus has an opportunity cost, and since various underwriters can commit the insurer's surplus by writing insurance contracts, management needs to measure their relative success. If surplus could be allocated to underwriting decision-making units, the use of surplus could be evaluated. The management of each unit could then be held accountable for the value of the use of the surplus that it had committed.

If an allocation of surplus could be made to lines and states, then regulators, insurer management, and guaranty fund authorities could examine how the amount of surplus allocated to different lines varied between insurers, in addition to measuring the absolute levels. This could provide important information about solvency. It could also indicate any lines where competitive markets were not effectively regulating prices.

An allocation of surplus is desirable for consumers, management, guarantors and regulators for the same reason. The specific underlying purpose of an allocation of surplus is to make informed economic decisions, such as pricing, that consider how each portion of the insurer's book restrict its ability to write other risks. This essay will address only this purpose of an allocation, and will not address the total amount of surplus that an insurer should have.

The actuary trying to do such an analysis may be encouraged by some trivial cases where a clear allocation of an insurer's surplus is possible. These cases include the one-line insurer, the over-capitalized insurer and the insolvent insurer (1).

The important case, the case where an allocation of the insurer's surplus to portions of its writings can influence decisions, is the complement of these cases: the solvent insurer, whose writings have several distinct sections, and whose underwriting decisions are constrained by the amount of its surplus.

________________________________________________________________
(1) The one-line insurer. An insurer whose writings are uniform in a dimension (such as all in one line of business, or all in one state, or all in one time period) can of course allocate all of its surplus to the one value that its writings take on in that dimension. Unfortunately, this allocation provides no information about how the surplus may support the separate parts of the insurer's writings along the other dimensions. A truly trivial insurer that writes one line of insurance, in one state, during one time period, etc. can fully allocate its surplus to that one cell. However the company and its regulators have no further economic decisions to make, except the basic question of solvency. Thus the allocation of surplus possible in the simple case of the mono-line insurer either leaves important questions unanswered, or addresses a company so simple that the trivial allocation which is possible is useless.

The over-capitalized insurer. If an insurer has enough surplus, relative to its writings and other exposures to loss, that its decisions are not affected by considerations of surplus, then an allocation of surplus is both possible and irrelevant. In fact, several very different allocations of the insurer's surplus are possible. Here also the allocation does not provide information useful in economic decision-making. And the question of solidity, by definition, is foregone.

The insolvent insurer. The insurer without surplus has only a trivial allocation to make.

Next