Academic journal article Journal of Risk and Insurance

Insurance Pricing, Reserving, and Performance Evaluation under External Constraints on Capitalization and Return on Equity

Academic journal article Journal of Risk and Insurance

Insurance Pricing, Reserving, and Performance Evaluation under External Constraints on Capitalization and Return on Equity

Article excerpt


We derive formulas for calculating the premiums that should be charged on policies in a discounted cash flow model with tax reserves and required assets that are determined by regulation. We also determine the unique division of required assets into "reserves" and "capital" that allows the product profitability to be correctly evaluated. That is, the profit after capital charges is zero if the product achieves the return assumed in pricing. We illustrate the concepts using whole life insurance and guaranteed minimum death benefit examples.


The importance of economic capital to insurance companies has been growing in recent years. To some extent, this has been driven by regulation, as illustrated by the introduction of the Solvency II capital standards in Europe. On the other hand, it is being increasingly seen as good business practice independent of any regulatory action. The implementation of an economic capital framework raises a number of practical questions, such as what solvency threshold to use, whether to use value-at-risk or a coherent risk measure and how to allocate the capital to lines of business. Both the determination of the capital level and the allocation of capital to individual lines of business are important for the evaluation of products and product managers. Typically, the income of the line is computed and the allocated capital is charged its cost and subtracted. A positive result indicates a profitable line. In a market-value-driven economic capital framework such as Solvency II in Europe, it is actually not capital per se but an asset level that is determined and allocated. This article addresses this issue of dividing the allocated assets into "capital" and "reserves" for the purposes of accurately evaluating the profitability of a product.

It may seem at first glance that this question is trivial. Insurance companies already routinely divide assets this way and often determine capital charges to the lines based on the hurdle rate. On closer inspection, however, the appropriate reserve to use is not obvious. There are at least six candidates for reserves:

1. U.S. Statutory Reserves;

2. U.S. GAAP Reserves;

3. U.S. Tax Reserves;

4. Fair Value of Liabilities;

5. Assets at a somewhat conservative solvency standard (Solvency II uses 75 percent);

6. Expected loss under the realistic measure discounted at the risk-free rate.

Each of these reserve bases has a corresponding capital level. The income less capital charges will be different for all six candidates because both the change in reserves is different and the capital level being charged (i.e., assets less reserves) is different. Therefore, each of the six corresponding profitability results will evaluate the line and manager differently. Before reading further, I would suggest that the reader decide whether one of these six capital amounts is the correct one for assessing capital charges when evaluating product profitability, or whether the correct answer is a seventh possibility.

The question of which definition is appropriate for evaluation purposes can be answered in the context of discounted cash flow analysis of insurance company profits. The method was first analyzed by Myers and Cohn (1987) and later by Cummins (1990) and Taylor (1994). A good overview of the current state can be found in Cummins and Phillips (2000). Although most of the analysis has been done in a property-casualty insurance framework, the papers include multiperiod models and are therefore applicable to life insurance as well.

In these models, it is assumed that the insurance company receives and pays cash flows every period. In addition, the company is required to hold assets every period in order to maintain a solvency standard. The interest on these assets is added to the product cash flows, and the combined flows are assumed to be paid out to shareholders net of funds needed to increase or decrease the assets held in the next period. …

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