Insurance Premium Pricing and Ratemaking in Competitive Insurance and Capital Asset Markets

This paper develops an equilibrium model of insurance pricing integrating both the insurance and capital asset markets from the insurers' viewpoint. In contrast to the capital assets based models, it emphasizes the importance of the insurance market, i.e., the claim payments by all insurers as a whole, in pricing insurance premiums. The premium for insurance is found to be a function of both the systematic insurance market risk and the systematic capital market risk. An important practical implication of this model is that the fair profit rates for most lines of insurance should be higher than those recommended by current models based on the CAPM. The purpose of this paper is to develop a general equilibrium model of insurance premium pricing under both competitive insurance and capital markets. Largely motivated by the need to find alternative solutions to the fair-rate-of-return problem, several researchers have applied the asset pricing models to insurance premium pricing. In particular, Cooper [4] develops and tests a model based on the portfolio theory. Biger and Kahane [2], Hill [8], and Fairley [6], Urrutia [15] applies the Capital Asset Pricing Model [CAPM] approach, while Kraus and Ross [10] adapts the Arbitrage Pricing Theory [APT] to the insurance case. Because these models are borrowed from the finance literature where the market of interest is the asset market, they share a common shortcoming: it is concerned mainly with the systematic risks associated with the asset market. The insurance market, ironically, is ignored. From the balance sheet relationship that equity is the residual claim in which the asset return is netted out by the insurance loss, the expected return on the insurance company equity is expressed as a function of both the systematic risk of the insurance portfolio with the asset market portfolio and the James S. Ang is the William 0. Cullom Professor of Finance at the Florida State University. He received his Ph.D. from Purdue University. Dr. Ang has published estensively in Finance and Economics Journals. Tsong-Yue Lai is an Assistant Professor of Finance at the Florida State University. He received his Ph.D. from Yale University. This content downloaded from 207.46. 13.120 on Thu, 15 Sep 2016 05:41:45 UTC All use subject to http://about.jstor. org/terms 768 The Journal of Risk and Insurance systematic risk of the investment portfolio with the asset market portfolio, e.g., [2], [6], [8]. However, it is important to note that in these models, the fair-rate-of-return for ratemaking purposes or the premium for pricing an insurance policy is a function of only the systematic risk of that insurance policy and the asset market [see equation (9) of Biger and Kahane [2], equation (8) of Hill [8], and equation (11) of Fairley [6]). From the insurance industry viewpoint, there are not one but two important markets. The first is the familiar asset market which encompasses all assets, traded or nontraded, that are held. The second, equally important but often neglected market, is the insurance market. The difference between these two markets is not trivial. The asset market has a positive net supply, while the insurance market has a zero net supply. In other words, if all the asset portfolios are aggregated, the resulting figure is the wealth of the economy. An increase (decrease) in the aggregate wealth (or shares of IBM) leads to a corresponding increase (decrease) of those who hold a diversified portfolio (or shares of IBM). On the other hand, an insurance policy is a contract between the insurer and the insured. When a loss occurs, money is transferred from the insurer to the insured. Wealth is being redistributed but the aggregate does not increase. Although it is tempting to include all insurance contracts in the definition of the asset market portfolio, it will not work. Because a zero net supply exists for each insurance policy, and for the insurance market as a whole, the distribution of wealth between the suppliers (insurer) and the demanders (the insured) has absolutely no effect on the asset market portfolio, i.e., the asset market portfolio will behave as if no insurance contracts existed. Here, a troubling question arises: if the insurance market does not affect the asset market portfolio, can it be ignored in the pricing of insurance policies? The answer is no. If needs for insurance exist in the society, individuals and insurers must either be suppliers or demanders of a particular type of insurance policy. Thus, insurance contracts, which are netted out in the aggregate, are in positive net supply or demand for individuals and insurers. Specifically, the insurers, being net suppliers of insurance, cannot ignore the aggregate insurance loss (payments on all insurance claims in a given period) in the pricing of insurance policies. For insurers with a diversified insurance portfolio, e.g., multi-line insurers and their competitors, i.e., all single line insurers, it is reasonable to expect that the price or premium on a policy, whose claim arises in a period when the aggregate insurance claim is high, i.e., a positive correlation with the aggregate insurance market, should also be high. In this case a higher premium is charged because the insurer is less able to shoulder the payment of many claims at the same time. The risk includes financial insolvency as well as possible ruin. This intuition is formally developed in an integrated model of insurance and capital markets. The model gives a pricing equation for an insurance premium which may be used for the calculation of the fair-rate-of-return. It is shown that this model generates all other models of insurance premium pricing in competitive markets as special cases. Conclusions are presented in the last section. This content downloaded from 207.46. 13.120 on Thu, 15 Sep 2016 05:41:45 UTC All use subject to http://about.jstor. org/terms Insurance Premium Pricing and Ratemaking 769