An Exposition of the Implications of Limited Liability and Asymmetric Taxes for Property-Liability Insurance

Abstract

ABSTRACT This article elaborates upon the intuition underlying Doherty and Garven's (1986) option pricing model and extends its basic results to a further consideration of the implications of limited liability and asymmetric taxes for pricing and incentives in property-liability insurance. When compared with CAPM-based models of the insurer, a number of important insights emerge. First, the option pricing framework is shown to encompass the CAPM framework as a special case and may help to explain a number of empirical phenomena. Second, the option pricing framework is used to develop a risk hypothesis which suggests that limited liability and asymmetric taxes provide mutuals with greater disincentives for riskbearing than stock companies, even in the absence of owner/manager conflicts. Although the property-liability insurance industry has been subject to price regulation for many years, researches have only recently derived valuation formulas for property-liability insurance firms. To date, the most promising approaches apply financial theories such as the capital asset pricing model (CAPM) (see Biger and Kahane, 1978; Fairley, 1979; Hill, 1979; Hill and Modigliani, 1987; and Myers and Cohn, 1987) and the option pricing model (see Doherty and Garven, 1986; Cummins, 1988b; and Derrig, 1989). Although details vary, these models are generally organized around the principle that the rate of underwriting profit must be set so as to produce a fair, or competitive rate of return on equity.(1) In spite of their common origins, CAPM and option-based insurance pricing models produce substantially different predictions concerning pricing and incentives for property-liability insurance. It will be shown that these differences are primarily due to the manner in which the effects of insolvency and taxes are modeled. Essentially, CAPM-based models implicitly assume that shareholders have unlimited liability, whereas option-based models assume that shareholders' liability is limited. Similarly, by assuming that losses are rebated at the same rate at which gains are taxed, CAPM-based models effectively assign unlimited liability to the government, whereas option-based models limit the government's liability by assuming that gains and losses are taxed in an asymmetric fashion. This article elaborates upon the intuition underlying Doherty and Garven's (1986) option pricing model and extends its basic results to a further consideration of the implications of limited liability and asymmetric taxes for pricing and incentives in property-liability insurance. This is accomplished by comparing and contrasting option-based with CAPM-based models of the insurance firm. This analysis yields a number of important insights, such as the fact that the option pricing framework encompasses the CAPM framework as a special case. The option pricing model also has several practical advantages over the CAPM. For example, it is not plagued by the CAPM's well-known parameter estimation problems; indeed, it may help to explain the causes of these problems.(2) The option pricing model also provides an explicit linkage between fair return and the risks of insolvency and tax shield underutilization, whereas the CAPM totally ignores these effects. The option pricing model also calls attention to some important incentive effects concerning risk-bearing that are not captured by the CAPM. Under the CAPM, asset and liability is not particularly important so long as these claims are priced to yield appropriate risk-adjusted rates of return. However, under the option pricing model, the extent to which firms will seek to increase or avoid through their investment and underwriting policy choices depends upon the likelihood of being taxed or becoming insolvent. Consequently, the application of the option pricing framework makes it possible to develop a risk hypothesis which predicts that mutual insurers will seek less exposure to than stock companies. …