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Article Excerpt
Abstract
The Capital Asset Pricing Model has been used frequently to derive a fair price of insurance. But the use of this model overestimates insurance premiums because it does not account for the insolvency risk of insurers. This paper examines how the insurance price should be fairly adjusted when insurers' default risk is considered. It develops a model which shows that fair insurance premiums are lower when insurance firms have a positive probability of being insolvent. Using data of property liability insurers during the period from 1943-99, the paper further estimates the effects of the insolvency risk on insurers' underwriting profit rate. It shows that the incorporation of the default risk of insurers in the model, by significantly reducing the required price for insurance, would lead to lower profit potentials. Some writers argue that including the insolvency risk when calculating insurance premiums is not so necessary because of the existence of states' guaranty insurance funds which protect consumers. How ever, as shown in the paper, these funds have provided inadequate protection to consumers. Therefore, because of the increase in the number of insolvencies in recent years, and because of the limited coverage provided by states' guaranty funds, it seems that considering the insolvency risk in insurance pricing has become very necessary. (JEL G22)
Introduction
Using the Capital Asset Pricing Model (CAPM) developed by Sharpe [1964], Litner [1965], and Mossin [1966], one is able to estimate the underwriting beta and further obtain the fair rate of return for insurance firms, as was previously done by Biger and Kahane [1978], Fairley [1979], Hill [1979], Bronars [1985], and Cummins and Harrington [1985]. The rate of return derived from such models is the competitive rate in the sense that all systematic risks an insurer faces are fairly compensated. The insurer is also compensated for its expected loss as well because of the relation between the rate of return of underwriting and the loss ratio. (1)
The rate of return and thus, the insurance premium derived using the CAPM, however, is overestimated because the model does not consider the insolvency risk of insurance firms. (2) Using such an overestimated rate of return to regulate the insurance industry will encourage investors to increase capital inflow to the industry. That in turn will cause over-supply of insurance which may lead to inefficiency.
In this paper, it is assumed that an insurance firm faces the risk of insolvency. As a result, policyholders' claims may not be fully recovered. With this assumption, the paper derives the formula for the fair price of underwriting using the CAPM. It shows that fair insurance premiums are lower when insurance firms have a positive probability of being insolvent. Using data of property liability insurers during the period from 1943-99, the paper further estimates the effects of the insolvency risk on insurers underwriting profit rate. It shows that the existence of the default risk of insurers significantly reduces the required underwriting rate of return. The paper also indicates that the traditional CAPM without including insolvency risk is misspecified and that the estimated underwriting beta is biased.
The Capital Asset Pricing and Option Pricing Models in Insurance
One main feature of this paper is combining the CAPM with the Option Pricing Model (OPM) for use in the insurance case. Such an approach alleviates the major weakness of solely using the CAPM while keeping the model simple and testable.
One distinction between the CAPM and OPM is that the CAPM ignores the insolvency risk of firms while the OPM explicitly considers such a risk. Since each firm has a positive probability of being insolvent, the results derived from the traditional CAPM have been questioned [Doherty and Garven, 1986; Brown and Hoyt, 1995]. An insurance firm earns premiums from consumers when it issues policies to them and invests some of its premiums in the financial market. Policyholders' claims, however, may not be fully paid if the insurer is declared to be insolvent because the insurer has a limited liability. Therefore, there is some value of insolvency to the insurer. The insurance price if calculated without including such a value will be unfair to consumers.
Researchers have long noticed the weakness of the CAPM due to its exclusion of insolvency risk. The problem was first pointed out by Fairley [1979]. Brown and Hoyt [1995] further urged that future research dealing with the CAPM should aim to incorporate the insolvency risk because of the significant relationship found between the insolvency rate and underwriting results. There are some reasons for excluding the insolvency risk in the CAPM as Fairley [1979] indicated. One is that the proper treatment of the insolvency risk in the context of the CAPM might be difficult. Fairley also thought that including the insolvency risk in the CAPM is not so urgent because of the existence of guaranty funds which he claims will provide adequate protection to consumers and also because the actual dollar volume of insolvency is small. However, the circumstances of the insurance market have changed greatly in the past two decades; in particular, the frequency of and the losses from insolvencies of insurance firms have increa sed dramatically since 1984. (3) From 1984-98, 480 property and liability insurers became insolvent (4) and, as a result, many policyholders' claims have not been recovered or fully recovered because of certain features of states' guaranty funds. A state's guaranty fund will not cover unpaid claims by insurers that are not licensed in that state. In addition, claim payments from a state's guaranty fund have upper limits. The total state's funds available to pay claims in a particular line of insurance (such as automobile insurance) are limited to the total assessment collected from all insurers doing business in that line and many states have annual assessment caps and usually do not start the levy of assessments to raise funds to pay claims until a failure has already occurred. The maximum assessment each insurer must pay in most states is two percent of total premiums written. In other words, if a state's total automobile insurance premiums written by all automobile insurers is $1 billion each year, then, t he maximum guaranty fund assessment from all automobile insurers will be $20 million per year. If, in a given year, the total deficit of insolvent automobile insurers exceeds $20 million, some claims will not be paid in that year. Instead, they will be paid over the next few years depending on the availability of the state's fund. Furthermore, the payment from a state's guaranty fund to each policyholder is usually subject to a prescribed limit. In property liability insurance, most states set $25,000 as the maximum amount a policyholder can receive from the state fund.
Because of the increases in the number of insolvencies in recent years and because of the limited coverage provided by states' guaranty funds, it seems that considering the insolvency risk in insurance pricing has become more necessary. In particular, since the fair rate of insurance (premium rate) derived from the CAPM has been used in insurance regulation, (for instance, Massachusetts sets up its rate regulation using the...
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