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  Insurance and Corporate Risk ManagementAuthor(s): Richard D. MacMinnSource: The Journal of Risk and Insurance, Vol. 54, No. 4 (Dec., 1987), pp. 658-677Published by: American Risk and Insurance Association Stable URL: http://www.jstor.org/stable/253115 . Accessed: 20/09/2014 00:05 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at  . http://www.jstor.org/page/info/about/policies/terms.jsp  . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact support@jstor.org.  .  American Risk and Insurance Association  is collaborating with JSTOR to digitize, preserve and extend accessto The Journal of Risk and Insurance. http://www.jstor.org This content downloaded from 103.26.198.254 on Sat, 20 Sep 2014 00:05:52 AMAll use subject to JSTOR Terms and Conditions  Insurance and Corporate Risk Management Richard D. MacMinn* Abstract This paper provides a model of a competitive financial market economy in which there are not only stock and bond markets but also insurance markets. In the model's most naive form, the analysis shows that the corporate value of the insured firm equals that of the uninsured firm and in this case the firm has no active role to assume in managing corporate risk. The model is then modified to incorporate costly bankruptcy and agency problems. Then the analysis shows that the corporation has an incentive to purchase insurance because it may eliminate or reduce the bankruptcy and/or agency costs. Introduction Insurance contracts are regularly purchased by corporations and play an important role in the management of corporate risk. This role has not been analyzed in finance even though insurance contracts are simply another type of financial contract in the nexus of contracts which is the corporation. The purpose of this paper is to provide a model which is robust enough to allow for an investigation of the scope of insurance contracts in the management of corporate risk. In the insurance literature, the incentive to buy insurance is often assumed to be risk aversion. Risk aversion is a sufficient motivation for the closely held corporation but, as Mayers and Smith observe, not for the publicly held corporation. Mayers and Smith claim that The corporate form provides an effective hedge since stockholders can eliminate insurable risk through diversification, [10, p. 282]. An equivalent claim is that the value of the insured corporation is the same as the value of the uninsured corporation. If *This research was partially funded by the University Research Institute and the Graduate School of Business, University of Texas. I would like to thank Karl Borch, Neil Doherty, Michael Smith, and an anonymous referee for their comments on earlier drafts of this paper. Richard D. MacMinn is a Visiting Associate Professor of Finance at the University of Missouri at Columbia and an Associate Professor of Finance at the University of Texas at Austin. He earned the Ph.D. from the University of Illinois in 1978 and was awarded the Ambassador Edward A. Clark Fellowship for 1986-87. Dr. MacMinn has published articles in eight major journals including The Journal of Political Economy, Journal of Finance, and The Geneva Papers on Risk and Insurance. This content downloaded from 103.26.198.254 on Sat, 20 Sep 2014 00:05:52 AMAll use subject to JSTOR Terms and Conditions  Insurance and Corporate Risk Management 659 this claim holds, then insurance is not a necessary tool in managing corporate risk. A characterization of the market economies in which the claim does and does not hold should be important to corporate managers as well as insurance companies. Apparently no model in the literature exists which addresses this claim.1 The purpose of this paper is, first, to characterize the corporate and market environment in which insurance is irrelevant (i.e., establish the claim) and, second, to modify the model in order to characterize the corporate and market environments in which insurance is an important tool in managing corporate risk. The first step is to establish the claim that corporations need not buy insurance since competitive risk markets already provide sufficient opportu- nity to diversify corporate risk. To establish or refute this claim requires a model of the economy which includes a stock market as well as an insurance market. Such a market model is provided in the Basic Model section of this paper. The basic model includes two types of financial contracts and two sources of uncertainty. The analysis demonstrates that any insurance decision made by the corporation may be reversed by any individual on personal account. Equivalently, a no arbitrage condition guarantees that stock and insurance contracts must be priced the same; then it is a simple matter to show that the net present value of the insurance decision is zero. Next, the basic model is extended so that it incorporates risky debt contracts as well as stock and insurance contracts. The analysis shows that as long as bankruptcy is costless the same reasoning applies. Since the value of the corporation is the sum of the values of its financial contracts and the net present value of the insurance is zero, the claim is established. In the section, Costly Bankruptcy, the model is altered to allow for the transaction costs of bankruptcy. Mayers and Smith [10] note that bankruptcy costs provide the firm with an incentive to insure because, by shifting risk to the insurance company, the firm decreases the probability that the cost is actually incurred. The analysis here shows that the total market value of the insured firm is equal to the total market value of the uninsured firm plus the present value of the savings on bankruptcy costs; equivalently, the analysis shows that the value of the insured firm exceeds the value of the uninsured firm. This would seem to provide the corporation with an incentive. However, it is also shown that insurance increases the value of the firm's debt but that it decreases the value of the firm's equity. The firm maximizing stock market value does not have an incentive to insure. In the section, Agency Problems, the basic model is generalized so that it incorporates the conflicts of interests between corporate management and 'The claim is certainly intuitively appealing. If the corporation is viewed as a set of financial contracts, then establishing this claim will provide a generalization of the 1958 Modigliani-Miller Theorem. The generalized theorem would say that the composition of the contract set is irrelevant. It may also be noted that this generalized theorem is implied by the Coase Theorem [3]. This content downloaded from 103.26.198.254 on Sat, 20 Sep 2014 00:05:52 AMAll use subject to JSTOR Terms and Conditions  660 The Journal of Risk and Insurance bondholders. Conflict of interest problems arise when the corporate manager, acting in the interests of stockholders, has the incentive to select actions which are not fully consistent with the interests of bondholders. Two classic examples of the conflict of interest problem are developed. Then the analysis necessary to show how the insurance contract may be used to limit the divergence between the interests of bondholders and management is developed. The first agency conflict considered is usually referred to as the under investment problem. In this example, the manager of a levered firm has an incentive to limit the scale of investment because the additional returns from further investment accrue primarily to bondholders. Although Mayers and Smith do not discuss this conflict of interests problem, one should expect the insurance contract to play an important role in limiting the divergence of interests between the two groups. The analysis here shows that an appropriately selected insurance portfolio will increase the safety of debt and allow stockholders to capture all the additional returns from further investment. In addition, the corporation may increase both the value of its debt and the value of its stock by selecting appropriate insurance coverage. The second agency conflict considered is usually referred to as the asset substitution problem, or equivalently, as the risk shifting problem. Once a corporation has obtained debt financing, it is well known that by switching from a relatively safe investment project to a riskier one, the corporation can increase the value of its equity at the expense of its bondholders. Mayers and Smith discuss this conflict and note that rational bondholders recognize this incentive to switch and incorporate it into the bond price. As a result, an agency cost is represented in the bond price and a reduction in the corporate value. Mayers and Smith also note that one role insurance plays, in this corporate environment, is in bonding the corporation's investment decision. They suggest that the incentive to include insurance covenants in bond contracts increases with firm leverage. The analysis here shows that the asset substitution problem only exists for highly levered firms and that an indenture provision, requiring insurance, can be structured so that any incentive for risk shifting is eliminated. Thus, the model shows how insurance may be used to eliminate this agency cost. The final section of this paper presents some conclusions and comments on the role which insurance contracts play in managing corporate risk. The Basic Model Assume that there are many individuals indexed by i in the set I and that there are many firms indexed by f in the set F. There are two dates, now and then . All decisions are made now and all payoffs from those decisions are received then. The payoffs depend on which state of nature w in the set Q occurs then. First, the model is developed with two financial markets: a stock market and an insurance market. Second, the model is generalized to This content downloaded from 103.26.198.254 on Sat, 20 Sep 2014 00:05:52 AMAll use subject to JSTOR Terms and Conditions
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