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On the Demand for Corporate Insurance: Creating Value

Abstract

Ever since Mayers and Smith first claimed, 30 years ago, that the corporate form provides an effective hedge that allows stockholders to eliminate insurable risk through diversification, the quest to explain the corporate demand for insurance has continued. Their claim is demonstrated here so that the corporate demand for insurance may be distinguished from the individual’s demand for insurance. Then some of the determinants of the demand for corporate insurance that exist in the literature are reviewed and generalized. The generalizations show how the corporation may use insurance to solve underinvestment and risk-shifting problems; the analysis includes a new simpler proof of how the risk-shifting problem may be solved with corporate insurance. Management compensation is also introduced here and the analysis shows the conditions which motivate the corporate insurance decision. Finally, some discussion is provided concerning the empirical implications of the extant theory, the tests that have been made, and the tests that should be made going forward.

Keywords

  • Agency Cost
  • Stock Option
  • Insurance Contract
  • Corporate Insurance
  • Convertible Bond

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Notes

  1. 1.

    See Fisher (1930). The Fisher model is developed under uncertainty in MacMinn (2005).

  2. 2.

    These stock contracts form a basis for the payoff space. This rather dramatic notion of financial market instruments was introduced by Arrow (1963).

  3. 3.

    This may be demonstrated by direct calculation, but it also clearly follows by a no-arbitrage argument.

  4. 4.

    See MacMinn (2005) for more on this interpretation.

  5. 5.

    The losses could also be increasing without affecting the results in this section.

  6. 6.

    See the appendix for a derivation of the function b(a, d).

  7. 7.

    This statement must be qualified. As long as the manager’s compensation is salary and stock, the incentives are aligned with shareholders and the statement holds. We note the qualifications of the statement in a subsequent section on executive compensation.

  8. 8.

    The legal trustee for the bondholders may be treated as the single principal. It should be added that the trustee acts on behalf of the bondholders. The trustee’s problem is the selection of bond covenants that limit the divergence of interests between corporate management and the bondholders. In general, the trustee may have a problem in selecting covenants that provide a solution to the conflict because of the different risk aversion measures of the bondholders. In the two cases considered here, however, the bondholders will unanimously support a covenant that provides management with the incentive to maximize the risk-adjusted net present value of the corporation. It should also be noted that in general there may be an agency problem between the trustee and bondholders, i.e., between the agent and the principals. In the cases considered here that problem does not arise because of the unanimity.

  9. 9.

    Jensen and Meckling (1976) also define the residual loss as the dollar equivalent of the loss in expected utility experienced by the principal. Although this notion of residual loss is measurable for a particular principal, this definition poses problems when a trustee represents many principals because the residual loss of any bondholder will depend on the bondholder’s measure of risk aversion and on the proportion of the contract owned.

  10. 10.

    It may be noted that if the bond payment isbVI(0) then no underinvestment problem exists

  11. 11.

    The risk-adjusted present value of the areas denoted in figure 1 is the value for debt, equity, and agency cost.

  12. 12.

    This is the stock value without any dividend.

  13. 13.

    See Modigliani and Miller (1958).

  14. 14.

    Here it suffices to think of the payoff as being the sum of old and new project payoffs, i.e. \(\Pi (I,\xi ) = \Pi (\xi ) + \Pi _{\mathrm{v}}(I,\xi )\).

  15. 15.

    This is efficiency in the Pareto sense. An investment is socially efficient if it is not possible to make one investor better off without making another worse off.

  16. 16.

    See Green (1984) and Hirshleifer (1965) for similar statements.

  17. 17.

    For a demonstration of the relation between values, see MacMinn (1993).

  18. 18.

    One known exception to this is theorem three in MacMinn and Garven (2000).

  19. 19.

    The assumption Π > 0 for allξ ∈ Ξ simply allows the result V iV u for any insurance scheme to be used here.

  20. 20.

    See Rothschild and Stiglitz (1970) or a definition of increasing risk and MacMinn and Holtmann (1983) for a demonstration of this equivalence result.

  21. 21.

    While the quasi-rent is concave that concavity does not always suffice to make the secondorder condition hold.

  22. 22.

    Also see MacMinn (2005).

  23. 23.

    Also see (Carpenter 2000) for the effects of a convex compensation scheme on the behavior of a risk averse manager.

  24. 24.

    Tufano studies the risk management practices in the gold mining industry and finds that managers who own more stock options manage gold price risk less using forward sales, gold loans, options, and other hedging activities as measures of risk management. While this may be consistent with the Smith and Stulz model, it is also consistent with the financial market theory developed in the work by MacMinn and Page; that work does not appeal to risk aversion.

  25. 25.

    Doherty et al. (2011) provide an alternative theory of management compensation based upon game theory which creates hedging incentives that do not depend upon risk aversion, as is the case in Tufano’s work In their model, management compensation contracts combine stock options along with firing provisions resulting in a fully revealing subgame-perfect equilibrium in which the manager retains “signal” risks but hedges “noise” risks “Signal” risks represent corporate risks which convey important information concerning the firm’s future earnings prospects whereas uninformative “noise” risks do not Thus Tufano (1996) empirical finding that option-compensated managers of gold mining firms tend not to hedge gold price risk is consistent with the Doherty, Garven, and Sinclair model since gold prices are presumably “signal” risks Although Tufano does not consider other forms of corporate hedging in his analysis the Doherty Garven, and Sinclair model predicts that these very same managers who prefer not to hedge gold prices will nevertheless be quite motivated to hedge “noise” risks e.g., by purchasing property–liability insurance.

  26. 26.

    There is a deductible such that ν u = η. For any smaller deductible the boundary of the bonus event decrease with the deductible.

  27. 27.

    The proof is like that for Theorem 1 and so is omitted here.

  28. 28.

    The bonus can be used to solve the risk-shifting problem noted in the last section, e.g., see MacMinn (1992).

  29. 29.

    The fixed deferred compensation is a liability claim on the earnings of the corporation and is a claim much like that of bondholders. The analysis in MacMinn, Ren, and Han (2012) assumes that the debt and other liability claims are equal in the pecking order.

  30. 30.

    In the case of the U.S property–liability insurance industry, there is virtually no discretion regarding disclosure of reinsurance transactions since the National Association of Insurance Commissioners (NAIC) requires all U.S domiciled property–liability insurers to systematically report all reinsurance arrangements that they have with other insurers as well as specialist reinsurance companies.

  31. 31.

    However, it is possible to measure contract duration using this database; see Garven and Grace (2011).

  32. 32.

    MacMinn and Han (1990) is an exception. There, however, only liability insurance is considered.

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MacMinn, R., Garven, J. (2013). On the Demand for Corporate Insurance: Creating Value. In: Dionne, G. (eds) Handbook of Insurance. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0155-1_18

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