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Optimal Portfolio Insurance

Published online by Cambridge University Press:  06 April 2009

M.J. Brennan  and
R. Solanki
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Extract

The form of the Pareto optimal general insurance contract has been investigated by Borch [5], Arrow [3], and Raviv [16]. This paper extends their work to the consideration of the optimal investment portfolio insurance contract. This is a contract whose payoff depends upon the investment performance of some specified portfolio of common stocks. Portfolio insurance differs from general insurance in two important ways. First, investment portfolio insurance lacks the property of stochastic independence between losses on different contracts which is characteristic of general insurance, and this has led some actuaries to question whether portfolio insurance contracts should be sold in view of the risks they pose for the solvency of insurance companies. Recent developments in the theory of option pricing suggest, however, that under certain assumptions an insurance company will be able to eliminate the risks associated with portfolio insurance contracts by following an appropriately defined investment strategy. Secondly, there exists a market for the pricing of investment risks, the securities market; and, under appropriate assumptions, the equilibrium price of portfolio insurance contracts may be determined without specification of the preferences of insurance companies. This permits consideration of insurance company preference functions to be dispensed with, in marked contrast to the earlier literature concerned with general insurance, which treats insurance company preferences symmetrically with those of the insurance purchaser. In addition, since the characteristics of the insured portfolio are known to the insurer, and the performance of the portfolio is beyond the control of the insured, portfolio insurance is not prone to the problems of adverse selection and moral hazard which are liable to arise in general insurance.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 16 , Issue 3 , September 1981 , pp. 279 - 300
Copyright
Copyright © School of Business Administration, University of Washington 1981

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References

[1]Aitchison, J., and Brown, J.M.C.. The Lognormal Distribution. Cambridge University Press (1963).Google Scholar
[2]Arrow, Kenneth J., and Kurz, Mordecai. Public Investment, The Rate of Return and Optimal Fiscal Policy. Baltimore: Johns Hopkins Press (1970).Google Scholar
[3]Arrow, Kenneth J.Essays in the Theory of Risk Bearing. Chicago (1971).Google Scholar
[4]Black, F., and Scholes, M.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, Vol. 81 (05–06 1973), pp. 637–654.CrossRefGoogle Scholar
[5]Borch, K. “The Safety Loading of Insurance Premiums.” Skandinavisk Aktuarietidskrift. Vol. 43 (1960), pp. 163–184.Google Scholar
[6]Breeden, D.T., and Litzenberger, R. H.. “Prices of State Contingent Claims Implicit in Option Prices.” Journal of Business, Vol. 51 (10 1978), pp. 621–652.CrossRefGoogle Scholar
[7]Brennan, M.J. “The Pricing of Contingent Claims in Discrete Time Models.” Journal of Finance, Vol. 34 (03 1979), pp. 63–68.CrossRefGoogle Scholar
[8]Brennan, M.J., and Schwartz, E.S.. “The Pricing of Equity Linked Insurance Policies with an Asset Value Guarantee.” Journal of Financial Economics, Vol. 3 (06 1978), pp. 195–213.CrossRefGoogle Scholar
[9]Cox, J.C., and Ross, S.A.. “The Valuation of Options for Alternative Stochastic Processes.” Journal of Financial Economics, Vol. 3 (01/03 1976), pp. 145–166.CrossRefGoogle Scholar
[10]Grant, A.T., and Kingsnorth, G.A.. “Unit Trusts and Equity Linked Endowment Insurance.” Institute of Actuaries Journal, Vol. 93 (1967), pp. 387–421.CrossRefGoogle Scholar
[11]Heaney, W.J. “The Equilibrium Valuation Operator and Financial Market Efficiency.” Unpublished dissertation, Simon Fraser University (1979).Google Scholar
[12]Ibbotson, R., and Sinquefield, R.. “Stocks, Bonds, Bills, and Inflation: Year by Year Historical Returns.” Journal of Business, Vol. 49 (1976), pp. 11–47.CrossRefGoogle Scholar
[13]Leland, Hayne E. “Who Should Buy Portfolio Insurance?” Journal of Finance, Vol. 35 (1980).CrossRefGoogle Scholar
[14]Merton, R.C. “Optimum Consumption and Portfolio Rules in a Continuous Time Model.” Journal of Economic Theory, Vol. 3 (12 1971), pp. 373–413.CrossRefGoogle Scholar
[15]Merton, R.C. “Theory of Rational Option Pricing.” Bell Journal of Economics and Management Science, Vol. 4 (Spring 1973), pp. 141–183.Google Scholar
[16]Raviv, A. “The Design of an Optimal Insurance Policy.” American Economic Review, Vol. 69 (03 1979), pp. 84–96.Google Scholar
[17]Rothschild, M., and Stiglitz, J.. “Equilibrium in Imperfect Insurance Markets: An Essay in the Economics of Imperfect Information.” Quarterly Journal of Economics, Vol. 90 (1976), pp. 629–650.CrossRefGoogle Scholar
[18]Rubinstein, M. “The Valuation of Uncertain Income Streams and the Pricing of Options.” Bell Journal of Economics and Management Science, Vol. 7 (Autumn 1976), pp. 407–425.CrossRefGoogle Scholar
[19]Spence, M., and Zeckhauser, R.. “Insurance, Information and Individual Action.” American Economic Review, Vol. 61 (1971), pp. 380–387.Google Scholar