Hostname: page-component-f554764f5-qhdkw Total loading time: 0 Render date: 2025-04-10T18:08:56.172Z Has data issue: false hasContentIssue false
  • English
  • Français

Normality, Solvency, and Portfolio Choice

Published online by Cambridge University Press:  06 April 2009

Robert R. Grauer
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper examines whether investors with power utility functions choose mean-variance-(MV) efficient portfolios when returns are approximately normally distributed and there is borrowing or lending at a riskless interest rate. The results show that the unlevered portfolios of power utility investors plot very closely to the MV-efficient frontier. However, there are marked differences in the mix of risky assets, regardless of whether the portfolios are highly concentrated or widely diversified. Such differences allow power investors to remain solvent even when they lever their optimal portfolios to a greater extent than “less risk-averse” MV investors who risk bankruptcy. It is concluded that the investment policies of power utility and MV investors with similar risk aversion measures are not as similar as is commonly believed. This is particularly true for high power investors, unless explicit solvency constraints are imposed on the MV problem, and for low power investors when quadratic utility approximations are made to the power utility functions. These differences in the investment policies of power utility and MV investors lead us to question the widely-accepted assertion that the assumptions of homogeneous beliefs, normality, a riskless asset, and risk-averse investors imply the simple MV CAPM where all investors, including power utility investors, hold combinations of the market portfolio and the riskless asset.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 21 , Issue 3 , September 1986 , pp. 265 - 278
Copyright
Copyright © School of Business Administration, University of Washington 1986

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

[1]Arrow, K. J. “The Theory of Risk-Bearing.” In Essays in the Theory of Risk-Bearing. Chicago: Markham Publ. Co. (1971).Google Scholar
[2]Best, M. J. “A Feasible Conjugate Direction Method to Solve Linearly Constrained Optimization Problems.” Journal of Optimization Theory and Applications, 16 (07 1975), 25–38.CrossRefGoogle Scholar
[3]Best, M. J., and Grauer, R. R.. “Capital Asset Pricing Compatible with Observed Value Weights.” Journal of Finance, 40 (03 1985), 85–103.CrossRefGoogle Scholar
[4]Cass, D., and Stiglitz, J.. “The Structure of Investor Preferences and Asset Returns, and Separability in Portfolio Selection: A Contribution to the Pure Theory of Mutual Funds.” Journal of Economic Theory, 2 (09 1970), 122–160.CrossRefGoogle Scholar
[5]Cheng, P. L., and Grauer, R. R.. “An Alternative Test of the Capital Asset Pricing Model.” American Economic Review, 70 (09 1980), 660–671.Google Scholar
[6]Fama, E. F., and MacBeth, J. D.. “Long-Term Growth in a Short-Term Market.” Journal of Finance, 29 (06 1974), 857–885.Google Scholar
[7]Grauer, R. R. “A Comparison of Growth Optimal and Mean Variance Investment Policies.” Journalof Financial and Quantitative Analysis, 16 (03 1981), 1–21.CrossRefGoogle Scholar
[8]Grauer, R. R. “Investment Policy Implications of the Capital Asset Pricing Model.” Journal of Finance, 36 (03 1981), 127–141.CrossRefGoogle Scholar
[9]Grauer, R. R., and Hakansson, N. H.. “Higher Return, Lower Risk: Historical Returns on Long-Run Actively Managed Portfolios of Stocks, Bonds and Bills, 1936–1978.” Financial Analysts Journal, 38 (03/04 1982), 39–53.CrossRefGoogle Scholar
[10]Hakansson, N. H. “Optimal Investment and Consumption Strategies under Risk for a Class of Utility Functions.” Econometrica, 38 (09 1970), 587–607.CrossRefGoogle Scholar
[11]Hakansson, N. H. “Capital Growth and the Mean-Variance Approach to Portfolio Selection.” Journalof Financial and Quantitative Analysis, 6 (01 1971), 517–557.CrossRefGoogle Scholar
[12]Hakansson, N. H. “On Optimal Myopic Portfolio Policies, with and without Serial Correlation of Yields.” Journal of Business, 44 (07 1971), 324–334.CrossRefGoogle Scholar
[13]Hakansson, N. H. “Convergence to Isoelastic Utility and Policy in Multiperiod Portfolio Choice.” Journal of Financial Economics, 1 (09 1974), 201–224.CrossRefGoogle Scholar
[14]Huberman, G., and Ross, S.. “Portfolio Turnpike Theorems, Risk Aversion, and Regularly Varying Utility Functions.” Econometrica, 51 (09 1983), 1345–1361.CrossRefGoogle Scholar
[15]Kallberg, J. G., and Ziemba, W. T.. “Comparison of Alternative Utility Functions in Portfolio Selection Problems.” Management Science, 9 (11 1983), 1257–1276.CrossRefGoogle Scholar
[16]Kroll, Y.; Levy, H.; and Markowitz, H. M.. “Mean-Variance versus Direct Utility Maximization.” Journal of Finance, 39 (03 1984), 47–75.Google Scholar
[17]Leland, H. “On Turnpike Portfolios.” In Mathematical Methods in Investment and Finance, Szego, G. P. and Shell, K., eds. Amsterdam: North Holland (1972).Google Scholar
[18]Levy, H., and Markowitz, H. M.. “Approximating Expected Utility by a Function of Mean and Variance.” American Economic Review, 69 (06 1979), 308–317.Google Scholar
[19]Lintner, J. “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.” Review of Economics and Statistics, 47 (02 1965), 13–47.CrossRefGoogle Scholar
[20]Loistl, O. “The Erroneous Approximation of Expected Utility by Means of a Taylor's Series Expansion: Analytic and Computational Results.” American Economic Review, 66 (12 1976), 904–910.Google Scholar
[21]Markowitz, H. M. “Portfolio Selection.” Journal of Finance, 7 (03 1952), 77–91.Google Scholar
[22]Markowitz, H. M.Portfolio Selection: Efficient Diversification of Investments. New York: John Wiley & Sons, Inc., (1959).Google Scholar
[23]Merton, R. C. “An Intertemporal Capital Asset Pricing Model.” Econometrica, 41 (09 1973), 867–887.CrossRefGoogle Scholar
[24]Mossin, J. “Optimal Multiperiod Portfolio Policies.” Journal of Business, 41 (04 1968), 215–229.CrossRefGoogle Scholar
[25]Naylor, T. H.; Balintfy, J. L.; Burdick, D. S.; and Chu, Kong. Computer Simulation Techniques. New York: John Wiley & Sons, Inc. (1966).Google Scholar
[26]Pratt, J. “Risk-Aversion in the Small and in the Large.” Econometrica, 32 (01–04 1964), 122–136.CrossRefGoogle Scholar
[27]Pulley, L. B. “A General Mean-Variance Approximation to Expected Utility for Short Holding Periods.” Journal of Financial and Quantitative Analysis, 16 (09 1981), 361–373.CrossRefGoogle Scholar
[28[Pulley, L. B. “Mean-Variance Approximations to Expected Logarithmic Utility.” Operations Research, 31 (07–08 1983), 685–696.CrossRefGoogle Scholar
[29]Ross, S. “Portfolio Turnpike Theorems for Constant Policies.” Journal of Financial Economics, 1 (07 1974), 171–198.CrossRefGoogle Scholar
[30]Ross, S. “Mutual Fund Separation in Financial Theory—The Separating Distributions.” Journal of Economic Theory, 17 (12 1978), 254–286.CrossRefGoogle Scholar
[31]Sharpe, W. F. “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk.” Journal of Finance, 19 (09 1964), 425–442.Google Scholar
[32]Sharpe, W. F.Portfolio Theory and Capital Markets. New York: McGraw-Hill, (1970).Google Scholar
[33]Ziemba, W. T.; Parkan, C.; and Brooks-Hill, R.. “Calculation of Investment Portfolios with Risk-Free Borrowing and Lending.” Management Science, 21 (10 1974), 209–222.CrossRefGoogle Scholar