Abstract
Markowitz’s breakthrough Mean–Variance theoretical article is the foundation of the CAPM and many other models in economics and finance. But the Mean–Variance rule is also widespread in practice, and this is the focus of this paper. While expected utility theory and Markowitz’s classical diversification theory assert that the optimal diversification depends on the joint distribution of returns, experiments reveal that subjects tend to ignore the joint distribution and adopt the naïve investment strategy called the “1 ∕ N rule,” which assigns an equal weight to each security the subjects face. We test the efficiency of the “1 ∕ N rule” and find that in in-sample, its employment induces a substantial expected utility loss. However, the out-of-sample case, which is the relevant framework for investors, reveals a relatively small loss and in many cases a gain. The advantage of the “1 ∕ N rule” in the out-of-sample analysis is that it is not exposed to estimation errors.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arrow, K.J. (1971), “Essays in the Theory of Risk-Bearing,” Makham Publishing Company, Chicago, IL.
Barber, B.M., and Odean, T. (1999), “Trading is Hazardous to Your Wealth: The Common Stock Investment Performance of Individual Investors,” Journal of Finance, 55, 773–806.
Bazaraa, M., and Shetty, C.M. (1979), “Nonlinear Programming – Theory and Algorithms,” Wiley, New York.
Benartzi, S., and Thaler, R.H. (2001), “Naive Diversification Strategies in Defined Contribution Saving Plans,” American Economic Review, 91, 79–98.
Best, M.J., and Grauer, R.R. (1991), “On the Sensitivity of Mean–Variance–Efficient Portfolios to Changes in Asset Means: Some Analytical and Computational Results,” Review of Financial Studies, 4, 315–342.
Blume, M.E., and Friend, I. (1975), “The Asset Structure of Individual Portfolios and Some Implications for Utility Functions,” Journal of Finance, 30, 585–603.
Blume, M.E., Crocket, J., and Friend, I. (1974), “Stock Ownership in the United States: Characteristics and Trends,” Survey of Current Business, 54, 16–40.
Frost, P.A., and Savarino, J.E. (1986), “An Empirical Bayes Approach to Efficient Portfolio Selection,” Journal of Financial and Quantitative Analysis, 21, 293–305.
Frost, P.A., and Savarino, J.E. (1988), “For Better Performance: Constrain Portfolio Weights,” Journal of Portfolio Management, 5, 29–34.
Green, R.C., and Hollifield, B. (1992), “When will mean–variance efficient portfolios be well diversified?,” Journal of Finance, 47, 1785–1809.
Jagannathan, R., and Ma, T. (2003). “Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps,” Journal of Finance, 58, 1651–1683.
Kandel, S., and Stambaugh, R. (1991), “Asset Returns and Intertemporal Preferences,” Journal of Monetary Economics, 27, 39–71.
Kroll, Y., Levy, H., and Markowitz, H.M. (1984). “Mean–Variance Versus Direct Utility Maximization,” Journal of Finance, 39, 47–61.
Kroll Y., Levy H., and Rapoport A. (1988), “Experimental Tests of the Separation Theorem and the Capital Asset Pricing Model,” American Economic Review, 78, 500–519.
Levy, H. (1978), “Equilibrium in an Imperfect Market: A Constraint on the Number of Securities in the Portfolio,” American Economic Review, 64, 643–659.
Levy, H. (1983), “The Capital Asset Pricing Model: Theory and Empiricism,” The Economic Journal, 93, 145–165.
Levy, H. (2006), “Stochastic Dominance: Investment Decision Making Under Uncertainty,” 2nd edition, Springer, New York.
Levy, H., and Markowitz, H.M. (1979), “Approximating Expected Utility by a Function of Mean and Variance,” American Economic Review, 69, 308–317.
Levy, H., and Sarnat, M. (1972), “Investment and Portfolio Analysis,” Wiley Series in Finance, New York.
Lintner, J. (1965), “Security Prices, Risk, and the Maximal Gains from Diversification,” Journal of Finance, 20, 587–615.
Markowitz, H.M. (1952a), “Portfolio Selection,” Journal of Finance, 7, 77–91.
Markowitz, H.M. (1952b), “The Utility of Wealth,” Journal of Political Economy, 60, 151–156.
Markowitz, H.M. (1991), “Foundation of Portfolio Theory,” Journal of Finance, 7, 469–477.
Merton, R. (1987), “An Equilibrium Market Model with Incomplete Information,” Journal of Finance, 42, 483–510.
Sharpe, W.F. (1964), “Capital Asset Prices: A Theory of Market Equilibrium,” Journal of Finance, 19, 425–442.
Von-Neumann, J., and Morgenstern, O. (1953), “Theory of Games and Economic Behavior,” 3rd edition, Princeton University Press, Princeton, NJ.
Zweig, J. (1998), “Five Investing Lessons from America’s Top Pension Funds,” Money (January), 115–118.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Levy, H., Duchin, R. (2010). Markowitz’s Mean–Variance Rule and the Talmudic Diversification Recommendation. In: Guerard, J.B. (eds) Handbook of Portfolio Construction. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-77439-8_4
Download citation
DOI: https://doi.org/10.1007/978-0-387-77439-8_4
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-77438-1
Online ISBN: 978-0-387-77439-8
eBook Packages: Business and EconomicsEconomics and Finance (R0)