Handbook of Portfolio Construction pp 97-123 | Cite as

# Markowitz’s Mean–Variance Rule and the Talmudic Diversification Recommendation

## 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.

## Keywords

Risk Aversion Versus Strategy Institutional Investor Investment Strategy Relative Risk Aversion## 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.Google Scholar
- 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.CrossRefGoogle Scholar - Bazaraa, M., and Shetty, C.M. (1979), “Nonlinear Programming – Theory and Algorithms,” Wiley, New York.Google Scholar
- Benartzi, S., and Thaler, R.H. (2001), “Naive Diversification Strategies in Defined Contribution Saving Plans,”
*American Economic Review, 91*, 79–98.CrossRefGoogle Scholar - 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.CrossRefGoogle Scholar - 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.CrossRefGoogle Scholar - 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.Google Scholar - 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.CrossRefGoogle Scholar - Frost, P.A., and Savarino, J.E. (1988), “For Better Performance: Constrain Portfolio Weights,”
*Journal of Portfolio Management, 5*, 29–34.CrossRefGoogle Scholar - Green, R.C., and Hollifield, B. (1992), “When will mean–variance efficient portfolios be well diversified?,”
*Journal of Finance, 47*, 1785–1809.CrossRefGoogle Scholar - Jagannathan, R., and Ma, T. (2003). “Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps,”
*Journal of Finance, 58*, 1651–1683.CrossRefGoogle Scholar - Kandel, S., and Stambaugh, R. (1991), “Asset Returns and Intertemporal Preferences,”
*Journal of Monetary Economics, 27*, 39–71.CrossRefGoogle Scholar - Kroll, Y., Levy, H., and Markowitz, H.M. (1984). “Mean–Variance Versus Direct Utility Maximization,”
*Journal of Finance, 39*, 47–61.CrossRefGoogle Scholar - 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.Google Scholar - Levy, H. (1978), “Equilibrium in an Imperfect Market: A Constraint on the Number of Securities in the Portfolio,”
*American Economic Review, 64*, 643–659.Google Scholar - Levy, H. (1983), “The Capital Asset Pricing Model: Theory and Empiricism,”
*The Economic Journal, 93*, 145–165.CrossRefGoogle Scholar - Levy, H. (2006), “Stochastic Dominance: Investment Decision Making Under Uncertainty,” 2nd edition, Springer, New York.Google Scholar
- Levy, H., and Markowitz, H.M. (1979), “Approximating Expected Utility by a Function of Mean and Variance,”
*American Economic Review, 69*, 308–317.Google Scholar - Levy, H., and Sarnat, M. (1972), “Investment and Portfolio Analysis,” Wiley Series in Finance, New York.Google Scholar
- Lintner, J. (1965), “Security Prices, Risk, and the Maximal Gains from Diversification,”
*Journal of Finance, 20*, 587–615.CrossRefGoogle Scholar - Markowitz, H.M. (1952a), “Portfolio Selection,”
*Journal of Finance, 7*, 77–91.CrossRefGoogle Scholar - Markowitz, H.M. (1952b), “The Utility of Wealth,”
*Journal of Political Economy, 60*, 151–156.CrossRefGoogle Scholar - Markowitz, H.M. (1991), “Foundation of Portfolio Theory,”
*Journal of Finance, 7*, 469–477.CrossRefGoogle Scholar - Merton, R. (1987), “An Equilibrium Market Model with Incomplete Information,”
*Journal of Finance, 42*, 483–510.CrossRefGoogle Scholar - Sharpe, W.F. (1964), “Capital Asset Prices: A Theory of Market Equilibrium,”
*Journal of Finance, 19*, 425–442.CrossRefGoogle Scholar - Von-Neumann, J., and Morgenstern, O. (1953), “Theory of Games and Economic Behavior,” 3rd edition, Princeton University Press, Princeton, NJ.Google Scholar
- Zweig, J. (1998), “Five Investing Lessons from America’s Top Pension Funds,”
*Money*(January), 115–118.Google Scholar