Hostname: page-component-6766d58669-nf276 Total loading time: 0 Render date: 2026-05-15T06:31:33.136Z Has data issue: false hasContentIssue false
  • English
  • Français

Portfolio Optimization with Mental Accounts

Published online by Cambridge University Press:  19 February 2010

Sanjiv Das ,
Harry Markowitz ,
Jonathan Scheid  and
Meir Statman
Sanjiv Das
Affiliation:
Leavey School of Business, Santa Clara University, 500 El Camino Real, Santa Clara, CA 95053. srdas@scu.edu
Harry Markowitz
Affiliation:
Rady School of Management, University of California San Diego, 9500 Gilman Dr., La Jolla, CA 92093. harryhmm@aol.com
Jonathan Scheid
Affiliation:
Bellatore, 333 W. San Carlos St., San Jose, CA 95110. jscheid@bellatore.com
Meir Statman
Affiliation:
Leavey School of Business, Santa Clara University, 500 El Camino Real, Santa Clara, CA 95053 and Tilburg University. mstatman@scu.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

We integrate appealing features of Markowitz’s mean-variance portfolio theory (MVT) and Shefrin and Statman’s behavioral portfolio theory (BPT) into a new mental accounting (MA) framework. Features of the MA framework include an MA structure of portfolios, a definition of risk as the probability of failing to reach the threshold level in each mental account, and attitudes toward risk that vary by account. We demonstrate a mathematical equivalence between MVT, MA, and risk management using value at risk (VaR). The aggregate allocation across MA subportfolios is mean-variance efficient with short selling. Short-selling constraints on mental accounts impose very minor reductions in certainty equivalents, only if binding for the aggregate portfolio, offsetting utility losses from errors in specifying risk-aversion coefficients in MVT applications. These generalizations of MVT and BPT via a unified MA framework result in a fruitful connection between investor consumption goals and portfolio production.

Information

Type
Research Articles
Information
Journal of Financial and Quantitative Analysis , Volume 45 , Issue 2 , April 2010 , pp. 311 - 334
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2010

References

Alexander, G. J., and Baptista, A. M.. “Active Portfolio Management with Benchmarking: Adding a Value-at-Risk Constraint.” Journal of Economic Dynamics and Control, 32 (2008), 779–820.CrossRefGoogle Scholar
Alexander, G. J.; Baptista, A. M.; and Yan, S.. “Mean-Variance Portfolio Selection with ‘At-Risk’ Constraints and Discrete Distributions.” Journal of Banking and Finance, 31 (2007), 3761–3781.CrossRefGoogle Scholar
Baptista, A. M. “Optimal Delegated Portfolio Management with Background Risk.” Journal of Banking and Finance, 32 (2008), 977–985.CrossRefGoogle Scholar
Barsky, R. B.; Juster, F. T.; Kimball, M. S.; and Shapiro, M. D.. “Preference Parameters and Behavioral Heterogeneity: An Experimental Approach in the Health and Retirement Study.” Quarterly Journal of Economics, 112 (1997), 537–579.CrossRefGoogle Scholar
Basak, S., and Shapiro, A.. “Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices.” Review of Financial Studies, 14 (2001), 371–405.CrossRefGoogle Scholar
Brunel, J. L. P. “How Sub-Optimal—If at All—Is Goal-Based Asset Allocation?” Journal of Wealth Management, 9 (2006), 19–34.CrossRefGoogle Scholar
De Giorgi, E.; Hens, T.; and Mayer, J.. “A Behavioral Foundation of Reward-Risk Portfolio Selection and the Asset Allocation Puzzle.” Working Paper, University of Lugano (2005).Google Scholar
DeMiguel, V.; Garlappi, L.; and Uppal, R.. “Optimal versus Naive Diversification: How Inefficient Is the 1/N Portfolio Strategy?” Review of Financial Studies, 22 (2009), 1915–1953.CrossRefGoogle Scholar
Huang, C.-F., and Litzenberger, R.. Foundations for Financial Economics. New York, NY: North-Holland (1988).Google Scholar
Jaeger, S.; Rudolf, M.; and Zimmermann, H.. “Efficient Shortfall Frontier.” Zeitschrift for betriebswirtschaftliche Forschung, 4 (1995), 355–365.Google Scholar
Levy, H., and Markowitz, H.. “Approximating Expected Utility by a Function of Mean and Variance.” American Economic Review, 69 (1979), 308–317.Google Scholar
Markowitz, H. “Portfolio Selection.” Journal of Finance, 7 (1952), 77–91.Google Scholar
Markowitz, H. “Investment for the Long Run: New Evidence for an Old Rule.” Journal of Finance, 31 (1976), 1273–1286.CrossRefGoogle Scholar
Markowitz, H. “Nonnegative or Not Nonnegative: A Question about CAPMs.” Journal of Finance, 38 (1983), 283–295.CrossRefGoogle Scholar
Markowitz, H. “Foundations of Portfolio Theory.” Journal of Finance, 46 (1991), 469–477.CrossRefGoogle Scholar
Mehra, R., and Prescott, E.. “The Equity Premium: A Puzzle.” Journal of Monetary Economics, 15 (1985), 145–161.CrossRefGoogle Scholar
Sharpe, W.; Alexander, G.; and Bailey, J.. Investments, 6th ed.Upper Saddle River, NJ: Prentice Hall (1999).Google Scholar
Shefrin, H., and Statman, M.. “Behavioral Portfolio Theory.” Journal of Financial and Quantitative Analysis, 35 (2000), 127–151.CrossRefGoogle Scholar
Telser, L. “Safety First and Hedging.” Review of Economic Studies, 23 (1956), 1–16.CrossRefGoogle Scholar