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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
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Abstract

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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.

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

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