Portfolio Optimization with Mental Accounts

Posted: 25 Jul 2008

See all articles by Sanjiv Ranjan Das

Sanjiv Ranjan Das

Santa Clara University - Leavey School of Business

Harry Markowitz

University of California at San Diego

Jonathan Scheid

Bellatore Financial, Inc.

Meir Statman

Santa Clara University - Department of Finance

Date Written: July 21, 2008

Abstract

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 a mental accounting 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 VaR. The aggregate allocation across MA sub-portfolios 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, or setting utility losses from errors in specifying risk aversion coefficients in MVT applications. These generalizations of MVT and BPT via a united MA framework result in a fruitful connection between investor consumption goals and portfolio production.

Suggested Citation

Das, Sanjiv Ranjan and Markowitz, Harry and Scheid, Jonathan and Statman, Meir, Portfolio Optimization with Mental Accounts (July 21, 2008). Journal of Financial and Quantitative Analysis (JFQA), Forthcoming. Available at SSRN: https://ssrn.com/abstract=1166899

Sanjiv Ranjan Das

Santa Clara University - Leavey School of Business ( email )

Department of Finance
316M Lucas Hall
Santa Clara, CA 95053
United States

HOME PAGE: http://algo.scu.edu/~sanjivdas/

Harry Markowitz

University of California at San Diego ( email )

9500 Gilman Drive
La Jolla, CA 92093-0508
United States
(858) 534-3383 (Phone)

Jonathan Scheid

Bellatore Financial, Inc. ( email )

1550 The Alameda, Suite 310
San Jose, CA 95126
United States

HOME PAGE: http://www.bellatore.com

Meir Statman (Contact Author)

Santa Clara University - Department of Finance ( email )

500 El Camino Real
Santa Clara, CA 95053
United States
408-554-4147 (Phone)
408-554-4029 (Fax)

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