Portfolio Optimization with Mental Accounts
Posted: 25 Jul 2008
Date Written: July 21, 2008
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.
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