Investors that follow mean-variance portfolio theory (MVT) by Markowitz (1952) determine optimal aggregate portfolios on the efficient frontier by balancing risk aversion and return preference. In fact, investors have difficulty specifying their respective “optimal” ones at times. In particular, some investors have more than one level of risk aversion, in another word, MVT to some extent fails to address the ultimate portfolio consumption goals. In addition, variance offers investors very little intuitive meaning, which adds to the likelihood of mis-specifying “optimals.” Portfolio inefficiency that arises from investors’ inability to specify accurate mean-variance trade-offs could be very large.
Unlike MVT, the behavioral portfolio theory (BPT) developed by Shefrin and Statman (2000) embodies such goals, in which they consider portfolios as collections of subportfolios where each subportfolio is associated with one goal with each goal has a threshold level. With that said, investors are better able to specify their level of risk aversion in units of threshold for each of the “sub” and the probabilities of failing to reach each threshold level. Although the portfolios constructed with a series of mean-variance efficient subportfolios are also mean-variance efficient, they are not optimized by the rules of MVT. To be more specific, when a few constraints such as short selling are placed, aggregates of subportfoikos will not be efficient.
An early attempt at BPT was the well-known Safety-First Portfolio Theory (Roy 1952), where that investors minimizing the probability of failure is defined as when their wealth falls below respective subsistence level (S). Later in 1987, Lola Lopez furthered the study with the introduction of SP/A theory, which can be regarded as an extension of Roy’s safety-first portfolio model. In the work, Lopez describes a single account (BPT-SA), where the portfolio is integrated into a single mental account. In reality, however, the true genius resides in the multiple account (BPT-MA), where the portfolio is segregated into multiple mental accounts, such that covariances among mental accounts are overlooked. According to Lopez, two emotions operate on the willingness to take risk: fear and hope, and both emotions function by balancing the relative weights attached to decumulative probabilities.
The Mental Account Framework
The mental account framework (MA) provides a “problem equivalence” among MVT, MA, and risk as measured by VaR. The generalizations of MVT and BPT via MA manage to connect investors’ consumption goals and portfolio construction.
The features of the MA framework include the probability of failing to reach the threshold level in each mental account, and the attitudes toward risk that vary by account. One benefit of such framework is that risk aversions are specified better (the research by Sanjiv Das, Harry Markowitz, Jonathan Scheid, and Meir Statman has found that the losses are in the range of 5 to 40 bps when investors mis-specify their risk aversion, and losses are higher for investors who are less risk averse).
However, MA may result in a loss in portfolio efficiency because the aggregate of optimized subportfolios is not always mean-variance efficient. Beyond that, it is important to note that after investors specify their subportfolio threshold levels and probabilities, the issue may be a standard mean-variance problem with an implied risk-aversion coefficient.
The Construction of Behavioral Portfolio
A behavioral portfolio is like a pyramid with distinct layers: each layer has a well-defined goal, with the base layer designed to prevent financial disaster, and the upper layer to maximize returns. This kind of design also incorporates the structure of Prospect Theory and Lopes’ Two Factor Theory.
Behavioral Portfolio vs. Mean-Variance Framework
The home bias, which refers to the finding that American investors hold more U.S. stocks and fewer foreign stocks than the amounts predicted by mean-variance optimization, is consistent for both MVT and BPT investors, although it is more prominent within the MVT framework. The differences between the two are relatively significant:
- MVT investors evaluate a security about its mean return, variance, and covariance with others; BPT investors are more concerned about the shape of the entire return distribution.
- Typical MVT portfolios feature large short and margined positions; by contrast, short and margin positions are uncommon in BPT portfolios (Green and Hollifield, 1992).
- Investment consultants argue that investors who prefer more aggressive portfolios increase the ratio of stocks to bonds, and attitudes toward risk in the CAPM are reflected only in the proportion allocated to the risk-free asset; however, for BPT investors, the parameters that are relevant to asset allocation are the relative importance of the upside potential goal relative to the downside protection goal, and the reference points of the upside and downside goals. The curvature of the value functions is of secondary importance.
- BPT predicts that payoff distributions of securities will feature “floors,” for instance, the floor created by a call option, but there is no such prediction in mean-variance portfolio theory.
- MVT investors have a uniform risk-averse attitude toward risk; BPT investors have a range of attitudes towards risk, attitudes that across the layers/subportfolios of the portfolio.
- Blume and Easley (1992) model implies that BPT investors are likely to lose wealth to mean-variance investors over the long run.
- A multi-period BPT model is also useful for analyzing risk and its relationship to time diversification. A multi-period BPT model would link time to perceptions of risk and show how investors revise portfolios when their original aspirations are reached.
- Probability weighting and reference point effects involving gains and losses, psychophysics, emotions, and aspirations (Kahneman and Tversky, 1979; Lopez, 1987)
- Mental accounting (Thaler, 1985, 2000)
- Ambiguity aversion (Fox and Tversky, 1995; Health and Tversky, 1991)
- Status quo bias (Mitchell, Mottola, Utkus, and Yamaguchi, 2006)
- The disposition effect (Shefrin and Statman, 1985)
- The attention hypothesis (Barber and Odean, 2008)
- Lack of diversification (Benartzi and Thaler, 2001; Goetzmann and Kumar, 2008)
- Realization and evaluation utility (Barberis and Xiong, 2008)
- Insufficient saving due to a lack of self-control (Shefrin and Thaler 1988, Benartzi and Thaler 2007)