DR.CHENJIAZI ZHONG

Investors that follow the mean-variance portfolio (MVT) theory (Markowitz, 1952) determine optimal aggregate portfolios on the efficient frontier by balancing risk aversion and return preference. Many investors have difficulty specifying their respective “optimal” ones at times, and some investors even have more than one level of risk aversion. That said, the MVT fails to address the ultimate portfolio consumption goals to some extent. Moreover, 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 the MVT, the behavioral portfolio theory (BPT) developed by Shefrin and Statman (2000) embodies such goals, in which they consider portfolios as collections of sub-portfolios where each sub-portfolio is associated with one goal with each goal has a threshold level. Using the BPT, investors are better able to specify their level of risk aversion in units of the threshold for each of the “sub” and the probabilities of failing to reach each threshold level. 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. 

An early attempt at the BPT is 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 their respective subsistence level. Later in 1987, Lola Lopez furthered the study and introduced the SP/A theory, which is an extension of Roy’s safety-first portfolio model. Lopez (1987) describes a single account, where the portfolio is integrated into a single mental account. In practice, however, the true genius resides in the multiple account, where the portfolio is segregated into multiple mental accounts, such that covariances among mental accounts are overlooked. According to Lopez (1987), two emotions operate on the willingness to take risks: fear and hope. Both emotions function by balancing the relative weights attached to decumulative probabilities.

The mental account (MA) framework provides a “problem equivalence” among MVT, MA and risks as measured by value at risk (VaR). The generalizations of MVT and BPT via MA connect investors’ consumption goals and portfolio construction. One benefit of the MA framework is that risk aversions are specified better. On the other hand, the weaknesses 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. Moreover, MA may result in a loss in portfolio efficiency because the aggregate of optimized sub-portfolios is not always mean-variance efficient. Further, after investors specify their sub-portfolio threshold levels and probabilities, the issue may be a standard mean-variance problem with an implied risk-aversion coefficient.

The differences between BPT portfolios and MVT portfolios are significant:

1. 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.
2. Typical MVT portfolios feature large short and margined positions; by contrast, short and margin positions are uncommon in BPT portfolios (Green & Hollifield, 1992).
3. Some 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. For BPT investors, however, the parameters relevant to asset allocation are the upside potential goal relative to the downside protection goal as well as the reference points of the upside and downside goals. The curvature of the value functions is of secondary importance.
4. BPT predicts that payoff distributions of securities will feature “floors” (e.g., the floor created by a call option). There is no such prediction in MVT.
5. MVT investors have a uniform risk-averse attitude toward risk, while BPT investors have a range of attitudes towards risks and the layers/sub-portfolios of the portfolio.
6. A multi-period BPT model is also useful for analyzing risk and its relationship to time diversification. A multi-period BPT model links time to perceptions of risk and it shows how investors revise portfolios when their original aspirations are reached.

References

Green, R. C., & Hollifield, B. (1992). When will mean-variance efficient portfolios be well diversified?. The Journal of Finance, 47(5), 1785-1809. https://doi.org/10.1111/j.1540-6261.1992.tb04683.x

Lopes, L. L. (1987). Between hope and fear: The psychology of risk. In L. Berkowitz (Ed.), Advances in Experimental Social Psychology, 20, 255–295. Academic Press. https://doi.org/10.1016/S0065-2601(08)60416-5

Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77-91. https://doi.org/10.1111/j.1540-6261.1952.tb01525.x

Roy, A. D. (1952). Safety first and the holding of assets. Econometrica, 20, 431-449. http://dx.doi.org/10.2307/1907413

Shefrin, H.,. & Statman, M. (2000). Behavioral portfolio theory. The Journal of Financial and Quantitative Analysis, 35(2), 127-151. Cambridge University Press