Rebalancing According to Behavioral Portfolio Theory

Central features in behavioral portfolio theory, developed by Shefrin and Statman (2000) rest on the observation that aspirations drive risk attitudes. We invest for a chance to reach our aspirations, and risk is payment for a chance to avoid falling short of our aspirations. Investors in mean-variance theory view their portfolios as a whole and are averse to variance in returns. In contrast, investors in behavioral portfolio theory view their portfolios as separate, distinct mental accounts and are averse to shortfalls from aspirations in each. One mental account might be a “downside protection” account, maintained to avoid shortfalls from a relatively low standard of living an investor considers poverty. Another might be an “upside potential” account, maintained to avoid shortfalls from a high standard of living an investor considers riches. Shortfall aversion takes the role of risk aversion in behavioral portfolio theory, whereas variance aversion and loss aversion take that role in mean-variance portfolio theory. Investors might seem variance-averse and loss-averse in downside protection mental accounts, while they appear variance-seeking and loss-seeking in the upside potential ones. Yet investors are risk-averse in both mental accounts when risk aversion is shortfall aversion. Both mean-variance and behavioral portfolio theories address the evolution of portfolios over time, reflected in rebalancing procedures—changing allocations to stocks, bonds, and other investments in a portfolio. The optimal portfolio at the beginning of one period is not necessarily optimal at the beginning of the following period. Rebalancing at the beginning of a period consists of changing portfolio allocations from optimal allocations at the beginning of the earlier period to optimal allocations at the beginning of the current period. The behavioral rebalancing method is different, however, from the fixed-proportions rebalancing method associated with mean-variance portfolio theory. Portfolios in the fixed-proportions rebalancing method are rebalanced to proportions in the optimal mean-variance portfolio, such as 60/40, with 60 percent allocated to stocks and 40 percent to bonds. High stock returns relative to bond returns increase the relative allocations to stocks and bonds, say to 70/30. Fixed-proportions rebalancing consists of selling stocks and buying bonds in amounts necessary to restore the 60/40 proportions. To see how rebalancing is done in behavioral portfolio theory, consider a 47-year-old investor. She places human capital, Social Security benefits, and home equity in her downside-protection mental account, and its total $1.1 million at age 67 satisfies her aspiration in the downside-protection account. She places her $300,000 401(k) in a diversified stock mutual fund in her upside-potential account, expecting an approximately 8 percent annual return that will increase that amount to approximately $1.4 million. This satisfies her aspiration in the upside-potential account. Next, suppose that the return on stocks in the following year was 12 percent, higher than that 8 percent expected return, and the return on bonds was 3 percent, as expected. By mean-variance rebalancing rules, her financial planner will sell some stocks and buy bonds with the proceeds, to restore her portfolio to the predetermined fixed proportion. By behavioral rebalancing rules, however, her planner will ask if her aspiration in the downside-protection account is still satisfied at $1.1 million and, if so, let her upside-potential account grow to more than $1.4 million, with no need for rebalancing. Or, she might choose to increase her aspiration in the downside-protection account, necessitating selling some stocks and buying bonds. The same applies if the return on stocks in the following year is 4 percent, rather than the expected 8 percent. She might choose to reduce her aspiration in the upside-potential account to reflect the lower stock return, in which case no rebalancing is necessary. Or she might choose to reduce her aspiration in the downside-potential account, necessitating selling some bonds in that account and buying stocks with the proceeds in the upside-potential account.