Journal of Financial Planning: February 2018
Meir Statmen, Ph.D., is the Glenn Klimek professor of finance at Santa Clara University’s Leavy School of business and the author of Finance for Normal People: How Investors and Markets Behave.
The stock market has climbed so very high. This might have you asking, “Should I rebalance my clients’ portfolios?” Mean-variance portfolio theory says you should rebalance, selling stocks and buying bonds. Behavioral portfolio theory says you may not need to rebalance, but if you do, behavioral rebalancing is different from mean-variance rebalancing.
Central features in behavioral portfolio theory 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.
Aspirations are broader and less specific than goals. We aspire to riches, but do not necessarily specify “the number” to reach by retirement. We aspire to avoid poverty, but do not necessarily specify the dollar amount that would suffice.
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.
The mental accounting structure of behavioral portfolios is reflected in “core and satellite” and “risk budget” portfolios composed of a well-diversified core mental account geared to downside protection, and a less diversified satellite mental account geared to upside potential.
Loss Aversion and Shortfall Aversion
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.
To see the difference between loss aversion and shortfall aversion, imagine an investment with a 50/50 chance to win or lose $1,000. Do you accept? Now imagine that you own another investment with a $1,000 “paper loss,” meaning you are offered a 50/50 chance to break even by winning $1,000, but also a 50/50 chance of losing an additional $1,000. Do you accept?
Most people reject a 50/50 chance to win or lose $1,000. This choice illustrates “risk” as “loss,” and “risk aversion” as “loss aversion,” consistent with the observation that the pain of losing $1,000 is greater than the joy of winning $1,000. In the typical example, people accept such offers only if the amount they can win is at least double the amount they can lose.
Yet most people with a $1,000 paper loss accept a 50/50 chance to break even by winning $1,000, or losing an additional $1,000, rather than realizing their $1,000 loss. This choice illustrates “risk” as “shortfall,” and “risk aversion” as “shortfall aversion,” consistent with the observation that people are eager for a chance to break even, avoiding shortfalls from their “reference point,” even if such chance is accompanied by potential of further losses. The reference point in this example is the amount people had before the $1,000 paper loss. Generally, the reference point is an aspiration, and shortfall aversion is aversion to falling short of that aspiration.
Shortfall aversion interacts with loss aversion, illustrated by the choice to buy a lottery ticket. The choice to buy a $1 lottery ticket is inconsistent with loss aversion. Loss aversion implies that people would be averse to the potential of losing $1 paid for a lottery ticket, even if the expected value of the payoff equals $1. They would be even more averse to buying such lottery ticket given that, in fact, the expected value of the payoff is much lower than $1.
Yet, consider a person with a high aspiration of $100,000, but with no assets other than $1. Shortfall aversion might overcome loss aversion in this person, leading him to buy the lottery ticket. Suppose that the probability to win $100,000 is 1/200,000 implying an expected value of payoff of only 50 cents. Yet a 1/200,000 probability of avoiding shortfall from a $100,000 aspiration is higher than the zero probability of avoiding shortfall with the $1 he keeps in his pocket. A person with lower aspirations than $100,000, however, might choose to keep the $1 in his pocket.
Shortfalls from Aspirations
Aspirations come from circumstances, like poverty or job loss, and from personality traits, like competitiveness or status-seeking. We can reduce shortfalls by improving our situations or lowering our aspirations, but we are constrained by both external and internal forces. Externally, we may lack the ability to improve our situations, unable to avoid shortfalls from downside-protection aspirations, such as for adequate food and shelter. Internally, our objective situations might be high but competitiveness or status-seeking push our aspirations even higher, away from realistic levels.
A person with a job might avoid shortfalls from aspirations in his downside-protection mental account if his aspirations rise no higher than the benefits of his current salary. But a person who has lost that job likely perceives shortfall from his aspirations. He might reduce that shortfall by lowering his aspirations to his lower situation. Or he might act to reduce his shortfall in the downside-protection mental account by switching jobs or careers, narrowing or eliminating his shortfall if he succeeds, but widening it if he fails.
A person might be assessed objectively as wealthy, among the top 1 percent of residents of her country. Yet competitive or status-seeking personality traits might lead her to perceive a shortfall from her aspiration in the upside-potential mental account. She might act, such as by investing all her wealth in a new venture that will narrow or eliminate the shortfall if successful, ascending to the top 0.1 percent, but exposing herself to wider shortfall, descending to the bottom 20 percent, if she fails.
Rebalancing Behavioral Portfolios
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.
Two rationales are offered for fixed-proportions rebalancing. First, investors who have chosen 60/40 portfolios have declared that their optimal portfolio on the mean-variance frontier is 60/40. This portfolio balances optimally their desire for high expected returns against their aversion to variance. Portfolios with other proportions are suboptimal for 60/40 investors. The second rationale for fixed-proportions rebalancing is built on the claim that returns are mean-reverting.
To see how rebalancing is done in behavioral portfolio theory, consider a 47-year-old investor with $300,000 in a diversified stock mutual fund in her 401(k) and $100,000 in home equity. She plans to retire at 67. The value of her human capital at age 67—reflecting accumulation from savings invested in bonds at an annual 3 percent return until age 67—is $500,000. The lifetime value of her Social Security benefits at age 67 is $400,000. Imagine further that she expects the value of her home equity to reach $200,000 when she is 67, implying an annual appreciation of approximately 3.5 percent.
Our investor 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.
The Work of Advisers
Regular rebalancing to fixed proportions does what is prescribed by mean-variance portfolio theory, and more.
First, it facilitates commingled transfers of money from stock and bond accounts to cash accounts for clients’ spending. Clients commonly prefer to spend from cash accounts because spending from stock and bond accounts opens the door to regret, if stocks or bonds boom soon after they are sold. Regular transfers lessen responsibility for timing the sale of stocks and bonds, thereby reducing likelihood of regret.
Second, regular rebalancing facilitates commingled withdrawals paying planner fees, making such withdrawals less transparent than if not commingled with rebalancing.
Third, rebalancing demonstrates to clients that planners “work” to serve them. Clients commonly wonder what work planners do for the fees they charge and see “procedures,” such as trading associated with rebalancing, as more valuable than “talk,” such as advice, including advice to refrain from rebalancing.
Behavioral rebalancing suffers the disadvantage that, at times, it involves no rebalancing and no “procedures” of selling or buying. On the advantages side, behavioral rebalancing highlights the need for planners to engage clients in conversations about changes in situations and aspirations before proceeding to rebalancing decisions.
Behavioral rebalancing is likely to lead to increasing share of the upside-potential mental account relative to the downside-protection one. Behavioral rebalancing is also likely to increase allocations to stocks relative to bonds over time if clients’ downside-protection mental accounts are heavy in bonds, and their upside-potential accounts are heavy in stocks. This is because, on average, stock returns exceed bond returns.
Planners can help retired clients to use ample upside-potential accounts to increase their standard of living, transferring some funds from the upside-potential accounts to the downside-protection ones, or begin distributing some money in the upside-potential accounts to family and charities.