Making Investment Choices as Simple as Possible, but Not Simpler

Target-date funds (TDFs) for retirement, also known as life-cycle funds, are being offered as a simple solution to the investment task of participants in self-directed retirement plans. A TDF is a “fund of funds” diversified across stocks, bonds, and cash with the feature that the proportion invested in stocks is automatically reduced as time passes. Empirical evidence suggests that a simple TDF strategy would be an improvement over the choices currently made by many uninformed plan participants. This article explores a way to achieve even greater improvement for people who are very risk averse and have high exposure to market risk through their labor.Many participants in self-directed retirement plans [401(k)s, IRAs, and so forth] do not know enough about investing to choose rationally among alternatives. Others may know enough but find the task unpleasant or too time-consuming. Target-date funds (TDFs), also known as life-cycle funds, are being offered as a simple solution to these participants’ needs.A TDF is a “fund of funds” diversified across stocks, bonds, and cash with the feature that the proportion invested in stocks is automatically reduced as time passes. Empirical evidence suggests that a simple TDF strategy would be an improvement over the choices currently made by many uninformed plan participants. Therefore, in 2006 the U.S. Department of Labor proposed that TDFs be considered a “safe harbor” investment alternative for employers to offer as the default in their defined-contribution plans. The prediction is that many plan sponsors will adopt TDFs as their default option in the near future. We explore in this article one way to achieve an even greater improvement by a simple procedure for taking account of two characteristics in addition to an individual’s target retirement date and age—namely, human capital risk and risk aversion.We use a compact continuous-time optimization model with a single market portfolio of risky assets and a single asset that is safe for an individual with a given target date. People start saving for retirement with an initial wealth consisting of their financial assets and human capital. Human capital is the present value of their future labor income. Human capital is normally the largest single asset in the early part of the working life of most people, and it declines in relative importance as people age and accumulate other assets. We assume that human capital is nontradable but perfectly correlated with the market portfolio of all risky assets. The beta of human capital is its volatility relative to the market portfolio of risky assets. For example, if the individual has human capital of $1,000,000 and β = 0.4, then the human capital is equivalent to a portfolio that has $400,000 invested in the risky asset and $600,000 invested in the safe asset. We consider a range of human capital betas from 1.0 to –0.5.The individual’s preferences are represented by an expected utility function of wealth at the date of retirement characterized by a parameter of relative risk aversion, γ. Research suggests that the normal range for gamma is from 1 at the low end (people who are willing to take substantial risk to achieve higher potential consumption) to 10 at the high end (people who crave security).To quantify the welfare resulting from any investment strategy, we rely on the concept of certainty-equivalent wealth. The certainty-equivalent wealth associated with a TDF strategy is defined as the certain dollar amount that provides the individual with the same level of welfare as the expected utility from the TDF strategy. To measure the reduction in welfare caused by adopting the TDF instead of the optimal strategy for a particular person, we use the ratio of the TDF’s certainty-equivalent wealth to the optimal strategy’s certainty-equivalent wealth. A ratio of 1 (or 100 percent) implies that no welfare losses are incurred as a result of adopting the TDF strategy, so the individual would be a natural TDF holder. The lower the value of the ratio, the greater the reduction in welfare from using the TDF portfolio.We show that the TDF strategy may be far from optimal for people who, although of the same age as the natural TDF holder, differ from the natural TDF holder in their risk aversion or exposure to human capital risk. To bring such plan participants much closer to their optimal strategy, it is enough to add a second simple investment alternative—a safe fund matched to the participant’s time horizon. Participants with the same time horizon can then consider their risk aversion and human capital risk in choosing (or being advised to choose) either the TDF or the safe target-date fund. We find that people who are very risk averse and who have a high exposure to market risk through their labor income would experience a substantial gain in welfare from being offered a safe target-date fund rather than a risky one.Recent empirical research suggests that human capital betas change over one’s working career. They are typically quite high during the early years when human capital represents the largest part of total wealth for most people. Unlike the linear TDFs currently offered to participants in 401(k) plans, the proportion of the portfolio invested in risky assets should be a hump-shaped function of age to reflect the gradual change of human capital from predominantly “stocklike” to mostly “bondlike” over the life cycle.