Journal of Financial Planning: October 2018
Meir Statman, Ph.D., is the Glenn Klimek Professor of Finance at Santa Clara University and author of Finance for Normal People: How Investors and Markets Behave.
“Mommy, I cannot sleep,” says a toddler, “there are monsters under my bed.” A mother can respond in two ways. She explains to her toddler that there are no monsters under the bed, and it is not rational to believe that monsters exist. Or, she bends down, waves her hand under the bed and says, “Monsters, go away!”
The first way is the rational way, and the second is the normal way. The normal way is wiser; it’s more likely to lull the toddler to sleep. As he grows up, the toddler will know that there are no monsters under beds, but he will nevertheless choose to go the normal way when he is a father and his toddler cannot fall asleep.
I argue that what is true for parent and toddler is also true for adviser and client. Commonly offered rationales for dollar-cost averaging (DCA) are not rational, but DCA is wise when normal clients cannot fall asleep because market monsters dwell under their beds.
The DCA Puzzle
Investors with cash destined for stocks employ DCA by dividing their cash into segments and committing to convert each segment into stocks according to a predetermined schedule. The alternative to DCA is lump-sum investing—investing the entire amount in stocks today. Both logic and simulations indicate that investors are more likely to increase their wealth with lump-sum investing than with DCA, yet the practice of DCA persists. Why do investors engage in DCA? This is the DCA puzzle.
DCA is popular among investors, yet puzzling to justify within standard finance that describes investors as rational. The solution to the puzzle is in behavioral finance that describes investors as normal. The solution combines wants for utilitarian, expressive, and emotional benefits; the application of expected utility and prospect theories; the roles of cognitive and emotional shortcuts and errors; and tools for correcting errors.1
Framing Shortcuts and Errors
Consider an investor with $2,000 in cash. He has chosen to invest in stocks because stocks are likely to yield higher long-term wealth than cash, even though they also impose higher variance of wealth. This choice is consistent with expected utility theory if the investor’s variance-aversion is not too high. Yet loss-aversion, a feature of prospect theory, might deter our investor from buying stocks altogether if his aversion to potential short-term losses imposed by stocks during the coming day or week exceeds his desire for high expected long-term gains. DCA overcomes loss-aversion in a frame that highlights gains and obscures losses.
Our investor employs DCA by dividing his $2,000 cash into two segments of $1,000 each, investing one segment in shares of a stock today and committing to invest the second segment in shares of that stock on a specific day next month. He buys 20 shares today at $50 per share. Imagine that the price of shares declined subsequently to $12.50, and he buys 80 shares next month (see the table below).
Average cost of shares held at the end of the two periods: $2,000/100 = $20.
Average price at which shares were bought during the two periods: ($50 + $12.5)/2 = $31.25.
Framed the rational way, as in standard finance, our investor started with $2,000 in cash and now, a month later, owns 100 shares worth $12.50 each for a total of $1,250, implying a $750 loss. Framed the normal way, as proponents of DCA do, our investor bought 100 shares at an average cost of $20 per share, while the average price per share on the two dates, $50 and $12.50, was $31.25, implying an $11.25 per-share gain. Indeed, framed the normal way, our investor sees gains in all circumstances except when stock prices never change.
Recent descriptions of the merit of DCA are similar to Fred Weston’s classic 1949 description: “In the usual exposition of the principle of DCA, its merit is urged on the basis of a relationship that holds without exception: at any point after a fluctuation in security prices the average cost of total shares held is less than the average price of the shares.”2
Weston exposed the irrelevance of this fact to rational investors: “The crucial test is whether the shares held can at any time be sold at a gain. For this to be possible, average cost must be less than the current market price per share.”
High volatility in stock prices causes large differences between the average cost per share and the average price per share, but DCA does not change uncertainty from vice to virtue. Yet the passage of time has done little to dampen investor enthusiasm for DCA.
Pride and Regret
The normal investors of behavioral finance anticipate the emotional benefits of pride and emotional costs of regret when they make choices, knowing that the emotional costs of regret at losses exceed the emotional benefits of pride at gains of equal dollar amounts.
Normal investors with $100,000 in cash might be inclined to keep it rather than buy stocks and suffer the emotional costs of regret that accompany losses relative to the $100,000 cash reference point, if stock prices subsequently decline. Normal investors with $100,000 in stocks might be equally inclined to keep them rather than sell for cash and suffer the emotional costs of regret that accompanies opportunity losses relative to the $100,000 stock reference point, if stock prices subsequently increase.
Investors mitigate their anticipated emotional costs of regret when they convert only one part of their cash into shares of stock today. This way, they can console themselves if share prices plunge during the coming month and even enjoy the emotional benefits of pride by the thought that they can now buy shares at lower prices with the other parts of their cash.
Similarly, investors mitigate their anticipated emotional costs of regret when they convert only one part their stocks into cash today. This way, they can console themselves if share prices zoom during the coming month and even enjoy the emotional benefits of pride by the thought that they can now sell the remaining shares at higher prices.
Self-Control
Suppose an investor starts her DCA stock buying plan with the expectation that the probability of an increase in stock prices in the coming period equals the probability of a decrease. Once several decrease periods occur, the investor finds it hard to refrain from revising her expectations by extrapolating past losses into higher probabilities of future losses. The stock-buying plan that was attractive by the old probabilities might no longer seem attractive, inclining her to abandon the plan. The strict rules of DCA combat self-control lapses, compelling her to stick to the stock-buying plan.
Periodic buying of stocks is a feature of 401(k)s and similar retirement savings programs, where money is automatically deducted from paychecks to buy stocks. Such periodic buying is different from DCA in that employees do not face a choice between investing in a lump sum or in installments, as in DCA. Nevertheless, 401(k)s and similar retirement saving programs offer normal investors benefits similar to those of DCA programs. Investors frame themselves as winners because they buy shares at an average cost lower than the average price of shares over time. And automatic transfers from salary to retirement saving accounts preclude the effects of lapses of self-control.
Reverse DCA and the Risk-Reduction Rationale
A prominent feature of DCA is that it is recommended with equal force to investors with cash who consider converting it into stocks, and investors with stocks who consider converting them into cash. This feature is useful in countering the argument that the benefits of DCA are in risk reduction.
The risk of stocks, measured by the variance of returns or by the probability and amount of potential loss, is higher than that of cash. An investor with $100,000 in cash who converts his entire amount into stocks today bears more variance risk and loss risk tomorrow than when he follows DCA and converts only $50,000 into stocks today, keeping the other $50,000 in cash.
This might support the argument that the benefits of DCA are in risk reduction. Consider, however, reverse DCA. An investor with $100,000 in stocks who converts her entire amount into cash today bears less variance risk and loss risk tomorrow than when she follows reverse DCA, converting only $50,000 into cash and keeping the other $50,000 in stocks. Risk reduction cannot be the rationale for both DCA and reverse DCA.
Conclusion
Investors want the utilitarian, expressive, and emotional benefits of the high expected returns of stocks, but they also want to avoid the expressive costs of the image of being a loser and the emotional costs of regret over losses. They tend to procrastinate when advised to invest in stocks immediately in a lump sum, but are willing to invest in stocks gradually through DCA.
Prescriptions of DCA are like prescriptions of eyeglass. Eyeglasses are wrong when they distort the sight of people with perfect vision, but they are right when they improve the sight of people with poor vision. Eyeglasses correct the distortion in the sight of people with poor vision by introducing another distortion. It is a case of two wrongs that make a right.
Compare an adviser who counsels a client to convert cash into stocks in a lump sum to an adviser who counsels the client to use DCA. Lump-sum conversion from cash to stock might be optimal for rational investors, as no glasses are optimal for people with perfect vision. But such conversion is unappealing to normal investors with less-than-perfect investment vision who are deterred from action as they contemplate the regret that they would feel if the stock market were to crash as soon as their cash is converted into stocks.
DCA provides corrective “financial” glasses that lead investors to allocate portions of their wealth to stocks.
Endnotes
- See “A Behavioral Framework for Dollar-Cost Averaging,” by Meir Statman in the Fall 1995 Journal of Portfolio Management.
- See “Some Theoretical Aspects of Formula Timing Plans,” by J. Fred Weston in the October 1949 Journal of Business of the University of Chicago.