Swedroe: Prospecting For Returns

Lottery odds don’t pay off.

Reviewed by: Larry Swedroe
Edited by: Larry Swedroe

Behavioral finance is the study of human behavior and how that behavior leads to investment errors, including the mispricing of assets. The field has provided many important insights that we can use to improve investor behavior and produce better investment results. If investors are made aware of their biases and the negative impact those are likely to have on their returns, they are more likely to change their behavior.

The field of behavioral finance has gained an increasing amount of attention in academia over the past 15 years or so as more pricing anomalies have been discovered. Pricing anomalies present a problem for believers in the efficient markets hypothesis. Among the many anomalies uncovered is that individual investors have a preference (or taste) for gambling when buying individual stocks.

Prospect Theory

For example, research has found that individuals prefer stocks with low nominal prices, high volatility (and high beta) and high positive skewness (returns to the right of the mean are fewer but further from it than returns to the left of the mean, like a lottery ticket).

This preference for gambling can be explained by prospect theory, which is a behavioral model describing how people decide between alternatives that involve risk and uncertainty (e.g., the likelihood, expressed as a percentage, of a gain or a loss). Prospect theory is about how our attitudes toward risks concerning gains may be quite different from our attitudes toward risks concerning losses, indicating that people are loss-averse.

Because people dislike losses more than they derive joy from an equivalent gain, they are more willing to take risks to avoid a loss. This preference leads individuals to overweight the tails of a return distribution, explaining the widespread preference for lotterylike gambles.

Prospect theory helps explain findings in the research showing poor average returns to IPO stocks, distressed stocks, high-volatility equities and “penny stocks” sold in over-the-counter markets and out-of-the-money options. These assets all have positively skewed returns. It can also explain the well-documented lack of diversification in many household portfolios.

An Empirical Study
Nicholas Barberis, Abhiroop Mukherjee and Baolian Wang contribute to the literature on investor behavior and pricing anomalies with their paper, “Prospect Theory and Stock Returns: An Empirical Test,” which appears in the November 2016 issue of The Review of Financial Studies.

They hypothesized: “For many investors, their mental representation of a stock is given by the distribution of the stock’s past returns. The most obvious reason why people might adopt this representation is because they believe the past return distribution to be a good and easily accessible proxy for the object they are truly interested in, namely the distribution of the stock’s future returns.” More sophisticated (institutional) investors would consider the potential future distribution of returns.

Prospect theory suggests that investors would prefer securities with a high-prospect-theory value (meaning they exhibit positive skewness, like a lottery ticket) and thus tilt their portfolios to such assets and away from stocks with low-prospect-theory value. Based on this hypothesis, Barberis, Mukherjee and Wang predicted that “stocks with high prospect theory values (exhibiting positive skewness) will have low subsequent returns, on average, while stocks with low prospect theory values will have high subsequent returns.”


The intuition is that “stocks with high prospect theory values are appealing to some investors; these investors tilt toward these stocks in their portfolios, causing them to become overvalued and to earn low subsequent returns.” The authors also noted we should expect the prediction about returns to hold more strongly among stocks that are more heavily traded by less sophisticated individual (versus institutional) investors, for example, among small-cap stocks.

To test their premise, the authors’ metric was the distribution of monthly returns over the past five years in excess of the market’s return. Their U.S. database consisted of all equities for which 60 months of data was available and covered the period 1926 through 2010. The results were consistent with their hypothesis.

They write: “We find that the coefficient on the stock’s prospect theory value, averaged across all the monthly regressions, is significantly negative: stocks with higher prospect theory values have lower subsequent returns. We also find, again consistent with our framework, that this result is particularly strong among small-cap stocks.”

Furthermore, the alphas on the portfolios they constructed decline in a near-monotonic fashion as they moved from portfolios with the lowest prospect theory value to the highest. In addition, consistent with prior research on limits to arbitrage and the role they play in allowing anomalies to persist, the authors also found that the “predictive power of prospect theory value for subsequent stock returns is stronger among stocks that are less subject to arbitrage—for example, among illiquid stocks and stocks with high idiosyncratic volatility.”

Their findings were consistent across 46 international markets they tested. And the results were robust over the two subperiods studied. They were also robust after controlling for exposure to well-known factors such as size, value, momentum, illiquidity and idiosyncratic volatility.

For investors, the implications of findings from studies into behavioral finance are striking. The combination of investor preference for skewness and limits to arbitrage can result in an equilibrium that leads to overpriced, positively skewed stocks. And price premiums caused by skewness preferences will underperform stocks that are not positively skewed.

These findings have implications for portfolio construction as well. First, investors buying individual stocks should avoid those with lotterylike characteristics. Second, mutual funds can improve performance by screening out stocks with these negative characteristics.

Larry Swedroe is the director of research for The BAM Alliance, a community of more than 140 independent registered investment advisors throughout the country.


Larry Swedroe is a principal and the director of research for Buckingham Strategic Wealth, an independent member of the BAM Alliance. Previously, he was vice chairman of Prudential Home Mortgage.