For example, studies have found an increase in the number of small shareholders after a split to lower a stock’s price level. And companies are well aware of this, as research has shown they’ve proactively managed share prices at a relatively constant nominal range since the Great Depression.

Academic research has sought to provide explanations for this anomalous behavior (meaning that it’s irrational from an economic perspective). One explanation is that individuals are searching for a cheap bet, as with lottery tickets, and thus find lower-priced stocks attractive. Another is that investors may perceive low-priced stocks as being closer to zero and farther from infinity. Thus, they have more upside potential and less to lose (of course, no matter how low the price is, you can always lose 100 percent of the investment). As evidence that Wall Street is well aware of investor preferences, there are even mutual funds that try to appeal to (or exploit) this behavioral anomaly by including the term “low-priced” in their names — such as the Fidelity Low-Priced Stock Fund (FLPSX) and the Royce Low Priced Stock Fund (RYLPX).

Justin Birru and Baolian Wang contribute to the literature on investor behavior with their study, Nominal Price Illusion which was published in the March 2016 issue of The Journal of Financial Economics. They supply evidence that investors do indeed exhibit a psychological bias in the manner in which they relate nominal prices to expectations of future returns. In attempting to assess expectations of upside potential, the variable on which the authors chose to focus was skewness. And to measure investors’ skewness expectations, they looked to the options market. Using the Ivy DB OptionMetrics database, their study covered the period from 1996 – 2012.

The following is a summary of their findings:

• Investors suffer from the illusion that low-priced stocks have more upside potential.
• Relative to high-priced stocks, low-priced stocks are smaller, have higher betas, lower book-to-market ratios and worse past performance. They also have higher past volatility, lower past skewness and lower trading volume and liquidity.
• Investors systematically overestimate the skewness (the lottery-like properties) of low-priced stocks and thus overpay for them. For example, investor expectations of skewness drastically increase (decrease) on the date of a stock split (reverse split) to a lower (higher) price.
• While there is a relatively strong inverse relationship between a stock’s price and skewness, this relationship is driven by the correlation of price with other firm characteristics. After controlling for firm characteristics such as size, there remains no significant relationship between price and skewness.
• Investors display increased optimism toward low-priced stocks. Specifically, the ratio of call to put open interest and volume is substantially higher for low-priced stocks than it is for high-priced stocks.
• Investors also have a preference for utilizing the leverage benefits that options provide to take lottery-like bets on these lottery-like stocks.
• The overpricing of call options increases as the underlying stock price decreases. Options on low-priced stocks are more overvalued than options on high-priced stocks. This is consistent with relative investor overestimation of skewness for low-priced stocks relative to high-priced stocks. The results are statistically significant at the one percent level.
• Consistent with the effect coming from biased investor expectations regarding the upside potential rather than downside potential of the stock, the underlying stock price is only related to the returns of out-of-the-money (OTM) calls, but not OTM puts.

The authors concluded: “Overall, the evidence is consistent with investors suffering from a nominal price illusion in which they tend to overestimate the ‘cheapness’ or ‘room to grow’ of low-priced stocks relative to high-priced stocks.” They also concluded: “Investors exhibit greater optimism toward low-priced stocks than high-priced stocks.”

Many investors may be negatively affecting their returns due to the anomalous preference for lower-priced stocks. It’s possible that this behavior is based on a rational preference for taking risks. Or, what seems more likely, it’s that investors are unaware that they are overpaying for investments with what they believe are lottery-like returns. Being aware of the research, that’s no longer an excuse.