This finding demonstrates that the market is inefficient insofar as it hasn’t priced distress risk appropriately, at least in a classical economic sense where risk and expected return should be related. The field of behavioral finance provides observers with an explanation for this anomaly. Securities with high failure probabilities have positive skewness, and individual investors—who exhibit a strong preference for positive skewness—bid up the prices of these securities, leading to low subsequent returns. Such investors accept the likelihood of negative excess returns in exchange for the small possibility of an extreme positive outcome. In other words, they have a preference for lottery-like distributions, or jackpots.

In theory, we would expect such anomalies to be arbitraged away by other investors who don’t have a preference for positive skewness. They should be willing to accept the risks of a large loss for the higher expected return that shorting overvalued assets can provide. However, in the real world, these anomalies can persist because there are limits to arbitrage. First, many institutional investors—such as pension plans, endowments and mutual funds—are prohibited by their charters from taking short positions. Second, the cost of borrowing a stock in order to short it can be expensive, and there also can be a limited supply of stocks available to short. Third, investors are often unwilling to accept the risks of shorting because of the potential for unlimited losses. This is prospect theory at work. The pain of a loss is much larger than the joy of an equal gain. And fourth, short-sellers run the risk that borrowed securities are recalled before the strategy pays off, as well as the risk that the strategy performs poorly in the short run, triggering an early liquidation.

Taken together, these factors suggest that investors may be unwilling to trade against the overpricing of skewed securities. This allows the anomaly to persist. The theory is supported by evidence that has found the “lottery effect” is strongest in stocks for which arbitrage trades may be relatively costly.

Jennifer Conrad, Nishad Kapadia and Yuhang Xing — authors of the study “Death and Jackpot: Why Do Individual Investors Hold Overpriced Stocks?,” published in the September 2014 issue of the Journal of Financial Economics — explain that the connection between high default risk and the lottery effect (what they called a high jackpot probability) can be understood by viewing equity as a call option on the assets of the firm. They write: “For firms close to the default boundary, this optionality is more important, leading to more skewed pay-off distributions.” The study covers the period from 1972 through 2009. The following is a summary of their findings:

• Stocks with a high default probability have a lottery-like distribution of returns and produce negative excess returns.
• Theory is supported by the evidence, which has found that the “lottery effect” is strongest in stocks for which arbitrage trades may be relatively costly. Low returns to jackpot stocks are associated with high limits to arbitrage in such stocks.
• Stocks with a high predicted probability of having a jackpot return subsequently earn low average returns and have negative four-factor alphas, with magnitudes similar to stocks with high default probability.
• Younger firms, firms with fewer tangible assets, lower stock market turnover and smaller stock market capitalization are more likely to have jackpot returns.
• Sixty-three percent of stocks that realize an ex-post jackpot return are in the top 1 percent of ex-ante predicted jackpot probability; 70 percent of stocks that realize a jackpot return are in the top 10 percent of predicted jackpot probability.
• Compared to the market, the “high-death” portfolio earns a return of -13.1 percent per year.
• The probabilities of high-death portfolios and jackpots are highly correlated. More than 50 percent of the firms in the highest quintile of predicted distress are also in the highest quintile of predicted jackpot.
• The degree of institutional ownership declines significantly as we move to higher default and jackpot probabilities. The preferences of individual investors are driving prices in these stocks. While owning over 80 percent of stocks, institutions own just 15 percent of high jackpot probability stocks.

The authors concluded that while the three Fama-French factors (beta, size and value) cannot explain the low average returns of high-distress stocks, a high probability of earning jackpot returns can. They also demonstrated that their findings were statistically significant.

The findings from the research indicate that investors would earn superior returns if they avoided assets with positive skewness. However, if you find that you are tempted by the siren’s call of such assets, consider doing what Ulysses did and tie yourself to the mast. If there’s no mast around, go and buy a lottery ticket. It will provide all the positive skewness you need, and will likely be far less costly.

Larry Swedroe is director of research for The BAM Alliance, a community of more than 150 independent registered investment advisors throughout the country. He has authored or co-authored 13 books, including his most recent, Think, Act, and Invest Like Warren Buffett. His opinions and comments expressed on this site are his own and may not accurately reflect those of the firm.