It is well-established that “lottery” stocks – those offering the potential for outsized returns, like penny and growth stocks – deliver poor performance. While one might expect that naïve, retail investors are the ones buying those stocks, new research shows that is not the case.
Academic research has found that there are investors who have a “taste,” or preference, for lottery-like investments – investments that exhibit positive skewness and excess kurtosis. This leads them to irrationally (from a traditional finance perspective) invest in high-volatility stocks (which have lottery-like distributions), driving their prices higher, with the result being poor returns.
They pay a premium to gamble.
If the markets were perfectly efficient, arbitrageurs would drive prices to their right levels. However, in the real world, limits to arbitrage, and the costs and fear of shorting, can prevent rational investors from correcting mispricings. The low-beta/low-volatility anomaly (low-volatility/low-beta stocks have higher risk-adjusted returns than high-beta/high-volatility stocks) is an example of the lottery effect and mispricings persisting.
Lottery-like distributions have been found in IPOs, “penny stocks,” extreme high-beta stocks, small-growth stocks with low profitability and high investment, and financially distressed stocks that are either in or near bankruptcy. The preference for lottery-like payout distributions has been found in other areas, not just in the world of investing. For example, the authors of the study, Do Investors Overpay for Stocks with Lottery-like Payoffs? An Examination of the Returns on OTC Stocks, noted that when it comes to horse racing, longshots are systematically overvalued. A $1 bet on a longshot (defined as a bet with 1:100 or worse odds of winning) has an average payoff of just $0.39. The average payoff to favorites, by contrast, is $0.95.
Academic literature contains 16 measures of lottery preference, including skewness, expected skewness, maximum daily return and return asymmetry. In their June 2020 study, Lottery Preference and Anomalies, Lei Jiang, Quan Wen, Guofu Zhou and Yifeng Zhu aggregated information on the 16 measures into a single factor and examined its performance in explaining anomalies to the Fama-French five-factor (market beta, size, value, profitability and investment) model and the four-factor (market beta, size, profitability and investment) q-factor model of Hou, Xue and Zhang. Their study covered the period January 1980 to December 2018. They found that all 16 individual lottery proxies are positively correlated with total skewness – the excess return spreads and alphas between the low- and high-skew portfolios ranged from -0.31% to -0.34% per month and were statistically significant. Stocks with more lottery preference are smaller in size, are growth stocks, have higher momentum, are less liquid and have higher market beta than stocks with lower lottery preference.
They also found that return-related anomalies such as stock momentum, idiosyncratic volatility and the beta premium are significantly stronger among stocks in the highest lottery preference quintile. In addition, fundamental-related anomalies such as financial distress, asset growth and profitability (e.g., operating or gross profitability) are also much stronger among stocks with high lottery preference. Importantly, the anomaly returns are mainly driven by the short leg of the anomalies among stocks with high lottery preference – relating the anomaly to short-sale constraints. Those constraints prevent arbitrageurs from correcting mispricings (stocks with high lottery features have lower short-sale volumes on average, and investors are reluctant to short sell stocks with high lottery features, which exacerbates the mispricing of lottery stocks).
New evidence
Turan Bali, Doruk Gunaydin, Thomas Jansson and Yigitcan Karabulut contribute to the literature on the lottery anomaly with their August 2020 study, Do the Rich Gamble in the Stock Market? Low Risk Anomalies and Wealthy Households. They proposed a low-risk anomaly (LRA) index with high values, indicating high-risk stocks with high-beta, high idiosyncratic volatility and high lottery payoffs. They investigated the significance of the LRA index for U.S. equities and international equities. To understand how and why individual investors contribute to the low-risk anomalies, they then used a large-scale, individual-level panel dataset from Sweden that allowed them to directly observe the stock investments of the entire population at the individual security level. The U.S. data sample covered the period July 1963 to December 2018. The international dataset covered the period January 1988 to December 2014. Following is a summary of their findings:
- Stocks with high LRA generated low risk-adjusted returns.
- The LRA index was highly persistent – 59% (49%) of stocks in the lowest (highest) LRA decile in a certain month continued to be in the same decile one month later. Moreover, the stocks had a 75% probability of being in deciles 9 and 10, which exhibited high LRA in the portfolio formation month and lower returns (negative alpha) in the subsequent month.
- The degree of underpricing of low-LRA stocks is so small that the low-risk anomaly is driven by retail investors’ demand for high-LRA stocks, leading to temporary overpricing and negative future abnormal returns for these high-beta, high-volatility stocks with large lottery payoffs.
- The magnitude of the negative alpha spread on LRA-sorted portfolios is larger for stocks predominantly held by retail investors, whereas the return predictability disappears for stocks primarily held by institutional investors. Institutions are the main lenders of securities. Thus, underweighting of high-LRA stocks creates a shortage of securities to borrow, increasing the hurdles for arbitrageurs.
- Depending on the asset pricing model used (three-, four-, five-, six- and seven-factor models as well as the q-factor model), the alpha spreads for the long-short portfolio were all negative and economically large, ranging from -0.54% to -1.26% per month, and highly significant, with t-statistics in the range of -2.50 and -6.05. However, the anomalous negative relation between risk and future abnormal returns is only confined to those stocks held by rich households – there is no evidence of low-risk anomaly for stocks held by non-rich households and institutional investors. Specifically, the zero-cost portfolio that takes a long position in the high-LRA stocks and a short position in the low-LRA stocks that are largely held by rich investors lost -2.61% to -3.67% per month depending on the asset pricing model used to calculate the alphas. Thus, the low-risk anomalies are not explained by the market, size, value, momentum, liquidity risk, investment and profitability factors. These results are robust to the exclusion of large-cap, microcap or popular stocks as well as to the different definitions of wealthy investors.
- The skewness preferences of rich households explain the demand of wealthy investors for high-risk stocks. In contrast, other potential explanations such as the overconfidence-based preferences, constraints on financial leverage, downside risk and hedging demand received little support from the data.
- The anomalous relationship between risk and future returns is more pronounced in countries where the rich households own a larger share of the aggregate wealth.
- The low-risk anomaly is pervasive, being significant in 22 developed markets as well as G10 and G7 countries.
Bali, Gunaydin, Jansson and Karabulut noted that their finding that individual investors play an important role in low-risk anomalies raises an important question: “Given that the direct stock ownership rate across the population is particularly low (e.g., 14% in the U.S.), and even conditional on participation, the direct stock investments of individuals are highly limited (i.e., they represent 5% of the financial wealth of the average U.S. household), how can so few individual investors affect equilibrium asset prices and contribute to the asset pricing puzzles?” They hypothesized that “highly skewed distribution of wealth offers a potential explanation for the low risk anomalies – if most of the wealth is concentrated in the hands of a small number of rich households, then a small subset of individual investors can affect asset prices despite the low stock market participation rates.”
Equity wealth is concentrated
Bali, Gunaydin, Jansson and Karabulut noted that according to the U.S. Survey of Consumer Finances, households in the top 10% of the wealth distribution hold more than 85% of the aggregate (direct) stock wealth in the U.S. In addition, in terms of investments of households in individual stocks, the direct stock ownership rate is significantly smaller (around 14%). And they represent only 2.7% of the financial wealth of the average U.S. household. Internationally, the figures are comparable – if anything, even lower. For example, the direct stock ownership rate in the euro area accounts for 8.2% – approximately 11% of German households are direct stockholders, whereas this number is only 3.1% in Italy. In Sweden, where the empirical analysis was performed, households in the top 10% of the wealth distribution hold approximately 83% of the aggregate direct stock wealth, whereas they hold approximately 60% of the net wealth in Sweden.
Swedish lottery bonds
Sweden provided a particularly interesting test of the hypothesis of a lottery preference by wealthy investors. The Swedish government offers a unique lottery bond, which makes coupon payments to bondholders on the basis of lottery-like drawings – coupons received by the bondholders are purely random, offering a highly positively skewed return distribution, as with standard lotteries. Using this information, Bali, Gunaydin, Jansson and Karabulut defined those households that invest in lottery bonds in a given year as skewness-seeking investors. They found that participation in lottery bonds significantly increases (monotonically) in the net wealth of households, demonstrating that wealthier households tend to display stronger preferences for lottery-type securities.
Bali, Gunaydin, Jansson and Karabulut concluded: “Our results imply that the low-risk anomalies are mainly driven by the demand of rich households.” The conclusion you should draw is that the surest way to win the lottery-stock game is to not play!
Fund families whose investments strategies are based on academic research, such as Alpha Architect, AQR, Bridgeway and Dimensional have long excluded stocks with lottery characteristics from their eligible universe. (Full disclosure: My firm, Buckingham Wealth Partners, recommends AQR, Bridgeway and Dimensional funds in constructing client portfolios.)
Larry Swedroe is the chief research officer for Buckingham Strategic Wealth and Buckingham Strategic Partners.
Important Disclosure: The information and opinions contained in this article are for informational purposes only. While reasonable care has been taken to ensure that the information contained herein is factually correct, there are no representations or guarantees as to its accuracy or completeness. Certain information has been provided by third-party sources, and it has not been independently verified and its accuracy/completeness cannot be guaranteed. No strategy assures success or protects against loss. The discussion of specific mutual funds is not intended to serve as specific investment or financial advice. This discussion does not constitute a recommendation to purchase a single specific security, and it should not be assumed that the funds referenced herein were or will prove to be profitable. R-20-1136
Read more articles by Larry Swedroe