The MAX Anomaly Revisited: What New Research Reveals About Lottery Stock Investing

If you’ve been following behavioral finance research, you’ve probably heard about the “MAX anomaly”—the puzzling finding that stocks with extreme positive daily returns tend to underperform going forward. The standard explanation? Retail investors love lottery-like stocks and overpay for them. Turan Bali, Baris Ince, and Han Ozsoylev, authors of the January 2026 study “MAX on Steroids: A New Measure of Investor Attraction to Lottery Stocks,” re-examines the economic underpinnings of the MAX anomaly, challenges this conventional wisdom on both empirical and conceptual grounds, and introduces a cleaner way to capture genuine lottery-seeking behavior.

What the Researchers Examined

The authors took a fresh look at the MAX anomaly which was originally documented by Turan Bali, Nusret Cakici, and Robert Whitelaw in their 2010 study “Maxing Out: Stocks as Lotteries and the Cross-Section of Expected Returns.” The MAX measure calculates the average of a stock’s five highest daily returns in a month. Stocks with high MAX values have historically delivered poor subsequent returns, which has been interpreted as evidence that investors overpay for lottery-like characteristics.

But here’s the twist: Bali, Ince, and Ozsoylev questioned whether MAX actually captures what it’s supposed to capture—idiosyncratic, lottery-like payoffs—or whether it’s contaminated by other factors.

Their data sample includes all common stocks traded on the NYSE, Amex, and Nasdaq exchanges from January 1968 to December 2022, excluding stocks priced below $5 per share to ensure that results are not driven by micro-cap or illiquid firms.

Key Findings: MAX Isn’t Really About Lottery Preferences

The paper delivers several interesting discoveries:

1. The Original MAX Anomaly Is Driven by Mispricing, Not Lottery Demand

When tested against modern factor models that account for mispricing—particularly the Stambaugh-Yuan and Daniel-Hirshleifer-Sun models—the MAX anomaly completely disappears. The real culprit? Equity issuance.

High-MAX stocks tend to be those where managers issue equity to capitalize on overvaluation—consistent with a long line of research showing that equity issuance is a strong negative predictor of future stock returns (see for example here and here). They also found that the link between high-MAX, mispricing, and equity issuance intensifies significantly during periods of high investor sentiment.

Importantly, they found that MAX’s predictive power only works for stocks that consistently exhibit extreme returns over multiple months—the opposite of what a lottery should be.

2. MAX Contains Too Much Systematic Risk

A stock’s extreme daily returns during bull markets might simply reflect high beta (market sensitivity) rather than idiosyncratic lottery-like characteristics. The MAX measure fails to separate these two effects, making it a noisy proxy for what investors are really after.

3. Introducing MAXβ: A Cleaner Measure

To isolate true lottery-seeking behavior, the authors created MAXβ—a beta-neutralized version of MAX that sorts stocks into groups by market beta, then sorts by MAX within each group. This removes the systematic component while preserving the idiosyncratic extreme-return characteristic. The results are striking:

• MAXβ delivers significant abnormal returns that survive all risk and mispricing factor controls. The average return spread between the high- and low-MAXβ portfolios was −0.81% per month and highly significant with a t-statistic of −3.62. In addition, the alpha spreads for MAXβ sorted portfolios were driven by both legs of the arbitrage portfolio.

• Unlike MAX, MAXβ doesn’t require persistence—it works even for one-off extreme return events—making it a more compelling and conceptually sound proxy for capturing an underlying investor preference for lottery-like features.

• The effect is strongest among retail-dominated stocks (low institutional ownership).

4. Different Investors, Different Drivers

Perhaps most intriguingly, the source of MAXβ returns varies by investor clientele:

• In retail-dominated stocks: Returns come from the underperformance of high-MAXβ stocks (consistent with overpaying for lottery features).

• In institution-dominated stocks: Returns come from the outperformance of low-MAXβ stocks (consistent with institutions demanding a premium to hold low-skewness assets).

This pattern aligns with theories of heterogeneous investor preferences for skewness.

5. MAXβ Delivers Consistent Results Across Market Conditions

· The strategy’s profitability isn’t limited to micro-cap stocks or driven by illiquidity. It generates significant abnormal returns across size, price, and liquidity subsamples, including the largest and most liquid segment of the market, and various definitions of extreme positive returns.

· It delivers superior risk-adjusted returns, as evidenced by high Sharpe ratios, and is not merely compensation for left-tail risk.

Key Investor Takeaways