Lottery Stocks and the MAX Effect: Why Investors Overpay for Skewness

What Makes a Stock Behave Like a Lottery Ticket?

Why do certain stocks with spectacular recent gains go on to deliver poor returns? The answer lies in how investors price the chance of a massive payoff. Bali, Cakici, and Whitelaw (2011) introduced the MAX variable, defined as the highest daily return a stock achieves within a given month, and demonstrated that this single measure captures a powerful cross-sectional return pattern: high-MAX stocks systematically underperform low-MAX stocks going forward.

The mechanism is rooted in skewness preference. Investors are drawn to securities that offer a small probability of an outsized gain, much like a lottery ticket. That demand pushes up the prices of lottery-like stocks, compressing their future expected returns. The MAX variable identifies precisely these names by flagging stocks that have already delivered the kind of extreme single-day spike that attracts speculative capital.

Measuring the MAX Effect

Bali, Cakici, and Whitelaw sorted all NYSE, AMEX, and NASDAQ stocks into decile portfolios based on their maximum daily return during the prior month. The spread in average monthly returns between the lowest and highest MAX deciles was stark.

The long-short spread of roughly 1% per month persists after controlling for the Fama-French three factors and the Carhart momentum factor. It holds in both value-weighted and equal-weighted constructions, across subperiods, and across size groups. Stocks that recently delivered extreme single-day gains carry a measurable return penalty going forward.

This is not simply a proxy for size or price level. While lottery-like stocks do tend to be smaller and cheaper, the MAX effect remains statistically and economically significant in multivariate regressions that control for market capitalization, book-to-market ratio, momentum, short-term reversal, and liquidity.

The Link to Idiosyncratic Volatility

One of the paper's most consequential findings connects MAX to the idiosyncratic volatility puzzle. Ang, Hodrick, Xing, and Zhang (2006) documented that stocks with high idiosyncratic volatility earn abnormally low returns, a result that contradicts standard asset pricing theory where only systematic risk should be priced.

Bali, Cakici, and Whitelaw showed that once MAX is included as a control variable, the negative idiosyncratic volatility-return relationship weakens substantially and in many specifications disappears entirely. Their interpretation: what prior research attributed to a volatility anomaly was largely capturing investor appetite for lottery-like payoffs. High-IVOL stocks earn low returns not because volatility itself is mispriced, but because high-IVOL stocks tend to be the same stocks with extreme positive daily returns that attract skewness-seeking capital.

This decomposition matters for portfolio construction. A low-volatility strategy and a MAX-avoidance strategy overlap but are not identical. The MAX variable isolates the speculative demand channel more precisely, and combining both screens can sharpen the betting-against-beta effect by separating volatility from lottery demand.

Why Do Investors Pay This Premium?

The theoretical foundation draws on cumulative prospect theory and probability weighting. Barberis and Huang (2008) showed that when investors overweight small probabilities of extreme gains, as Kahneman and Tversky's probability weighting function predicts, securities with positively skewed return distributions become overpriced in equilibrium.

Kumar (2009) provided direct evidence that retail investors disproportionately hold lottery-type stocks: low-priced securities with high idiosyncratic volatility and high idiosyncratic skewness. This demand is concentrated among investors with lower income, less education, and in geographic areas where state lottery spending is higher, consistent with behavioral biases rather than rational portfolio optimization.

Mitton and Vorkink (2007) formalized this in an equilibrium model where heterogeneous skewness preferences produce underdiversification. Investors who value positive skewness concentrate their holdings in lottery-like stocks, forgoing diversification benefits. The resulting demand pressure inflates prices and depresses expected returns on those names.

Robustness and Out-of-Sample Evidence

The MAX effect has proven durable across settings. Eraker and Ready (2015) examined OTC stocks, where lottery characteristics are most extreme, and found that these securities deliver returns so poor that investors who hold them are effectively paying for the privilege of gambling. The return shortfall in OTC lottery stocks exceeds what risk models predict, suggesting a genuine preference-driven mispricing rather than a hidden tail risk compensation story.

International evidence reinforces the domestic findings. Studies across European and Asian equity markets have documented that high-MAX stocks underperform in markets with varying institutional structures, short-selling constraints, and investor composition. The pattern appears wherever retail participation is meaningful and skewness-seeking capital flows into lottery-like names.

Implications for Systematic Portfolios

The MAX effect sits at the intersection of several factor anomalies. It connects the low-volatility anomaly, the idiosyncratic volatility puzzle, and behavioral theories of speculative demand into a single, measurable channel. For systematic investors, the practical takeaway is straightforward: screening out stocks with the highest maximum daily returns in the prior month removes a pocket of chronic underperformance from the investable universe.

This filter is complementary to standard factor exposures. A portfolio that combines quality, low-volatility, and MAX-avoidance screens does not merely stack independent alphas; it addresses overlapping sources of speculative mispricing through multiple lenses. The MAX variable, precisely because it is simple to compute and grounded in observable daily returns, offers an accessible entry point for investors seeking to avoid the lottery-stock drag on their portfolios.