Is there a way to amplify the MAX overpricing anomaly (measured as the average of the five highest daily returns for a stock over the past month), which is driven by the desire of some investors for a lottery-like payoff? In their January 2026 paper entitled "MAX on Steroids: A New Measure of Investor Attraction to Lottery Stocks", Baris Ince, Turan Bali and Han Ozsoylev introduce MAXᵝ as a variable that distills lottery-seeking behavior by removing the systematic return component from MAX. Specifically, they each month:
- Sort stocks into tenths (deciles) based on their market betas as measured by a rolling window of 252 daily returns.
- Within each beta-sorted decile, sort stocks based on MAX.
They then focus on excess returns (relative to U.S. Treasury bills) and factor model alphas of the value-weighted extreme deciles of MAX aggregated across beta deciles, plus a hedge portfolio that is long (short) the stocks in the highest (lowest) decile. Using daily returns and ownership data for U.S. listed common stocks, excluding utility/financial stocks and stocks priced under $5, during January 1968 through December 2022, they find that:
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