Maxing Out: Stocks as Lotteries and the Cross-Section of Expected Returns
Source: Bali, T. G., Cakici, N. & Whitelaw, R. F. (2011) · Journal of Financial Economics 99(2), 427–446 · doi:10.1016/j.jfineco.2010.08.014
TL;DR
Stocks with high maximum daily returns over the previous month (MAX) — a lottery-like feature — earn low subsequent returns. The value-weighted decile spread (high-MAX minus low-MAX) is −1.03%/month (t = 2.83) raw and −1.18%/month (t = 4.71) as a Fama–French–Carhart four-factor alpha over July 1962–December 2005. Controlling for MAX also reverses the puzzling negative idiosyncratic-volatility/return relation of Ang, Hodrick, Xing & Zhang (2006).
What anomaly it documents
Predictor: MAX — the single maximum daily return of a stock during the prior month (the paper's baseline; robust to averaging the 2–5 highest days).
Direction: negative — high-MAX stocks underperform; the long-low / short-high portfolio earns a positive spread.
Shape: returns are roughly flat across MAX deciles 1–7, then drop sharply from decile 7 to decile 10 (average raw returns fall from ~1.00% to 0.02%/month).
Interpretation: investors overpay for the small chance of a large payoff (positive skewness / lottery demand), so these stocks are overpriced.
OSAP predictor: MaxRet.
How to construct it
Sorting variable: MAX(1) = the highest single daily return of the stock in the prior month. MAX(N) = average of the N highest daily returns (N = 2…5) as robustness.
Universe: US common stocks (NYSE/AMEX/NASDAQ), daily returns from CRSP.
Portfolio: decile sort each month; long decile 1 (low MAX), short decile 10 (high MAX).
Robust to size, B/M, momentum, short-term reversal, illiquidity, and skewness controls; alpha spreads 0.68–0.74%/month (t ≈ 2.5–2.9) after such controls
this paper
Interaction
Including MAX reverses the negative IVOL–return relation of Ang et al. (2006)
this paper
Like most anomalies, expect out-of-sample decay; the short leg sits in volatile small-caps where costs bite.
Why it might work
Lottery / skewness preference: cumulative prospect theory (Tversky & Kahneman 1992) as modeled by Barberis & Huang (2008); probability-weighting errors overvalue small-probability large payoffs.
Transaction costs and shorting constraints on the high-MAX short leg (volatile small-caps).
Overlap with idiosyncratic volatility, MIN, and illiquidity effects (MAX is highly correlated with IVOL).
Out-of-sample decay and sensitivity to the MAX definition (N).
Key references
Bali, T., Cakici, N. & Whitelaw, R. (2011) — Maxing Out: Stocks as Lotteries — Journal of Financial Economics
Ang, A., Hodrick, R., Xing, Y. & Zhang, X. (2006) — The Cross-Section of Volatility and Expected Returns — Journal of Finance
Barberis, N. & Huang, M. (2008) — Stocks as Lotteries — American Economic Review
Kumar, A. (2009) — Who Gambles in the Stock Market? — Journal of Finance
Provenance: verified/generated from the paper's full text.
Reference replication on ConvexPi
An open, verified replication of this strategy is maintained at convexpi/replications. It recomputes the strategy from underlying building blocks and scores it out of sample (the McLean & Pontiff test):
