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rejectedno_edge· equity· anomaly· factor· lottery· max-return

Max Return / Lottery Effect (US S&P 500)

slug: max-return-lottery-us-sp500

Max Return / Lottery Effect (US S&P 500) backtest. Median Sharpe across 320 parameter sets is -0.76. p-value is 0.09. Max DD is -46.4%. Period: 2022-02-01 to 2026-09-01. Best Sharpe +0.14 is not the representative figure.

Verdict: rejected. The median reaches neither promising (Sharpe > 0.5 and p-value < 0.05) nor marginal (Sharpe > 0.05 and best p-value < 0.10). Primary reason: no_edge. It is not regime, frequency, or cost, and the median does not clear the bar.

Performance summary

Sharpe (median)
-0.76
Max DD
-46.4%
Win rate
—
Alpha (ann.)
—
p-value
0.09
backtest period: 2022-02-01 → 2026-09-01
Sharpe across 320 grid runs:median -0.76best 0.14 (not representative)worst -1.65p25–p75 -1.05–-0.51

Hypothesis

Bali, Cakici, Whitelaw (2011): stocks with extreme positive daily returns subsequently underperform. Applied to S&P 500 constituents.

Why it didn't work

Across 320 grid combinations, median Sharpe=-0.76, best=0.14. Primary failure mode: no_edge.

Facts (5)

Best grid Sharpe ratio is 0.14 (p=0.76).
period 2022-02-01–2026-09-01; cost=5bps
sharpe_ratio0.14
cite ↗ /cite/max-return-lottery-us-sp500-fact-best-sharpevia r-max-return-lottery-us-sp500-0017
Median Sharpe across 320 grid runs is -0.76.
Full grid of 320 parameter combinations.
sharpe_ratio-0.76
cite ↗ /cite/max-return-lottery-us-sp500-fact-median-sharpe
Median Sharpe in DOWN regime is -0.66 across 320 runs.
Regime=DOWN, N225 SMA20/SMA60 classification.
sharpe_ratio-0.66
cite ↗ /cite/max-return-lottery-us-sp500-fact-regime-down
Median Sharpe in FLAT regime is -1.11 across 320 runs.
Regime=FLAT, N225 SMA20/SMA60 classification.
sharpe_ratio-1.11
cite ↗ /cite/max-return-lottery-us-sp500-fact-regime-flat
Median Sharpe in UP regime is -0.79 across 320 runs.
Regime=UP, N225 SMA20/SMA60 classification.
sharpe_ratio-0.79
cite ↗ /cite/max-return-lottery-us-sp500-fact-regime-up

Runs (30)

runparamssharpeUPFLATDOWN
formation_days=5, holding_days=1, n_stocks=5, cost_bps=5, regime_gate=False
r-max-return-lottery-us-sp500-0000
cost_bps: 5
n_stocks: 5
regime_gate: false
-0.21-0.79-0.25+0.48
formation_days=5, holding_days=1, n_stocks=5, cost_bps=5, regime_gate=True
r-max-return-lottery-us-sp500-0001
cost_bps: 5
n_stocks: 5
regime_gate: true
+0.07+0.01-0.25+0.48
formation_days=5, holding_days=1, n_stocks=5, cost_bps=10, regime_gate=False
r-max-return-lottery-us-sp500-0002
cost_bps: 10
n_stocks: 5
regime_gate: false
-0.42-1.07-0.49+0.35
formation_days=5, holding_days=1, n_stocks=5, cost_bps=10, regime_gate=True
r-max-return-lottery-us-sp500-0003
cost_bps: 10
n_stocks: 5
regime_gate: true
-0.10-0.20-0.49+0.35
formation_days=5, holding_days=1, n_stocks=50, cost_bps=5, regime_gate=False
r-max-return-lottery-us-sp500-0012
cost_bps: 5
n_stocks: 50
regime_gate: false
-0.96-1.15-1.86-0.05
formation_days=5, holding_days=5, n_stocks=5, cost_bps=5, regime_gate=True
r-max-return-lottery-us-sp500-0017
cost_bps: 5
n_stocks: 5
regime_gate: true
+0.14+0.93-0.52-0.01
formation_days=5, holding_days=5, n_stocks=5, cost_bps=10, regime_gate=True
r-max-return-lottery-us-sp500-0019
cost_bps: 10
n_stocks: 5
regime_gate: true
+0.04+0.84-0.66-0.09
formation_days=5, holding_days=10, n_stocks=5, cost_bps=5, regime_gate=True
r-max-return-lottery-us-sp500-0033
cost_bps: 5
n_stocks: 5
regime_gate: true
-0.18+0.41-0.38-0.50
formation_days=5, holding_days=10, n_stocks=50, cost_bps=10, regime_gate=True
r-max-return-lottery-us-sp500-0047
cost_bps: 10
n_stocks: 50
regime_gate: true
-0.41+0.56-0.84-0.88
formation_days=5, holding_days=20, n_stocks=50, cost_bps=5, regime_gate=True
r-max-return-lottery-us-sp500-0061
cost_bps: 5
n_stocks: 50
regime_gate: true
-0.23+0.81-0.51-0.76
formation_days=5, holding_days=60, n_stocks=5, cost_bps=5, regime_gate=False
r-max-return-lottery-us-sp500-0064
cost_bps: 5
n_stocks: 5
regime_gate: false
-0.60-0.53-1.26-0.22
formation_days=5, holding_days=60, n_stocks=50, cost_bps=5, regime_gate=False
r-max-return-lottery-us-sp500-0076
cost_bps: 5
n_stocks: 50
regime_gate: false
-0.92-1.04-1.29-0.37
formation_days=10, holding_days=1, n_stocks=20, cost_bps=10, regime_gate=False
r-max-return-lottery-us-sp500-0090
cost_bps: 10
n_stocks: 20
regime_gate: false
-1.38-2.37-1.53-0.19
formation_days=10, holding_days=5, n_stocks=20, cost_bps=5, regime_gate=False
r-max-return-lottery-us-sp500-0104
cost_bps: 5
n_stocks: 20
regime_gate: false
-1.10-1.25-0.91-1.18
formation_days=10, holding_days=10, n_stocks=10, cost_bps=10, regime_gate=False
r-max-return-lottery-us-sp500-0118
cost_bps: 10
n_stocks: 10
regime_gate: false
-1.20-1.10-1.47-0.96
formation_days=10, holding_days=20, n_stocks=10, cost_bps=5, regime_gate=False
r-max-return-lottery-us-sp500-0132
cost_bps: 5
n_stocks: 10
regime_gate: false
-0.90-1.19-0.71-1.01
formation_days=10, holding_days=60, n_stocks=5, cost_bps=10, regime_gate=False
r-max-return-lottery-us-sp500-0146
cost_bps: 10
n_stocks: 5
regime_gate: false
-1.06-1.04-1.58-0.70
formation_days=20, holding_days=1, n_stocks=5, cost_bps=5, regime_gate=False
r-max-return-lottery-us-sp500-0160
cost_bps: 5
n_stocks: 5
regime_gate: false
-0.72-1.04-0.89+0.27
formation_days=20, holding_days=1, n_stocks=50, cost_bps=10, regime_gate=False
r-max-return-lottery-us-sp500-0174
cost_bps: 10
n_stocks: 50
regime_gate: false
-1.65-2.35-2.18-0.26
formation_days=20, holding_days=1, n_stocks=50, cost_bps=10, regime_gate=True
r-max-return-lottery-us-sp500-0175
cost_bps: 10
n_stocks: 50
regime_gate: true
-1.17-1.34-2.18-0.26
formation_days=20, holding_days=5, n_stocks=50, cost_bps=5, regime_gate=True
r-max-return-lottery-us-sp500-0189
cost_bps: 5
n_stocks: 50
regime_gate: true
-0.67+0.30-1.19-0.78
formation_days=20, holding_days=10, n_stocks=20, cost_bps=10, regime_gate=True
r-max-return-lottery-us-sp500-0203
cost_bps: 10
n_stocks: 20
regime_gate: true
-0.77+0.46-1.45-0.75
formation_days=20, holding_days=20, n_stocks=20, cost_bps=5, regime_gate=True
r-max-return-lottery-us-sp500-0217
cost_bps: 5
n_stocks: 20
regime_gate: true
-0.45+0.80-0.68-1.22
formation_days=20, holding_days=60, n_stocks=10, cost_bps=10, regime_gate=True
r-max-return-lottery-us-sp500-0231
cost_bps: 10
n_stocks: 10
regime_gate: true
-0.29+0.75-1.05-0.06
formation_days=60, holding_days=1, n_stocks=5, cost_bps=5, regime_gate=False
r-max-return-lottery-us-sp500-0240
cost_bps: 5
n_stocks: 5
regime_gate: false
-0.86-0.56-1.21-0.77
formation_days=60, holding_days=1, n_stocks=10, cost_bps=10, regime_gate=False
r-max-return-lottery-us-sp500-0246
cost_bps: 10
n_stocks: 10
regime_gate: false
-1.26-1.17-1.26-1.39
formation_days=60, holding_days=5, n_stocks=10, cost_bps=5, regime_gate=False
r-max-return-lottery-us-sp500-0260
cost_bps: 5
n_stocks: 10
regime_gate: false
-0.95-1.09-0.81-0.82
formation_days=60, holding_days=10, n_stocks=5, cost_bps=10, regime_gate=False
r-max-return-lottery-us-sp500-0274
cost_bps: 10
n_stocks: 5
regime_gate: false
-1.17-0.99-1.92-0.29
formation_days=60, holding_days=20, n_stocks=5, cost_bps=5, regime_gate=False
r-max-return-lottery-us-sp500-0288
cost_bps: 5
n_stocks: 5
regime_gate: false
-0.92-0.98-1.11-0.31
formation_days=60, holding_days=20, n_stocks=50, cost_bps=10, regime_gate=False
r-max-return-lottery-us-sp500-0302
cost_bps: 10
n_stocks: 50
regime_gate: false
-1.28-1.23-1.13-1.68

Target universe

S&P 500 constituents, ~503 stocks

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same_strategy:max-return-lottery-jp-allsame_strategy:max-return-lottery-jp-growth
source: qbuntu-analysis · kabu STATION REST API + J-Quants daily bars
computed asof: 2026-09-24T02:22:20
view as Markdown ↗view as JSON ↗license: CC-BY-4.0

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