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

- **Slug**: `max-return-lottery-us-sp500`
- **Verdict**: rejected (no_edge)
- **Asset class**: equity
- **Categories**: anomaly, factor, lottery, max-return
- **Source**: qbuntu-analysis (computed asof 2026-08-01T07:31:00)
- **Reproducibility**: analysis-engine@18193e9, backtest-lib@711b855, grid tier=shallow (python 3.10.11, numpy 2.2.6, pandas 2.3.3)
- **HTML**: https://qbuntu.ai/strategies/max-return-lottery-us-sp500
- **JSON**: https://qbuntu.ai/v1/strategies/max-return-lottery-us-sp500
- **License**: CC-BY-4.0

## 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=-0.91, best=0.04. Primary failure mode: no_edge.

## Performance summary

Headline figures are the **median across the parameter grid**, not the best run.

| Metric | Value |
|---|---|
| Sharpe (median) | -0.9135 |
| Max drawdown | -46.1% |
| p-value | 0.052 |
| Backtest period | 2022-02-01 to 2026-06-01 |

Sharpe distribution across 320 grid runs: median -0.91, best 0.04 (best-case — not representative), worst -1.76, p25 -1.16, p75 -0.62.

## Methodology

- Notes: {"walk_forward_definition": {"type": "single_pass", "description": "Full period backtest without walk-forward split", "verdict_basis": "full_period"}}
- Slippage model: open-on-open + variable bps fixed
- Position sizing: equal_weight
- Regime definition: GSPC SMA20/SMA60 three-class: UP (close>SMA20 AND SMA20>SMA60), DOWN (close<SMA20 AND SMA20<SMA60), FLAT (else)
- Transaction cost bps: 5

## Target universe

S&P 500 constituents, ~503 stocks

## Runs (30)

| run_id | params | sharpe | UP | FLAT | DOWN |
|---|---|---:|---:|---:|---:|
| `r-max-return-lottery-us-sp500-0000` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=1 | -0.41 | -0.79 | -1.31 | 0.48 |
| `r-max-return-lottery-us-sp500-0001` | cost_bps=5, n_stocks=5, regime_gate=true, holding_days=1 | -0.11 | 0.01 | -1.31 | 0.48 |
| `r-max-return-lottery-us-sp500-0002` | cost_bps=10, n_stocks=5, regime_gate=false, holding_days=1 | -0.63 | -1.07 | -1.66 | 0.35 |
| `r-max-return-lottery-us-sp500-0003` | cost_bps=10, n_stocks=5, regime_gate=true, holding_days=1 | -0.3 | -0.2 | -1.66 | 0.35 |
| `r-max-return-lottery-us-sp500-0012` | cost_bps=5, n_stocks=50, regime_gate=false, holding_days=1 | -1.05 | -1.15 | -2.34 | -0.05 |
| `r-max-return-lottery-us-sp500-0017` | cost_bps=5, n_stocks=5, regime_gate=true, holding_days=5 | 0.04 | 0.93 | -0.97 | -0.01 |
| `r-max-return-lottery-us-sp500-0019` | cost_bps=10, n_stocks=5, regime_gate=true, holding_days=5 | -0.06 | 0.84 | -1.12 | -0.09 |
| `r-max-return-lottery-us-sp500-0033` | cost_bps=5, n_stocks=5, regime_gate=true, holding_days=10 | -0.27 | 0.44 | -0.74 | -0.5 |
| `r-max-return-lottery-us-sp500-0047` | cost_bps=10, n_stocks=50, regime_gate=true, holding_days=10 | -0.56 | 0.42 | -1.23 | -0.88 |
| `r-max-return-lottery-us-sp500-0061` | cost_bps=5, n_stocks=50, regime_gate=true, holding_days=20 | -0.39 | 0.7 | -0.83 | -0.76 |
| `r-max-return-lottery-us-sp500-0064` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=60 | -0.56 | -0.59 | -1.26 | 0.92 |
| `r-max-return-lottery-us-sp500-0076` | cost_bps=5, n_stocks=50, regime_gate=false, holding_days=60 | -0.95 | -1.19 | -1.29 | 0.44 |
| `r-max-return-lottery-us-sp500-0090` | cost_bps=10, n_stocks=20, regime_gate=false, holding_days=1 | -1.55 | -2.37 | -2.15 | -0.19 |
| `r-max-return-lottery-us-sp500-0104` | cost_bps=5, n_stocks=20, regime_gate=false, holding_days=5 | -1.36 | -1.25 | -1.75 | -1.18 |
| `r-max-return-lottery-us-sp500-0118` | cost_bps=10, n_stocks=10, regime_gate=false, holding_days=10 | -1.63 | -1.53 | -2.49 | -0.96 |
| `r-max-return-lottery-us-sp500-0132` | cost_bps=5, n_stocks=10, regime_gate=false, holding_days=20 | -1.19 | -1.55 | -1.16 | -1.01 |
| `r-max-return-lottery-us-sp500-0146` | cost_bps=10, n_stocks=5, regime_gate=false, holding_days=60 | -1.1 | -1.2 | -1.58 | -0.32 |
| `r-max-return-lottery-us-sp500-0160` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=1 | -0.73 | -1.04 | -0.95 | 0.27 |
| `r-max-return-lottery-us-sp500-0174` | cost_bps=10, n_stocks=50, regime_gate=false, holding_days=1 | -1.74 | -2.35 | -2.59 | -0.26 |
| `r-max-return-lottery-us-sp500-0188` | cost_bps=5, n_stocks=50, regime_gate=false, holding_days=5 | -1.33 | -1.38 | -1.64 | -0.78 |
| `r-max-return-lottery-us-sp500-0202` | cost_bps=10, n_stocks=20, regime_gate=false, holding_days=10 | -1.66 | -1.78 | -2.17 | -0.75 |
| `r-max-return-lottery-us-sp500-0206` | cost_bps=10, n_stocks=50, regime_gate=false, holding_days=10 | -1.76 | -1.85 | -2.22 | -1.18 |
| `r-max-return-lottery-us-sp500-0217` | cost_bps=5, n_stocks=20, regime_gate=true, holding_days=20 | -0.65 | 0.67 | -1.09 | -1.22 |
| `r-max-return-lottery-us-sp500-0231` | cost_bps=10, n_stocks=10, regime_gate=true, holding_days=60 | -0.22 | 0.79 | -1.05 | 0.31 |
| `r-max-return-lottery-us-sp500-0240` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=1 | -0.83 | -0.56 | -1.18 | -0.77 |
| `r-max-return-lottery-us-sp500-0246` | cost_bps=10, n_stocks=10, regime_gate=false, holding_days=1 | -1.26 | -1.17 | -1.26 | -1.39 |
| `r-max-return-lottery-us-sp500-0260` | cost_bps=5, n_stocks=10, regime_gate=false, holding_days=5 | -1.01 | -1.09 | -0.95 | -0.82 |
| `r-max-return-lottery-us-sp500-0274` | cost_bps=10, n_stocks=5, regime_gate=false, holding_days=10 | -1.36 | -1.34 | -2 | -0.29 |
| `r-max-return-lottery-us-sp500-0288` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=20 | -1.1 | -1.23 | -1.27 | -0.31 |
| `r-max-return-lottery-us-sp500-0302` | cost_bps=10, n_stocks=50, regime_gate=false, holding_days=20 | -1.46 | -1.53 | -1.25 | -1.68 |

## Facts (5)

Each fact has a permanent citation URL. AI agents quoting qbuntu should use these.

- **Best grid Sharpe ratio is 0.04 (p=0.92).**
  - Value: 0.04 sharpe_ratio
  - Context: period 2022-02-01–2026-06-01; cost=5bps
  - Supports verdict: `rejected`
  - Cite: https://qbuntu.ai/cite/max-return-lottery-us-sp500-fact-best-sharpe

- **Median Sharpe across 320 grid runs is -0.91.**
  - Value: -0.91 sharpe_ratio
  - Context: Full grid of 320 parameter combinations.
  - Supports verdict: `rejected`
  - Cite: https://qbuntu.ai/cite/max-return-lottery-us-sp500-fact-median-sharpe

- **Median Sharpe in DOWN regime is -0.40 across 320 runs.**
  - Value: -0.4 sharpe_ratio
  - Context: Regime=DOWN, N225 SMA20/SMA60 classification.
  - Supports verdict: `rejected`
  - Cite: https://qbuntu.ai/cite/max-return-lottery-us-sp500-fact-regime-down

- **Median Sharpe in FLAT regime is -1.32 across 320 runs.**
  - Value: -1.32 sharpe_ratio
  - Context: Regime=FLAT, N225 SMA20/SMA60 classification.
  - Supports verdict: `rejected`
  - Cite: https://qbuntu.ai/cite/max-return-lottery-us-sp500-fact-regime-flat

- **Median Sharpe in UP regime is -0.86 across 320 runs.**
  - Value: -0.86 sharpe_ratio
  - Context: Regime=UP, N225 SMA20/SMA60 classification.
  - Supports verdict: `rejected`
  - Cite: https://qbuntu.ai/cite/max-return-lottery-us-sp500-fact-regime-up

## Related strategies

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- same_strategy: [max-return-lottery-jp-growth](https://qbuntu.ai/strategies/max-return-lottery-jp-growth)

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Cite as: qbuntu (2026). Max Return / Lottery Effect (US S&P 500). https://qbuntu.ai/strategies/max-return-lottery-us-sp500

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