# Information Discreteness (US S&P 500)

- **Slug**: `info-discreteness-us-sp500`
- **Verdict**: marginal (no_edge)
- **Asset class**: equity
- **Categories**: factor, information, momentum-quality
- **Source**: qbuntu-analysis (computed asof 2026-08-01T07:30:59)
- **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/info-discreteness-us-sp500
- **JSON**: https://qbuntu.ai/v1/strategies/info-discreteness-us-sp500
- **License**: CC-BY-4.0

## Hypothesis

Da, Gurun, Warachka (2014): information discreteness measures whether a stock's return is from few large moves or many small moves. Applied to S&P 500 constituents.

## Why it didn't work

Across 320 grid combinations, median Sharpe=0.23, best=1.58. Primary failure mode: no_edge.

## Performance summary

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

| Metric | Value |
|---|---|
| Sharpe (median) | 0.2268 |
| Max drawdown | -9.5% |
| p-value | 0.38 |
| Backtest period | 2022-02-01 to 2026-06-01 |

Sharpe distribution across 320 grid runs: median 0.23, best 1.58 (best-case — not representative), worst -1.2, p25 -0.19, 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-info-discreteness-us-sp500-0000` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=1 | -0.25 | 0.07 | -0.87 | -0.22 |
| `r-info-discreteness-us-sp500-0001` | cost_bps=5, n_stocks=5, regime_gate=true, holding_days=1 | -0.28 | 0.12 | -0.87 | -0.22 |
| `r-info-discreteness-us-sp500-0002` | cost_bps=10, n_stocks=5, regime_gate=false, holding_days=1 | -0.58 | -0.23 | -1.23 | -0.66 |
| `r-info-discreteness-us-sp500-0003` | cost_bps=10, n_stocks=5, regime_gate=true, holding_days=1 | -0.57 | -0.08 | -1.23 | -0.66 |
| `r-info-discreteness-us-sp500-0012` | cost_bps=5, n_stocks=50, regime_gate=false, holding_days=1 | -0.22 | 0.23 | -0.39 | -1.09 |
| `r-info-discreteness-us-sp500-0018` | cost_bps=10, n_stocks=5, regime_gate=false, holding_days=5 | -0.39 | 0.01 | -0.17 | -1.25 |
| `r-info-discreteness-us-sp500-0030` | cost_bps=10, n_stocks=50, regime_gate=false, holding_days=5 | -1.2 | -1.07 | -0.73 | -2.06 |
| `r-info-discreteness-us-sp500-0033` | cost_bps=5, n_stocks=5, regime_gate=true, holding_days=10 | 0.16 | 1.14 | -0.14 | -0.49 |
| `r-info-discreteness-us-sp500-0047` | cost_bps=10, n_stocks=50, regime_gate=true, holding_days=10 | -0.29 | 0.71 | -1.09 | -1.09 |
| `r-info-discreteness-us-sp500-0061` | cost_bps=5, n_stocks=50, regime_gate=true, holding_days=20 | 0.24 | 1.5 | -0.28 | -1.65 |
| `r-info-discreteness-us-sp500-0064` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=60 | -0.06 | 0.1 | -0.36 | 0.06 |
| `r-info-discreteness-us-sp500-0076` | cost_bps=5, n_stocks=50, regime_gate=false, holding_days=60 | 0.14 | 0.38 | 0.12 | -0.36 |
| `r-info-discreteness-us-sp500-0090` | cost_bps=10, n_stocks=20, regime_gate=false, holding_days=1 | 0.12 | 0.46 | -0.64 | 0.34 |
| `r-info-discreteness-us-sp500-0104` | cost_bps=5, n_stocks=20, regime_gate=false, holding_days=5 | -0.24 | 0.03 | 0.05 | -1.45 |
| `r-info-discreteness-us-sp500-0118` | cost_bps=10, n_stocks=10, regime_gate=false, holding_days=10 | -0.03 | -0.27 | 0.18 | 0.05 |
| `r-info-discreteness-us-sp500-0132` | cost_bps=5, n_stocks=10, regime_gate=false, holding_days=20 | 0.55 | 0.48 | 0.57 | 0.71 |
| `r-info-discreteness-us-sp500-0146` | cost_bps=10, n_stocks=5, regime_gate=false, holding_days=60 | 0.82 | 0.75 | 0.66 | 1.56 |
| `r-info-discreteness-us-sp500-0160` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=1 | 0.36 | 0.22 | -1.19 | 3.56 |
| `r-info-discreteness-us-sp500-0174` | cost_bps=10, n_stocks=50, regime_gate=false, holding_days=1 | -0.55 | -0.92 | -3 | 1.85 |
| `r-info-discreteness-us-sp500-0188` | cost_bps=5, n_stocks=50, regime_gate=false, holding_days=5 | -0.66 | -1.76 | 0.19 | -0.29 |
| `r-info-discreteness-us-sp500-0202` | cost_bps=10, n_stocks=20, regime_gate=false, holding_days=10 | -0.2 | -0.78 | 0.45 | 0.02 |
| `r-info-discreteness-us-sp500-0209` | cost_bps=5, n_stocks=5, regime_gate=true, holding_days=20 | 1.58 | 1.55 | 1.27 | 3.28 |
| `r-info-discreteness-us-sp500-0217` | cost_bps=5, n_stocks=20, regime_gate=true, holding_days=20 | 1.14 | 1.3 | 0.89 | 1.11 |
| `r-info-discreteness-us-sp500-0231` | cost_bps=10, n_stocks=10, regime_gate=true, holding_days=60 | 0.93 | 1.38 | 0.61 | -0.08 |
| `r-info-discreteness-us-sp500-0240` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=1 | 0.41 | -0.14 | 0.67 | 2.29 |
| `r-info-discreteness-us-sp500-0246` | cost_bps=10, n_stocks=10, regime_gate=false, holding_days=1 | -0.65 | -1.13 | -0.28 | 1 |
| `r-info-discreteness-us-sp500-0260` | cost_bps=5, n_stocks=10, regime_gate=false, holding_days=5 | -0.29 | -0.49 | -0.78 | 1.03 |
| `r-info-discreteness-us-sp500-0274` | cost_bps=10, n_stocks=5, regime_gate=false, holding_days=10 | -0.25 | -1.12 | -0.18 | 2.33 |
| `r-info-discreteness-us-sp500-0288` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=20 | -0.08 | -0.83 | 1.03 | 1.39 |
| `r-info-discreteness-us-sp500-0302` | cost_bps=10, n_stocks=50, regime_gate=false, holding_days=20 | 0.2 | 0.06 | 0 | 0.73 |

## Facts (5)

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

- **Best grid Sharpe ratio is 1.58 (p=0.0019).**
  - Value: 1.58 sharpe_ratio
  - Context: period 2022-02-01–2026-06-01; cost=5bps
  - Supports verdict: `marginal`
  - Cite: https://qbuntu.ai/cite/info-discreteness-us-sp500-fact-best-sharpe

- **Median Sharpe across 320 grid runs is 0.23.**
  - Value: 0.23 sharpe_ratio
  - Context: Full grid of 320 parameter combinations.
  - Supports verdict: `marginal`
  - Cite: https://qbuntu.ai/cite/info-discreteness-us-sp500-fact-median-sharpe

- **Median Sharpe in DOWN regime is 0.29 across 320 runs.**
  - Value: 0.29 sharpe_ratio
  - Context: Regime=DOWN, N225 SMA20/SMA60 classification.
  - Supports verdict: `marginal`
  - Cite: https://qbuntu.ai/cite/info-discreteness-us-sp500-fact-regime-down

- **Median Sharpe in FLAT regime is 0.11 across 320 runs.**
  - Value: 0.11 sharpe_ratio
  - Context: Regime=FLAT, N225 SMA20/SMA60 classification.
  - Supports verdict: `marginal`
  - Cite: https://qbuntu.ai/cite/info-discreteness-us-sp500-fact-regime-flat

- **Median Sharpe in UP regime is 0.39 across 320 runs.**
  - Value: 0.39 sharpe_ratio
  - Context: Regime=UP, N225 SMA20/SMA60 classification.
  - Supports verdict: `marginal`
  - Cite: https://qbuntu.ai/cite/info-discreteness-us-sp500-fact-regime-up

## Related strategies

- same_strategy: [info-discreteness-jp-all](https://qbuntu.ai/strategies/info-discreteness-jp-all)
- same_strategy: [info-discreteness-jp-growth](https://qbuntu.ai/strategies/info-discreteness-jp-growth)

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Cite as: qbuntu (2026). Information Discreteness (US S&P 500). https://qbuntu.ai/strategies/info-discreteness-us-sp500

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