# Cross-Sectional Dispersion Trading (US S&P 500)

- **Slug**: `dispersion-us-sp500`
- **Verdict**: marginal (no_edge)
- **Asset class**: equity
- **Categories**: dispersion, regime, timing
- **Source**: qbuntu-analysis (computed asof 2026-07-31T01:31:48)
- **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/dispersion-us-sp500
- **JSON**: https://qbuntu.ai/v1/strategies/dispersion-us-sp500
- **License**: CC-BY-4.0

## Hypothesis

Stivers (2010), Jiang (2010): cross-sectional return dispersion as a market timing signal. Applied to S&P 500 constituents.

## Why it didn't work

Across 384 grid combinations, median Sharpe=0.14, best=0.64. Primary failure mode: no_edge.

## Performance summary

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

| Metric | Value |
|---|---|
| Sharpe (median) | 0.1438 |
| Max drawdown | -30.1% |
| p-value | 0.34 |
| Backtest period | 2022-02-01 to 2026-06-01 |

Sharpe distribution across 384 grid runs: median 0.14, best 0.64 (best-case — not representative), worst -1.07, p25 -0.36, p75 0.43.

## 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-dispersion-us-sp500-0000` | cost_bps=5, n_stocks=5, base_signal="momentum_20", holding_days=5 | 0.47 | 0.39 | 0.57 | 0.56 |
| `r-dispersion-us-sp500-0001` | cost_bps=10, n_stocks=5, base_signal="momentum_20", holding_days=5 | 0.4 | 0.32 | 0.48 | 0.47 |
| `r-dispersion-us-sp500-0002` | cost_bps=5, n_stocks=10, base_signal="momentum_20", holding_days=5 | 0.55 | 0.42 | 0.47 | 1.18 |
| `r-dispersion-us-sp500-0006` | cost_bps=5, n_stocks=50, base_signal="momentum_20", holding_days=5 | 0.19 | 0.41 | -0.39 | 0.7 |
| `r-dispersion-us-sp500-0008` | cost_bps=5, n_stocks=5, base_signal="momentum_60", holding_days=5 | 0.59 | 0.64 | 0.22 | 1.46 |
| `r-dispersion-us-sp500-0016` | cost_bps=5, n_stocks=5, base_signal="mean_reversion", holding_days=5 | -0.79 | -0.55 | -1.88 | -0.26 |
| `r-dispersion-us-sp500-0022` | cost_bps=5, n_stocks=50, base_signal="mean_reversion", holding_days=5 | -0.65 | -0.28 | -1.21 | -1.17 |
| `r-dispersion-us-sp500-0039` | cost_bps=10, n_stocks=50, base_signal="momentum_60", holding_days=10 | -0.32 | 0.4 | -0.85 | -0.67 |
| `r-dispersion-us-sp500-0050` | cost_bps=5, n_stocks=10, base_signal="momentum_20", holding_days=20 | 0.64 | 1.1 | -0.08 | 0.98 |
| `r-dispersion-us-sp500-0057` | cost_bps=10, n_stocks=5, base_signal="momentum_60", holding_days=20 | 0.4 | 1.34 | -0.49 | 0.02 |
| `r-dispersion-us-sp500-0072` | cost_bps=5, n_stocks=5, base_signal="momentum_20", holding_days=60 | 0.38 | 0.64 | -0.03 | -0.06 |
| `r-dispersion-us-sp500-0075` | cost_bps=10, n_stocks=10, base_signal="momentum_20", holding_days=60 | 0.47 | 0.7 | 0.32 | -0.08 |
| `r-dispersion-us-sp500-0092` | cost_bps=5, n_stocks=20, base_signal="mean_reversion", holding_days=60 | -0.25 | -0.18 | -0.44 | -0.17 |
| `r-dispersion-us-sp500-0109` | cost_bps=10, n_stocks=20, base_signal="momentum_60", holding_days=5 | 0.26 | 0.17 | 0.03 | 1.09 |
| `r-dispersion-us-sp500-0126` | cost_bps=5, n_stocks=50, base_signal="momentum_20", holding_days=10 | 0.01 | 1.04 | -0.77 | -0.41 |
| `r-dispersion-us-sp500-0143` | cost_bps=10, n_stocks=50, base_signal="mean_reversion", holding_days=10 | -0.52 | -1.03 | 0.09 | -0.27 |
| `r-dispersion-us-sp500-0160` | cost_bps=5, n_stocks=5, base_signal="mean_reversion", holding_days=20 | -0.24 | -0.8 | -0.66 | 1.54 |
| `r-dispersion-us-sp500-0177` | cost_bps=10, n_stocks=5, base_signal="momentum_60", holding_days=60 | 0.55 | 0.98 | 0.4 | -1.63 |
| `r-dispersion-us-sp500-0194` | cost_bps=5, n_stocks=10, base_signal="momentum_20", holding_days=5 | 0.55 | 0.42 | 0.47 | 1.18 |
| `r-dispersion-us-sp500-0211` | cost_bps=10, n_stocks=10, base_signal="mean_reversion", holding_days=5 | -1.03 | -0.64 | -2.16 | -0.96 |
| `r-dispersion-us-sp500-0228` | cost_bps=5, n_stocks=20, base_signal="momentum_60", holding_days=10 | 0.12 | 1.1 | -0.64 | -0.02 |
| `r-dispersion-us-sp500-0245` | cost_bps=10, n_stocks=20, base_signal="momentum_20", holding_days=20 | 0.4 | 1.2 | -0.28 | 0.25 |
| `r-dispersion-us-sp500-0262` | cost_bps=5, n_stocks=50, base_signal="mean_reversion", holding_days=20 | -0.5 | -0.73 | -0.44 | -0.07 |
| `r-dispersion-us-sp500-0279` | cost_bps=10, n_stocks=50, base_signal="momentum_60", holding_days=60 | 0.12 | 0.56 | 0.24 | -1.79 |
| `r-dispersion-us-sp500-0288` | cost_bps=5, n_stocks=5, base_signal="momentum_20", holding_days=5 | 0.48 | 0.39 | 0.57 | 0.59 |
| `r-dispersion-us-sp500-0297` | cost_bps=10, n_stocks=5, base_signal="momentum_60", holding_days=5 | 0.52 | 0.56 | 0.16 | 1.39 |
| `r-dispersion-us-sp500-0307` | cost_bps=10, n_stocks=10, base_signal="mean_reversion", holding_days=5 | -1.07 | -0.64 | -2.16 | -1.12 |
| `r-dispersion-us-sp500-0315` | cost_bps=10, n_stocks=10, base_signal="momentum_20", holding_days=10 | 0.47 | 1.36 | 0.13 | -0.83 |
| `r-dispersion-us-sp500-0332` | cost_bps=5, n_stocks=20, base_signal="mean_reversion", holding_days=10 | -0.49 | -0.74 | -0.49 | -0.04 |
| `r-dispersion-us-sp500-0349` | cost_bps=10, n_stocks=20, base_signal="momentum_60", holding_days=20 | 0.27 | 0.98 | -0.36 | -0 |

## Facts (5)

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

- **Best grid Sharpe ratio is 0.64 (p=0.18).**
  - Value: 0.64 sharpe_ratio
  - Context: period 2022-02-01–2026-06-01; cost=5bps
  - Supports verdict: `marginal`
  - Cite: https://qbuntu.ai/cite/dispersion-us-sp500-fact-best-sharpe

- **Median Sharpe across 384 grid runs is 0.14.**
  - Value: 0.14 sharpe_ratio
  - Context: Full grid of 384 parameter combinations.
  - Supports verdict: `marginal`
  - Cite: https://qbuntu.ai/cite/dispersion-us-sp500-fact-median-sharpe

- **Median Sharpe in DOWN regime is -0.06 across 384 runs.**
  - Value: -0.06 sharpe_ratio
  - Context: Regime=DOWN, N225 SMA20/SMA60 classification.
  - Supports verdict: `marginal`
  - Cite: https://qbuntu.ai/cite/dispersion-us-sp500-fact-regime-down

- **Median Sharpe in FLAT regime is -0.34 across 384 runs.**
  - Value: -0.34 sharpe_ratio
  - Context: Regime=FLAT, N225 SMA20/SMA60 classification.
  - Supports verdict: `marginal`
  - Cite: https://qbuntu.ai/cite/dispersion-us-sp500-fact-regime-flat

- **Median Sharpe in UP regime is 0.43 across 384 runs.**
  - Value: 0.43 sharpe_ratio
  - Context: Regime=UP, N225 SMA20/SMA60 classification.
  - Supports verdict: `marginal`
  - Cite: https://qbuntu.ai/cite/dispersion-us-sp500-fact-regime-up

## Related strategies

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

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Cite as: qbuntu (2026). Cross-Sectional Dispersion Trading (US S&P 500). https://qbuntu.ai/strategies/dispersion-us-sp500

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