# Low Volatility Anomaly (US S&P 500)

- **Slug**: `low-volatility-anomaly-us-sp500`
- **Verdict**: rejected (no_edge)
- **Asset class**: equity
- **Categories**: anomaly, factor, low-volatility
- **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/low-volatility-anomaly-us-sp500
- **JSON**: https://qbuntu.ai/v1/strategies/low-volatility-anomaly-us-sp500
- **License**: CC-BY-4.0

## Hypothesis

Baker, Bradley, Wurgler (2011): low-volatility stocks earn higher risk-adjusted returns. Applied to S&P 500 constituents.

## Why it didn't work

Across 316 grid combinations, median Sharpe=-1.00, best=-0.31. Primary failure mode: no_edge.

## Performance summary

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

| Metric | Value |
|---|---|
| Sharpe (median) | -0.999 |
| Max drawdown | -58.9% |
| p-value | 0.036 |
| Backtest period | 2022-02-01 to 2026-06-01 |

Sharpe distribution across 316 grid runs: median -1, best -0.31 (best-case — not representative), worst -1.8, p25 -1.2, p75 -0.69.

## 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-low-volatility-anomaly-us-sp500-0000` | cost_bps=5, n_stocks=5, vol_window=20, regime_gate=false | -0.95 | -1.27 | -1.18 | -0.1 |
| `r-low-volatility-anomaly-us-sp500-0001` | cost_bps=5, n_stocks=5, vol_window=20, regime_gate=true | -0.63 | -0.55 | -1.18 | -0.1 |
| `r-low-volatility-anomaly-us-sp500-0002` | cost_bps=10, n_stocks=5, vol_window=20, regime_gate=false | -1.1 | -1.49 | -1.3 | -0.23 |
| `r-low-volatility-anomaly-us-sp500-0003` | cost_bps=10, n_stocks=5, vol_window=20, regime_gate=true | -0.76 | -0.95 | -1.3 | -0.23 |
| `r-low-volatility-anomaly-us-sp500-0012` | cost_bps=5, n_stocks=50, vol_window=20, regime_gate=false | -0.75 | -0.8 | -1.65 | 0.26 |
| `r-low-volatility-anomaly-us-sp500-0017` | cost_bps=5, n_stocks=5, vol_window=20, regime_gate=true | -0.69 | 0.22 | -1.25 | -0.56 |
| `r-low-volatility-anomaly-us-sp500-0030` | cost_bps=10, n_stocks=50, vol_window=20, regime_gate=false | -1.43 | -1.78 | -1.67 | -0.58 |
| `r-low-volatility-anomaly-us-sp500-0043` | cost_bps=10, n_stocks=20, vol_window=20, regime_gate=true | -1.12 | 0.37 | -2.36 | -0.92 |
| `r-low-volatility-anomaly-us-sp500-0056` | cost_bps=5, n_stocks=20, vol_window=20, regime_gate=false | -1.34 | -1.62 | -1.09 | -1.29 |
| `r-low-volatility-anomaly-us-sp500-0065` | cost_bps=5, n_stocks=5, vol_window=20, regime_gate=true | -0.31 | 0.68 | -0.85 | -0.16 |
| `r-low-volatility-anomaly-us-sp500-0072` | cost_bps=5, n_stocks=20, vol_window=20, regime_gate=false | -1.14 | -1.48 | -1.27 | -0.23 |
| `r-low-volatility-anomaly-us-sp500-0085` | cost_bps=5, n_stocks=10, vol_window=40, regime_gate=true | -0.64 | -0.99 | -1.11 | -0.27 |
| `r-low-volatility-anomaly-us-sp500-0098` | cost_bps=10, n_stocks=5, vol_window=40, regime_gate=false | -1.19 | -1.58 | -1.25 | -0.11 |
| `r-low-volatility-anomaly-us-sp500-0111` | cost_bps=10, n_stocks=50, vol_window=40, regime_gate=true | -0.67 | -0.45 | -1.26 | -0.32 |
| `r-low-volatility-anomaly-us-sp500-0124` | cost_bps=5, n_stocks=50, vol_window=40, regime_gate=false | -1.54 | -1.58 | -1.93 | -1.1 |
| `r-low-volatility-anomaly-us-sp500-0137` | cost_bps=5, n_stocks=20, vol_window=40, regime_gate=true | -0.64 | 0.35 | -1.01 | -0.91 |
| `r-low-volatility-anomaly-us-sp500-0150` | cost_bps=10, n_stocks=10, vol_window=40, regime_gate=false | -1.09 | -1.42 | -1.28 | 0.01 |
| `r-low-volatility-anomaly-us-sp500-0163` | cost_bps=10, n_stocks=5, vol_window=60, regime_gate=true | -0.75 | -1.04 | -1.1 | -0.63 |
| `r-low-volatility-anomaly-us-sp500-0176` | cost_bps=5, n_stocks=5, vol_window=60, regime_gate=false | -0.93 | -1.29 | -0.85 | -0.23 |
| `r-low-volatility-anomaly-us-sp500-0189` | cost_bps=5, n_stocks=50, vol_window=60, regime_gate=true | -0.51 | -0.08 | -1.15 | -0.18 |
| `r-low-volatility-anomaly-us-sp500-0202` | cost_bps=10, n_stocks=20, vol_window=60, regime_gate=false | -1.65 | -1.9 | -1.96 | -1 |
| `r-low-volatility-anomaly-us-sp500-0215` | cost_bps=10, n_stocks=10, vol_window=60, regime_gate=true | -0.68 | 0.42 | -0.83 | -1.46 |
| `r-low-volatility-anomaly-us-sp500-0228` | cost_bps=5, n_stocks=10, vol_window=60, regime_gate=false | -1.07 | -1.28 | -1.04 | -0.41 |
| `r-low-volatility-anomaly-us-sp500-0240` | cost_bps=5, n_stocks=5, vol_window=120, regime_gate=false | -1.2 | -1.25 | -0.85 | -2.14 |
| `r-low-volatility-anomaly-us-sp500-0242` | cost_bps=10, n_stocks=5, vol_window=120, regime_gate=false | -1.35 | -1.46 | -0.96 | -2.28 |
| `r-low-volatility-anomaly-us-sp500-0255` | cost_bps=10, n_stocks=50, vol_window=120, regime_gate=true | -1.26 | -0.86 | -1.58 | -1.84 |
| `r-low-volatility-anomaly-us-sp500-0268` | cost_bps=5, n_stocks=50, vol_window=120, regime_gate=false | -1.17 | -1.41 | -1.04 | -0.76 |
| `r-low-volatility-anomaly-us-sp500-0281` | cost_bps=5, n_stocks=20, vol_window=120, regime_gate=true | -1.09 | 0.32 | -1.96 | -1.44 |
| `r-low-volatility-anomaly-us-sp500-0286` | cost_bps=10, n_stocks=50, vol_window=120, regime_gate=false | -1.8 | -1.8 | -1.98 | -1.6 |
| `r-low-volatility-anomaly-us-sp500-0295` | cost_bps=10, n_stocks=10, vol_window=120, regime_gate=true | -0.73 | 0.36 | -0.97 | -1.47 |

## Facts (5)

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

- **Best grid Sharpe ratio is -0.31 (p=0.28).**
  - Value: -0.31 sharpe_ratio
  - Context: period 2022-02-01–2026-06-01; cost=5bps
  - Supports verdict: `rejected`
  - Cite: https://qbuntu.ai/cite/low-volatility-anomaly-us-sp500-fact-best-sharpe

- **Median Sharpe across 316 grid runs is -1.00.**
  - Value: -1 sharpe_ratio
  - Context: Full grid of 316 parameter combinations.
  - Supports verdict: `rejected`
  - Cite: https://qbuntu.ai/cite/low-volatility-anomaly-us-sp500-fact-median-sharpe

- **Median Sharpe in DOWN regime is -0.85 across 316 runs.**
  - Value: -0.85 sharpe_ratio
  - Context: Regime=DOWN, N225 SMA20/SMA60 classification.
  - Supports verdict: `rejected`
  - Cite: https://qbuntu.ai/cite/low-volatility-anomaly-us-sp500-fact-regime-down

- **Median Sharpe in FLAT regime is -1.26 across 316 runs.**
  - Value: -1.26 sharpe_ratio
  - Context: Regime=FLAT, N225 SMA20/SMA60 classification.
  - Supports verdict: `rejected`
  - Cite: https://qbuntu.ai/cite/low-volatility-anomaly-us-sp500-fact-regime-flat

- **Median Sharpe in UP regime is -0.95 across 316 runs.**
  - Value: -0.95 sharpe_ratio
  - Context: Regime=UP, N225 SMA20/SMA60 classification.
  - Supports verdict: `rejected`
  - Cite: https://qbuntu.ai/cite/low-volatility-anomaly-us-sp500-fact-regime-up

## Related strategies

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

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Cite as: qbuntu (2026). Low Volatility Anomaly (US S&P 500). https://qbuntu.ai/strategies/low-volatility-anomaly-us-sp500

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