# Garman-Klass Volatility Factor (US S&P 500)

- **Slug**: `garman-klass-vol-us-sp500`
- **Verdict**: rejected (no_edge)
- **Asset class**: equity
- **Categories**: anomaly, factor, volatility
- **Source**: qbuntu-analysis (computed asof 2026-07-30T01:20:51)
- **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/garman-klass-vol-us-sp500
- **JSON**: https://qbuntu.ai/v1/strategies/garman-klass-vol-us-sp500
- **License**: CC-BY-4.0

## Hypothesis

Garman & Klass (1980): OHLC-based volatility estimator. Testing low-volatility anomaly using GK vol on S&P 500 constituents.

## Why it didn't work

Across 222 grid combinations, median Sharpe=-0.83, best=-0.29. Primary failure mode: no_edge.

## Performance summary

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

| Metric | Value |
|---|---|
| Sharpe (median) | -0.8333 |
| Max drawdown | -52.5% |
| p-value | 0.082 |
| Backtest period | 2022-02-01 to 2026-06-01 |

Sharpe distribution across 222 grid runs: median -0.83, best -0.29 (best-case — not representative), worst -1.87, p25 -1.07, p75 -0.66.

## 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-garman-klass-vol-us-sp500-0000` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=1 | -1 | -1.28 | -1.39 | -0.11 |
| `r-garman-klass-vol-us-sp500-0001` | cost_bps=5, n_stocks=5, regime_gate=true, holding_days=1 | -0.63 | -0.48 | -1.39 | -0.11 |
| `r-garman-klass-vol-us-sp500-0002` | cost_bps=10, n_stocks=5, regime_gate=false, holding_days=1 | -1.13 | -1.44 | -1.51 | -0.21 |
| `r-garman-klass-vol-us-sp500-0003` | cost_bps=10, n_stocks=5, regime_gate=true, holding_days=1 | -0.74 | -0.96 | -1.51 | -0.21 |
| `r-garman-klass-vol-us-sp500-0012` | cost_bps=5, n_stocks=50, regime_gate=false, holding_days=1 | -0.83 | -0.82 | -1.61 | -0.01 |
| `r-garman-klass-vol-us-sp500-0013` | cost_bps=5, n_stocks=50, regime_gate=true, holding_days=1 | -0.67 | -0.48 | -1.61 | -0.01 |
| `r-garman-klass-vol-us-sp500-0023` | cost_bps=10, n_stocks=10, regime_gate=true, holding_days=5 | -0.62 | -0.73 | -1.18 | -0.29 |
| `r-garman-klass-vol-us-sp500-0033` | cost_bps=5, n_stocks=5, regime_gate=true, holding_days=10 | -0.85 | 0.38 | -1.46 | -0.94 |
| `r-garman-klass-vol-us-sp500-0046` | cost_bps=10, n_stocks=50, regime_gate=false, holding_days=10 | -1.87 | -1.75 | -2.44 | -1.31 |
| `r-garman-klass-vol-us-sp500-0047` | cost_bps=10, n_stocks=50, regime_gate=true, holding_days=10 | -1.23 | 0.14 | -2.44 | -1.31 |
| `r-garman-klass-vol-us-sp500-0062` | cost_bps=10, n_stocks=50, regime_gate=false, holding_days=20 | -1.43 | -1.71 | -1.06 | -1.6 |
| `r-garman-klass-vol-us-sp500-0065` | cost_bps=5, n_stocks=5, regime_gate=true, holding_days=60 | -0.29 | 1.04 | -0.86 | -0.19 |
| `r-garman-klass-vol-us-sp500-0080` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=1 | -1.06 | -1.48 | -1.41 | -0.1 |
| `r-garman-klass-vol-us-sp500-0089` | cost_bps=5, n_stocks=20, regime_gate=true, holding_days=1 | -0.57 | -0.39 | -1.43 | 0.08 |
| `r-garman-klass-vol-us-sp500-0100` | cost_bps=5, n_stocks=10, regime_gate=false, holding_days=5 | -1.1 | -1.44 | -1.29 | -0.32 |
| `r-garman-klass-vol-us-sp500-0109` | cost_bps=5, n_stocks=50, regime_gate=true, holding_days=5 | -0.53 | 0.14 | -1.2 | -0.26 |
| `r-garman-klass-vol-us-sp500-0123` | cost_bps=10, n_stocks=20, regime_gate=true, holding_days=10 | -1.12 | 0.21 | -2.17 | -1.04 |
| `r-garman-klass-vol-us-sp500-0137` | cost_bps=5, n_stocks=20, regime_gate=true, holding_days=20 | -0.65 | 0.7 | -0.98 | -1.26 |
| `r-garman-klass-vol-us-sp500-0155` | cost_bps=10, n_stocks=20, regime_gate=true, holding_days=60 | -0.41 | 1.25 | -1.27 | -0.16 |
| `r-garman-klass-vol-us-sp500-0166` | cost_bps=10, n_stocks=10, regime_gate=false, holding_days=1 | -0.89 | -1.09 | -1.24 | -0.27 |
| `r-garman-klass-vol-us-sp500-0175` | cost_bps=10, n_stocks=50, regime_gate=true, holding_days=1 | -0.87 | -0.87 | -1.74 | -0.34 |
| `r-garman-klass-vol-us-sp500-0186` | cost_bps=10, n_stocks=20, regime_gate=false, holding_days=5 | -1.21 | -1.65 | -1.18 | -0.44 |
| `r-garman-klass-vol-us-sp500-0199` | cost_bps=10, n_stocks=10, regime_gate=true, holding_days=10 | -1.04 | -0.02 | -1.75 | -1.11 |
| `r-garman-klass-vol-us-sp500-0211` | cost_bps=10, n_stocks=5, regime_gate=true, holding_days=20 | -0.64 | -0.08 | -0.79 | -1.07 |
| `r-garman-klass-vol-us-sp500-0237` | cost_bps=5, n_stocks=50, regime_gate=true, holding_days=60 | -0.38 | 1.12 | -1.26 | -0.27 |
| `r-garman-klass-vol-us-sp500-0240` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=1 | -0.95 | -1.02 | -0.94 | -0.89 |
| `r-garman-klass-vol-us-sp500-0248` | cost_bps=5, n_stocks=20, regime_gate=false, holding_days=1 | -1.01 | -0.77 | -1.31 | -0.98 |
| `r-garman-klass-vol-us-sp500-0257` | cost_bps=5, n_stocks=5, regime_gate=true, holding_days=5 | -0.69 | -0.47 | -0.9 | -0.93 |
| `r-garman-klass-vol-us-sp500-0267` | cost_bps=10, n_stocks=20, regime_gate=true, holding_days=5 | -0.68 | -0.41 | -1.21 | -0.48 |
| `r-garman-klass-vol-us-sp500-0281` | cost_bps=5, n_stocks=20, regime_gate=true, holding_days=10 | -1.06 | 0.21 | -1.93 | -1.22 |

## Facts (5)

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

- **Best grid Sharpe ratio is -0.29 (p=0.32).**
  - Value: -0.29 sharpe_ratio
  - Context: period 2022-02-01–2026-06-01; cost=5bps
  - Supports verdict: `rejected`
  - Cite: https://qbuntu.ai/cite/garman-klass-vol-us-sp500-fact-best-sharpe

- **Median Sharpe across 222 grid runs is -0.83.**
  - Value: -0.83 sharpe_ratio
  - Context: Full grid of 222 parameter combinations.
  - Supports verdict: `rejected`
  - Cite: https://qbuntu.ai/cite/garman-klass-vol-us-sp500-fact-median-sharpe

- **Median Sharpe in DOWN regime is -0.45 across 222 runs.**
  - Value: -0.45 sharpe_ratio
  - Context: Regime=DOWN, N225 SMA20/SMA60 classification.
  - Supports verdict: `rejected`
  - Cite: https://qbuntu.ai/cite/garman-klass-vol-us-sp500-fact-regime-down

- **Median Sharpe in FLAT regime is -1.30 across 222 runs.**
  - Value: -1.3 sharpe_ratio
  - Context: Regime=FLAT, N225 SMA20/SMA60 classification.
  - Supports verdict: `rejected`
  - Cite: https://qbuntu.ai/cite/garman-klass-vol-us-sp500-fact-regime-flat

- **Median Sharpe in UP regime is -0.44 across 222 runs.**
  - Value: -0.44 sharpe_ratio
  - Context: Regime=UP, N225 SMA20/SMA60 classification.
  - Supports verdict: `rejected`
  - Cite: https://qbuntu.ai/cite/garman-klass-vol-us-sp500-fact-regime-up

## Related strategies

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

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Cite as: qbuntu (2026). Garman-Klass Volatility Factor (US S&P 500). https://qbuntu.ai/strategies/garman-klass-vol-us-sp500

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