# Liquidity Premium / Amihud Illiquidity (US S&P 500)

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

## Hypothesis

Amihud (2002): illiquid stocks earn a premium. Applied to S&P 500 constituents.

## Why it didn't work

Across 320 grid combinations, median Sharpe=0.31, best=1.36. Primary failure mode: no_edge.

## Performance summary

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

| Metric | Value |
|---|---|
| Sharpe (median) | 0.3092 |
| Max drawdown | -12.9% |
| p-value | 0.29 |
| Backtest period | 2022-02-01 to 2026-06-01 |

Sharpe distribution across 320 grid runs: median 0.31, best 1.36 (best-case — not representative), worst -1.06, p25 -0.2, p75 0.73.

## 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-liquidity-premium-us-sp500-0000` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=1 | -0.46 | -0.53 | -0.15 | -0.99 |
| `r-liquidity-premium-us-sp500-0001` | cost_bps=5, n_stocks=5, regime_gate=true, holding_days=1 | -0.28 | -0.14 | -0.15 | -0.99 |
| `r-liquidity-premium-us-sp500-0002` | cost_bps=10, n_stocks=5, regime_gate=false, holding_days=1 | -0.76 | -0.84 | -0.41 | -1.36 |
| `r-liquidity-premium-us-sp500-0003` | cost_bps=10, n_stocks=5, regime_gate=true, holding_days=1 | -0.53 | -0.33 | -0.41 | -1.36 |
| `r-liquidity-premium-us-sp500-0012` | cost_bps=5, n_stocks=50, regime_gate=false, holding_days=1 | -0.34 | -0.16 | -0.61 | -0.58 |
| `r-liquidity-premium-us-sp500-0018` | cost_bps=10, n_stocks=5, regime_gate=false, holding_days=5 | -0.16 | -0.03 | 0.47 | -2.11 |
| `r-liquidity-premium-us-sp500-0032` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=10 | 0.21 | 0.82 | -0.37 | -1.25 |
| `r-liquidity-premium-us-sp500-0046` | cost_bps=10, n_stocks=50, regime_gate=false, holding_days=10 | -0.28 | 0.09 | -0.61 | -0.91 |
| `r-liquidity-premium-us-sp500-0060` | cost_bps=5, n_stocks=50, regime_gate=false, holding_days=20 | 0.43 | 0.58 | 0.34 | 0.04 |
| `r-liquidity-premium-us-sp500-0064` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=60 | 0.75 | 0.87 | 0.68 | 0.76 |
| `r-liquidity-premium-us-sp500-0075` | cost_bps=10, n_stocks=20, regime_gate=true, holding_days=60 | 0.79 | 1.38 | -0.21 | 1.57 |
| `r-liquidity-premium-us-sp500-0089` | cost_bps=5, n_stocks=20, regime_gate=true, holding_days=1 | -0.1 | 0.68 | -0.71 | -0.72 |
| `r-liquidity-premium-us-sp500-0103` | cost_bps=10, n_stocks=10, regime_gate=true, holding_days=5 | 0.3 | 1.37 | -0.09 | -1.63 |
| `r-liquidity-premium-us-sp500-0117` | cost_bps=5, n_stocks=10, regime_gate=true, holding_days=10 | 0.41 | 1.45 | -0.61 | -0.86 |
| `r-liquidity-premium-us-sp500-0131` | cost_bps=10, n_stocks=5, regime_gate=true, holding_days=20 | 1.06 | 2.09 | 0.73 | -1.05 |
| `r-liquidity-premium-us-sp500-0145` | cost_bps=5, n_stocks=5, regime_gate=true, holding_days=60 | 0.92 | 1.21 | 0.62 | 0.87 |
| `r-liquidity-premium-us-sp500-0159` | cost_bps=10, n_stocks=50, regime_gate=true, holding_days=60 | 0.81 | 1.27 | -0.28 | 2.76 |
| `r-liquidity-premium-us-sp500-0173` | cost_bps=5, n_stocks=50, regime_gate=true, holding_days=1 | 0.05 | 0.65 | -0.9 | -0.21 |
| `r-liquidity-premium-us-sp500-0187` | cost_bps=10, n_stocks=20, regime_gate=true, holding_days=5 | 0.18 | 1.64 | -0.82 | -1.89 |
| `r-liquidity-premium-us-sp500-0201` | cost_bps=5, n_stocks=20, regime_gate=true, holding_days=10 | 0.32 | 1.42 | -1.11 | -0.98 |
| `r-liquidity-premium-us-sp500-0209` | cost_bps=5, n_stocks=5, regime_gate=true, holding_days=20 | 1.36 | 2.46 | 1.05 | -0.69 |
| `r-liquidity-premium-us-sp500-0216` | cost_bps=5, n_stocks=20, regime_gate=false, holding_days=20 | 0.39 | 1.14 | 0.15 | -0.65 |
| `r-liquidity-premium-us-sp500-0230` | cost_bps=10, n_stocks=10, regime_gate=false, holding_days=60 | 0.69 | 0.92 | 0.24 | 1.55 |
| `r-liquidity-premium-us-sp500-0240` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=1 | -0.66 | -0.56 | -0.54 | -1.15 |
| `r-liquidity-premium-us-sp500-0245` | cost_bps=5, n_stocks=10, regime_gate=true, holding_days=1 | -0.55 | 0.63 | -1.23 | -2 |
| `r-liquidity-premium-us-sp500-0254` | cost_bps=10, n_stocks=50, regime_gate=false, holding_days=1 | -1.06 | -0.67 | -1.78 | -1.08 |
| `r-liquidity-premium-us-sp500-0260` | cost_bps=5, n_stocks=10, regime_gate=false, holding_days=5 | -0.21 | 0.55 | -0.26 | -2.76 |
| `r-liquidity-premium-us-sp500-0274` | cost_bps=10, n_stocks=5, regime_gate=false, holding_days=10 | 0.06 | 0.91 | -1.22 | -0.76 |
| `r-liquidity-premium-us-sp500-0288` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=20 | 0.78 | 1.98 | 0.29 | -0.75 |
| `r-liquidity-premium-us-sp500-0302` | cost_bps=10, n_stocks=50, regime_gate=false, holding_days=20 | 0.08 | 0.5 | 0.14 | -0.96 |

## Facts (5)

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

- **Best grid Sharpe ratio is 1.36 (p=0.006).**
  - Value: 1.36 sharpe_ratio
  - Context: period 2022-02-01–2026-06-01; cost=5bps
  - Supports verdict: `marginal`
  - Cite: https://qbuntu.ai/cite/liquidity-premium-us-sp500-fact-best-sharpe

- **Median Sharpe across 320 grid runs is 0.31.**
  - Value: 0.31 sharpe_ratio
  - Context: Full grid of 320 parameter combinations.
  - Supports verdict: `marginal`
  - Cite: https://qbuntu.ai/cite/liquidity-premium-us-sp500-fact-median-sharpe

- **Median Sharpe in DOWN regime is -0.82 across 320 runs.**
  - Value: -0.82 sharpe_ratio
  - Context: Regime=DOWN, N225 SMA20/SMA60 classification.
  - Supports verdict: `marginal`
  - Cite: https://qbuntu.ai/cite/liquidity-premium-us-sp500-fact-regime-down

- **Median Sharpe in FLAT regime is -0.22 across 320 runs.**
  - Value: -0.22 sharpe_ratio
  - Context: Regime=FLAT, N225 SMA20/SMA60 classification.
  - Supports verdict: `marginal`
  - Cite: https://qbuntu.ai/cite/liquidity-premium-us-sp500-fact-regime-flat

- **Median Sharpe in UP regime is 0.95 across 320 runs.**
  - Value: 0.95 sharpe_ratio
  - Context: Regime=UP, N225 SMA20/SMA60 classification.
  - Supports verdict: `marginal`
  - Cite: https://qbuntu.ai/cite/liquidity-premium-us-sp500-fact-regime-up

## Related strategies

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

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Cite as: qbuntu (2026). Liquidity Premium / Amihud Illiquidity (US S&P 500). https://qbuntu.ai/strategies/liquidity-premium-us-sp500

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