# Amihud Illiquidity Premium (US S&P 500)

- **Slug**: `amihud-illiquidity-premium-us-sp500`
- **Verdict**: marginal (regime_dependent)
- **Asset class**: equity
- **Categories**: factor, liquidity
- **Source**: qbuntu-analysis (computed asof 2026-08-02T16:26:49)
- **Reproducibility**: analysis-engine@2f23bb7, backtest-lib@711b855, grid tier=shallow (python 3.10.11, numpy 2.2.6, pandas 2.3.3)
- **HTML**: https://qbuntu.ai/strategies/amihud-illiquidity-premium-us-sp500
- **JSON**: https://qbuntu.ai/v1/strategies/amihud-illiquidity-premium-us-sp500
- **License**: CC-BY-4.0

## Hypothesis

Amihud (2002): illiquid stocks (high |return| per unit of trading volume) must compensate holders with higher expected returns. Ranking on the Amihud illiquidity measure tests whether the premium survives transaction costs in this universe.

## Why it didn't work

Across 144 grid combinations, median Sharpe=0.12, best=1.36. Primary failure mode: regime_dependent.

## Performance summary

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

| Metric | Value |
|---|---|
| Sharpe (median) | 0.1208 |
| Max drawdown | -10.8% |
| p-value | 0.31 |
| Backtest period | 2022-02-01 to 2026-06-01 |

Sharpe distribution across 144 grid runs: median 0.12, best 1.36 (best-case — not representative), worst -1, p25 -0.38, p75 0.61.

## 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
- Transaction cost bps: 5

## Target universe

S&P 500 constituents, ~503 stocks

## Runs (30)

| run_id | params | sharpe | UP | FLAT | DOWN |
|---|---|---:|---:|---:|---:|
| `r-amihud-illiquidity-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-amihud-illiquidity-premium-us-sp500-0001` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=5 | -0.02 | 0.09 | 0.61 | -1.92 |
| `r-amihud-illiquidity-premium-us-sp500-0002` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=20 | 0.83 | 1.43 | 1.02 | -1.05 |
| `r-amihud-illiquidity-premium-us-sp500-0003` | cost_bps=5, n_stocks=5, regime_gate=true, holding_days=1 | -0.28 | -0.14 | -0.15 | -0.99 |
| `r-amihud-illiquidity-premium-us-sp500-0006` | cost_bps=10, n_stocks=5, regime_gate=false, holding_days=1 | -0.76 | -0.84 | -0.41 | -1.36 |
| `r-amihud-illiquidity-premium-us-sp500-0010` | cost_bps=10, n_stocks=5, regime_gate=true, holding_days=5 | 0.31 | 0.89 | 0.47 | -2.11 |
| `r-amihud-illiquidity-premium-us-sp500-0016` | cost_bps=5, n_stocks=10, regime_gate=true, holding_days=5 | 0.4 | 1.42 | 0.15 | -1.51 |
| `r-amihud-illiquidity-premium-us-sp500-0022` | cost_bps=10, n_stocks=10, regime_gate=true, holding_days=5 | 0.26 | 1.32 | -0.03 | -1.7 |
| `r-amihud-illiquidity-premium-us-sp500-0028` | cost_bps=5, n_stocks=20, regime_gate=true, holding_days=5 | 0.5 | 1.96 | -0.21 | -1.63 |
| `r-amihud-illiquidity-premium-us-sp500-0034` | cost_bps=10, n_stocks=20, regime_gate=true, holding_days=5 | 0.32 | 1.83 | -0.45 | -1.87 |
| `r-amihud-illiquidity-premium-us-sp500-0036` | cost_bps=5, n_stocks=50, regime_gate=false, holding_days=1 | -0.34 | -0.16 | -0.61 | -0.58 |
| `r-amihud-illiquidity-premium-us-sp500-0041` | cost_bps=5, n_stocks=50, regime_gate=true, holding_days=20 | 0.98 | 1.53 | 0.34 | 0.04 |
| `r-amihud-illiquidity-premium-us-sp500-0042` | cost_bps=10, n_stocks=50, regime_gate=false, holding_days=1 | -1 | -0.72 | -1.58 | -1.18 |
| `r-amihud-illiquidity-premium-us-sp500-0048` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=1 | -0.52 | -0.47 | -0.84 | -0.14 |
| `r-amihud-illiquidity-premium-us-sp500-0054` | cost_bps=10, n_stocks=5, regime_gate=false, holding_days=1 | -0.81 | -0.75 | -1.14 | -0.4 |
| `r-amihud-illiquidity-premium-us-sp500-0060` | cost_bps=5, n_stocks=10, regime_gate=false, holding_days=1 | -0.62 | -0.3 | -1.12 | -0.62 |
| `r-amihud-illiquidity-premium-us-sp500-0066` | cost_bps=10, n_stocks=10, regime_gate=false, holding_days=1 | -0.95 | -0.64 | -1.48 | -0.87 |
| `r-amihud-illiquidity-premium-us-sp500-0072` | cost_bps=5, n_stocks=20, regime_gate=false, holding_days=1 | -0.23 | 0.21 | -0.71 | -0.72 |
| `r-amihud-illiquidity-premium-us-sp500-0078` | cost_bps=10, n_stocks=20, regime_gate=false, holding_days=1 | -0.69 | -0.22 | -1.36 | -1.07 |
| `r-amihud-illiquidity-premium-us-sp500-0084` | cost_bps=5, n_stocks=50, regime_gate=false, holding_days=1 | -0.34 | -0.11 | -0.54 | -0.69 |
| `r-amihud-illiquidity-premium-us-sp500-0090` | cost_bps=10, n_stocks=50, regime_gate=false, holding_days=1 | -0.97 | -0.68 | -1.4 | -1.21 |
| `r-amihud-illiquidity-premium-us-sp500-0096` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=1 | -0.64 | -0.44 | -1.1 | -0.26 |
| `r-amihud-illiquidity-premium-us-sp500-0097` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=5 | 0.1 | 0.39 | 0.39 | -1.2 |
| `r-amihud-illiquidity-premium-us-sp500-0101` | cost_bps=5, n_stocks=5, regime_gate=true, holding_days=20 | 1.36 | 2.46 | 1.05 | -0.69 |
| `r-amihud-illiquidity-premium-us-sp500-0104` | cost_bps=10, n_stocks=5, regime_gate=false, holding_days=20 | 1.04 | 1.98 | 0.98 | -0.76 |
| `r-amihud-illiquidity-premium-us-sp500-0110` | cost_bps=5, n_stocks=10, regime_gate=false, holding_days=20 | 0.51 | 1.09 | 0.62 | -0.43 |
| `r-amihud-illiquidity-premium-us-sp500-0116` | cost_bps=10, n_stocks=10, regime_gate=false, holding_days=20 | 0.42 | 0.99 | 0.51 | -0.49 |
| `r-amihud-illiquidity-premium-us-sp500-0122` | cost_bps=5, n_stocks=20, regime_gate=false, holding_days=20 | 0.39 | 1.14 | 0.15 | -0.65 |
| `r-amihud-illiquidity-premium-us-sp500-0128` | cost_bps=10, n_stocks=20, regime_gate=false, holding_days=20 | 0.27 | 1.01 | 0 | -0.75 |
| `r-amihud-illiquidity-premium-us-sp500-0134` | cost_bps=5, n_stocks=50, regime_gate=false, holding_days=20 | 0.42 | 0.69 | 0.25 | -0.01 |

## 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/amihud-illiquidity-premium-us-sp500-fact-best-sharpe

- **Median Sharpe across 144 grid runs is 0.12.**
  - Value: 0.12 sharpe_ratio
  - Context: Full grid of 144 parameter combinations.
  - Supports verdict: `marginal`
  - Cite: https://qbuntu.ai/cite/amihud-illiquidity-premium-us-sp500-fact-median-sharpe

- **Median Sharpe in DOWN regime is -0.86 across 144 runs.**
  - Value: -0.86 sharpe_ratio
  - Context: Regime=DOWN, N225 SMA20/SMA60 classification.
  - Supports verdict: `marginal`
  - Cite: https://qbuntu.ai/cite/amihud-illiquidity-premium-us-sp500-fact-regime-down

- **Median Sharpe in FLAT regime is -0.10 across 144 runs.**
  - Value: -0.1 sharpe_ratio
  - Context: Regime=FLAT, N225 SMA20/SMA60 classification.
  - Supports verdict: `marginal`
  - Cite: https://qbuntu.ai/cite/amihud-illiquidity-premium-us-sp500-fact-regime-flat

- **Median Sharpe in UP regime is 0.63 across 144 runs.**
  - Value: 0.63 sharpe_ratio
  - Context: Regime=UP, N225 SMA20/SMA60 classification.
  - Supports verdict: `marginal`
  - Cite: https://qbuntu.ai/cite/amihud-illiquidity-premium-us-sp500-fact-regime-up

## Related strategies

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

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

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