# Downside Beta (US S&P 500)

- **Slug**: `downside-beta-us-sp500`
- **Verdict**: rejected (no_edge)
- **Asset class**: equity
- **Categories**: anomaly, beta, downside-risk, factor
- **Source**: qbuntu-analysis (computed asof 2026-07-31T01:31:49)
- **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/downside-beta-us-sp500
- **JSON**: https://qbuntu.ai/v1/strategies/downside-beta-us-sp500
- **License**: CC-BY-4.0

## Hypothesis

Ang, Chen, Xing (2006): downside beta commands a higher risk premium. Applied to S&P 500 constituents.

## Why it didn't work

Across 318 grid combinations, median Sharpe=-1.25, best=-0.32. Primary failure mode: no_edge.

## Performance summary

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

| Metric | Value |
|---|---|
| Sharpe (median) | -1.2483 |
| Max drawdown | -52.3% |
| p-value | 0.011 |
| Backtest period | 2022-04-01 to 2026-06-01 |

Sharpe distribution across 318 grid runs: median -1.25, best -0.32 (best-case — not representative), worst -2.62, p25 -1.57, p75 -1.01.

## 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-downside-beta-us-sp500-0000` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=1 | -1.24 | -1.18 | -1.25 | -1.3 |
| `r-downside-beta-us-sp500-0001` | cost_bps=5, n_stocks=5, regime_gate=true, holding_days=1 | -0.99 | -0.61 | -1.25 | -1.3 |
| `r-downside-beta-us-sp500-0002` | cost_bps=10, n_stocks=5, regime_gate=false, holding_days=1 | -1.42 | -1.4 | -1.42 | -1.44 |
| `r-downside-beta-us-sp500-0003` | cost_bps=10, n_stocks=5, regime_gate=true, holding_days=1 | -1.14 | -0.83 | -1.42 | -1.44 |
| `r-downside-beta-us-sp500-0012` | cost_bps=5, n_stocks=50, regime_gate=false, holding_days=1 | -1.16 | -0.78 | -1.88 | -0.87 |
| `r-downside-beta-us-sp500-0018` | cost_bps=10, n_stocks=5, regime_gate=false, holding_days=5 | -0.99 | -0.83 | -0.56 | -2.4 |
| `r-downside-beta-us-sp500-0032` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=10 | -1.07 | -0.35 | -1.16 | -2.91 |
| `r-downside-beta-us-sp500-0046` | cost_bps=10, n_stocks=50, regime_gate=false, holding_days=10 | -2.01 | -1.57 | -2.38 | -2.42 |
| `r-downside-beta-us-sp500-0060` | cost_bps=5, n_stocks=50, regime_gate=false, holding_days=20 | -1.58 | -1.32 | -1.23 | -2.86 |
| `r-downside-beta-us-sp500-0064` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=60 | -0.8 | -0.74 | -0.85 | -0.84 |
| `r-downside-beta-us-sp500-0065` | cost_bps=5, n_stocks=5, regime_gate=true, holding_days=60 | -0.32 | 0.6 | -0.85 | -0.84 |
| `r-downside-beta-us-sp500-0076` | cost_bps=5, n_stocks=50, regime_gate=false, holding_days=60 | -1.25 | -1.17 | -1.23 | -1.41 |
| `r-downside-beta-us-sp500-0090` | cost_bps=10, n_stocks=20, regime_gate=false, holding_days=1 | -1.62 | -1.41 | -1.92 | -1.44 |
| `r-downside-beta-us-sp500-0104` | cost_bps=5, n_stocks=20, regime_gate=false, holding_days=5 | -1.61 | -2.38 | -1.01 | -1.66 |
| `r-downside-beta-us-sp500-0118` | cost_bps=10, n_stocks=10, regime_gate=false, holding_days=10 | -1.82 | -1.7 | -1.88 | -2 |
| `r-downside-beta-us-sp500-0132` | cost_bps=5, n_stocks=10, regime_gate=false, holding_days=20 | -1.61 | -2.24 | -0.67 | -2.06 |
| `r-downside-beta-us-sp500-0146` | cost_bps=10, n_stocks=5, regime_gate=false, holding_days=60 | -1.08 | -1.23 | -0.96 | -0.79 |
| `r-downside-beta-us-sp500-0160` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=1 | -1.39 | -1.57 | -1.32 | -1.35 |
| `r-downside-beta-us-sp500-0174` | cost_bps=10, n_stocks=50, regime_gate=false, holding_days=1 | -1.25 | -1.22 | -1.5 | -0.9 |
| `r-downside-beta-us-sp500-0188` | cost_bps=5, n_stocks=50, regime_gate=false, holding_days=5 | -1.71 | -1.59 | -1.45 | -2.45 |
| `r-downside-beta-us-sp500-0202` | cost_bps=10, n_stocks=20, regime_gate=false, holding_days=10 | -2.06 | -1.8 | -2.53 | -2.01 |
| `r-downside-beta-us-sp500-0216` | cost_bps=5, n_stocks=20, regime_gate=false, holding_days=20 | -1.67 | -1.76 | -1.27 | -2.27 |
| `r-downside-beta-us-sp500-0230` | cost_bps=10, n_stocks=10, regime_gate=false, holding_days=60 | -1.34 | -1.39 | -1.45 | -0.86 |
| `r-downside-beta-us-sp500-0240` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=1 | -1.15 | -1.05 | -1.58 | -0.7 |
| `r-downside-beta-us-sp500-0245` | cost_bps=5, n_stocks=10, regime_gate=true, holding_days=1 | -1.07 | -0.7 | -1.8 | -0.97 |
| `r-downside-beta-us-sp500-0259` | cost_bps=10, n_stocks=5, regime_gate=true, holding_days=5 | -1.22 | -0.07 | -1.53 | -5.09 |
| `r-downside-beta-us-sp500-0273` | cost_bps=5, n_stocks=5, regime_gate=true, holding_days=10 | -1.32 | 0.34 | -2.41 | -2.59 |
| `r-downside-beta-us-sp500-0278` | cost_bps=10, n_stocks=10, regime_gate=false, holding_days=10 | -2.62 | -2.31 | -3.1 | -2.69 |
| `r-downside-beta-us-sp500-0288` | cost_bps=5, n_stocks=5, regime_gate=false, holding_days=20 | -1.93 | -2.16 | -1.42 | -2.85 |
| `r-downside-beta-us-sp500-0302` | cost_bps=10, n_stocks=50, regime_gate=false, holding_days=20 | -2.06 | -2.11 | -1.74 | -2.51 |

## Facts (5)

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

- **Best grid Sharpe ratio is -0.32 (p=0.27).**
  - Value: -0.32 sharpe_ratio
  - Context: period 2022-04-01–2026-06-01; cost=5bps
  - Supports verdict: `rejected`
  - Cite: https://qbuntu.ai/cite/downside-beta-us-sp500-fact-best-sharpe

- **Median Sharpe across 318 grid runs is -1.25.**
  - Value: -1.25 sharpe_ratio
  - Context: Full grid of 318 parameter combinations.
  - Supports verdict: `rejected`
  - Cite: https://qbuntu.ai/cite/downside-beta-us-sp500-fact-median-sharpe

- **Median Sharpe in DOWN regime is -2.01 across 318 runs.**
  - Value: -2.01 sharpe_ratio
  - Context: Regime=DOWN, N225 SMA20/SMA60 classification.
  - Supports verdict: `rejected`
  - Cite: https://qbuntu.ai/cite/downside-beta-us-sp500-fact-regime-down

- **Median Sharpe in FLAT regime is -1.52 across 318 runs.**
  - Value: -1.52 sharpe_ratio
  - Context: Regime=FLAT, N225 SMA20/SMA60 classification.
  - Supports verdict: `rejected`
  - Cite: https://qbuntu.ai/cite/downside-beta-us-sp500-fact-regime-flat

- **Median Sharpe in UP regime is -0.80 across 318 runs.**
  - Value: -0.8 sharpe_ratio
  - Context: Regime=UP, N225 SMA20/SMA60 classification.
  - Supports verdict: `rejected`
  - Cite: https://qbuntu.ai/cite/downside-beta-us-sp500-fact-regime-up

## Related strategies

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

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Cite as: qbuntu (2026). Downside Beta (US S&P 500). https://qbuntu.ai/strategies/downside-beta-us-sp500

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