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rejectedno_edge· equity· anomaly· beta· downside-risk· factor

Downside Beta (US S&P 500)

slug: downside-beta-us-sp500

Downside Beta (US S&P 500) backtest. Median Sharpe across 318 parameter sets is -1.15. p-value is 0.01. Max DD is -52.4%. Period: 2022-04-01 to 2026-07-01. Best Sharpe -0.37 is not the representative figure.

Verdict: rejected. The median reaches neither promising (Sharpe > 0.5 and p-value < 0.05) nor marginal (Sharpe > 0.05 and best p-value < 0.10). Primary reason: no_edge. It is not regime, frequency, or cost, and the median does not clear the bar.

Performance summary

Sharpe (median)
-1.15
Max DD
-52.4%
Win rate
—
Alpha (ann.)
—
p-value
0.01
backtest period: 2022-04-01 → 2026-07-01
Sharpe across 318 grid runs:median -1.15best -0.37 (not representative)worst -2.26p25–p75 -1.45–-0.90

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=-1.15, best=-0.37. Primary failure mode: no_edge.

Facts (5)

Best grid Sharpe ratio is -0.37 (p=0.19).
period 2022-04-01–2026-07-01; cost=5bps
sharpe_ratio-0.37
cite ↗ /cite/downside-beta-us-sp500-fact-best-sharpevia r-downside-beta-us-sp500-0065
Median Sharpe across 318 grid runs is -1.15.
Full grid of 318 parameter combinations.
sharpe_ratio-1.15
cite ↗ /cite/downside-beta-us-sp500-fact-median-sharpe
Median Sharpe in DOWN regime is -2.01 across 318 runs.
Regime=DOWN, N225 SMA20/SMA60 classification.
sharpe_ratio-2.01
cite ↗ /cite/downside-beta-us-sp500-fact-regime-down
Median Sharpe in FLAT regime is -1.24 across 318 runs.
Regime=FLAT, N225 SMA20/SMA60 classification.
sharpe_ratio-1.24
cite ↗ /cite/downside-beta-us-sp500-fact-regime-flat
Median Sharpe in UP regime is -0.77 across 318 runs.
Regime=UP, N225 SMA20/SMA60 classification.
sharpe_ratio-0.77
cite ↗ /cite/downside-beta-us-sp500-fact-regime-up

Runs (30)

runparamssharpeUPFLATDOWN
formation_days=40, holding_days=1, n_stocks=5, cost_bps=5, regime_gate=False
r-downside-beta-us-sp500-0000
cost_bps: 5
n_stocks: 5
regime_gate: false
-1.15-1.18-1.03-1.30
formation_days=40, holding_days=1, n_stocks=5, cost_bps=5, regime_gate=True
r-downside-beta-us-sp500-0001
cost_bps: 5
n_stocks: 5
regime_gate: true
-0.90-0.61-1.03-1.30
formation_days=40, holding_days=1, n_stocks=5, cost_bps=10, regime_gate=False
r-downside-beta-us-sp500-0002
cost_bps: 10
n_stocks: 5
regime_gate: false
-1.34-1.40-1.20-1.44
formation_days=40, holding_days=1, n_stocks=5, cost_bps=10, regime_gate=True
r-downside-beta-us-sp500-0003
cost_bps: 10
n_stocks: 5
regime_gate: true
-1.06-0.83-1.20-1.44
formation_days=40, holding_days=1, n_stocks=50, cost_bps=5, regime_gate=False
r-downside-beta-us-sp500-0012
cost_bps: 5
n_stocks: 50
regime_gate: false
-1.10-0.78-1.64-0.87
formation_days=40, holding_days=5, n_stocks=5, cost_bps=10, regime_gate=False
r-downside-beta-us-sp500-0018
cost_bps: 10
n_stocks: 5
regime_gate: false
-0.96-0.83-0.49-2.40
formation_days=40, holding_days=10, n_stocks=5, cost_bps=5, regime_gate=False
r-downside-beta-us-sp500-0032
cost_bps: 5
n_stocks: 5
regime_gate: false
-0.79-0.08-0.82-2.91
formation_days=40, holding_days=10, n_stocks=50, cost_bps=10, regime_gate=False
r-downside-beta-us-sp500-0046
cost_bps: 10
n_stocks: 50
regime_gate: false
-1.78-1.66-1.69-2.42
formation_days=40, holding_days=20, n_stocks=50, cost_bps=5, regime_gate=False
r-downside-beta-us-sp500-0060
cost_bps: 5
n_stocks: 50
regime_gate: false
-1.42-1.35-0.83-2.86
formation_days=40, holding_days=60, n_stocks=5, cost_bps=5, regime_gate=False
r-downside-beta-us-sp500-0064
cost_bps: 5
n_stocks: 5
regime_gate: false
-0.76-0.58-0.85-1.15
formation_days=40, holding_days=60, n_stocks=5, cost_bps=5, regime_gate=True
r-downside-beta-us-sp500-0065
cost_bps: 5
n_stocks: 5
regime_gate: true
-0.37+0.69-0.85-1.15
formation_days=40, holding_days=60, n_stocks=50, cost_bps=5, regime_gate=False
r-downside-beta-us-sp500-0076
cost_bps: 5
n_stocks: 50
regime_gate: false
-1.15-0.94-1.23-1.59
formation_days=60, holding_days=1, n_stocks=20, cost_bps=10, regime_gate=False
r-downside-beta-us-sp500-0090
cost_bps: 10
n_stocks: 20
regime_gate: false
-1.53-1.41-1.64-1.44
formation_days=60, holding_days=5, n_stocks=20, cost_bps=5, regime_gate=False
r-downside-beta-us-sp500-0104
cost_bps: 5
n_stocks: 20
regime_gate: false
-1.59-2.38-0.99-1.66
formation_days=60, holding_days=10, n_stocks=10, cost_bps=10, regime_gate=False
r-downside-beta-us-sp500-0118
cost_bps: 10
n_stocks: 10
regime_gate: false
-1.62-1.74-1.37-2.00
formation_days=60, holding_days=20, n_stocks=10, cost_bps=5, regime_gate=False
r-downside-beta-us-sp500-0132
cost_bps: 5
n_stocks: 10
regime_gate: false
-1.45-2.24-0.39-2.06
formation_days=60, holding_days=60, n_stocks=5, cost_bps=10, regime_gate=False
r-downside-beta-us-sp500-0146
cost_bps: 10
n_stocks: 5
regime_gate: false
-1.04-1.06-0.96-1.10
formation_days=120, holding_days=1, n_stocks=5, cost_bps=5, regime_gate=False
r-downside-beta-us-sp500-0160
cost_bps: 5
n_stocks: 5
regime_gate: false
-1.27-1.57-1.02-1.35
formation_days=120, holding_days=1, n_stocks=50, cost_bps=10, regime_gate=False
r-downside-beta-us-sp500-0174
cost_bps: 10
n_stocks: 50
regime_gate: false
-1.12-1.22-1.13-0.90
formation_days=120, holding_days=5, n_stocks=50, cost_bps=5, regime_gate=False
r-downside-beta-us-sp500-0188
cost_bps: 5
n_stocks: 50
regime_gate: false
-1.66-1.59-1.35-2.45
formation_days=120, holding_days=10, n_stocks=20, cost_bps=10, regime_gate=False
r-downside-beta-us-sp500-0202
cost_bps: 10
n_stocks: 20
regime_gate: false
-1.74-1.46-1.97-2.01
formation_days=120, holding_days=20, n_stocks=20, cost_bps=5, regime_gate=False
r-downside-beta-us-sp500-0216
cost_bps: 5
n_stocks: 20
regime_gate: false
-1.40-1.57-0.85-2.27
formation_days=120, holding_days=60, n_stocks=10, cost_bps=10, regime_gate=False
r-downside-beta-us-sp500-0230
cost_bps: 10
n_stocks: 10
regime_gate: false
-1.29-1.22-1.45-1.20
formation_days=250, holding_days=1, n_stocks=5, cost_bps=5, regime_gate=False
r-downside-beta-us-sp500-0240
cost_bps: 5
n_stocks: 5
regime_gate: false
-0.92-1.05-0.79-0.70
formation_days=250, holding_days=1, n_stocks=10, cost_bps=5, regime_gate=True
r-downside-beta-us-sp500-0245
cost_bps: 5
n_stocks: 10
regime_gate: true
-0.85-0.70-1.09-0.97
formation_days=250, holding_days=5, n_stocks=5, cost_bps=10, regime_gate=True
r-downside-beta-us-sp500-0259
cost_bps: 10
n_stocks: 5
regime_gate: true
-1.17-0.07-1.38-5.09
formation_days=250, holding_days=10, n_stocks=5, cost_bps=5, regime_gate=True
r-downside-beta-us-sp500-0273
cost_bps: 5
n_stocks: 5
regime_gate: true
-1.18+0.49-1.95-2.59
formation_days=250, holding_days=10, n_stocks=10, cost_bps=10, regime_gate=False
r-downside-beta-us-sp500-0278
cost_bps: 10
n_stocks: 10
regime_gate: false
-2.26-2.09-2.31-2.69
formation_days=250, holding_days=20, n_stocks=5, cost_bps=5, regime_gate=False
r-downside-beta-us-sp500-0288
cost_bps: 5
n_stocks: 5
regime_gate: false
-1.72-2.02-1.12-2.85
formation_days=250, holding_days=20, n_stocks=50, cost_bps=10, regime_gate=False
r-downside-beta-us-sp500-0302
cost_bps: 10
n_stocks: 50
regime_gate: false
-1.67-1.90-1.10-2.51

Target universe

S&P 500 constituents, ~503 stocks

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source: qbuntu-analysis · kabu STATION REST API + J-Quants daily bars
computed asof: 2026-09-24T02:22:20
view as Markdown ↗view as JSON ↗license: CC-BY-4.0

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