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

ダウンサイドベータ（米国S&P500）のバックテスト

Downside Beta (US S&P 500)

slug: downside-beta-us-sp500

米国S&P500（約503銘柄）でダウンサイドベータをバックテストした。318通りの中央値 Sharpe は -1.15。p-value は 0.01。Max DD は -52.4%。期間は 2022-04-01〜2026-07-01。最良 Sharpe -0.37 は代表値ではない。

判定は rejected。中央値は promising（Sharpe > 0.5 かつ p-value < 0.05）にも marginal（Sharpe > 0.05 かつ最良 p-value < 0.10）にも届いていない。主因は no_edge。レジーム・取引回数・コストには分類されず、中央値が採用ラインに届いていない。

成績の中央値

Sharpe（中央値）

-1.15

Max DD

-52.4%

勝率

—

Alpha（年率）

—

p-value

0.01

期間: 2022-04-01 → 2026-07-01

318通りの Sharpe:中央値 -1.15最良 -0.37 （代表値ではない）最悪 -2.26p25–p75 -1.45–-0.90

仮説

原文は英語。

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

採用しなかった理由

Across 318 grid combinations, median Sharpe=-1.15, best=-0.37. Primary failure mode: no_edge.

検証ファクト (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

検証ラン (30)

run	params	sharpe	UP	FLAT	DOWN
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

対象ユニバース

S&P 500 constituents, ~503 stocks