Pair detail

BAC / MS

Market: SPY | As of May 20, 2026 | Source: live

Pair overview

Bias uses the latest z-score sign (positive → short A / long B).

Bias	Symbol	Company	Sector / Industry	Market cap USD	Last Close	Div Yield
Long	BAC	Bank of America Corporation	Financial Services · Banks - Diversified	363.6B	$51.23	2.15%
Short	MS	Morgan Stanley	Financial Services · Financial - Capital Markets	311.9B	$197.77	2.02%

Key metrics

Decision signals

Entry, sizing, and stability anchors for the trade.

Z-score?Z = (S - μ) / σ. Higher absolute values mean larger deviation; |z| >= 2 is often a potential entry.

-1.72

Hedge ratio (γ)?Units of B needed to hedge 1 unit of A. More stable ratios are easier to trade.

0.990

Correlation?Higher correlation is better for pair stability. Values close to 1 imply strong co-movement.

0.72

Half-life (days)?Estimated mean-reversion speed. Lower days mean faster reversion.

9.6

ADF p-value?Stationarity test on the spread. Lower is better; below 0.05 is preferred.

0.003

Quality34/100

FGrade

Signal?Signal is derived from z-score vs entry/exit thresholds. Long spread means long A and short B; short spread is the opposite.

Watching

z = -1.72?Current standardized spread. Positive means A rich vs B; negative means A cheap vs B.

Entry threshold?Entry zone for trades. Higher absolute z means more extreme deviation.|z| ≥ 2.0

Exit threshold?Exit zone. When |z| returns near zero, the spread has mean-reverted.|z| ≤ 0.5

Distance to entry?How far the current |z| is from the entry threshold.0.28

Trade bias?Explicit long/short legs for the spread. Positive z implies A rich vs B; negative z implies A cheap vs B.No trade now. If z >= +2.0: short BAC, long MS. If z <= -2.0: long BAC, short MS. Size: 1x BAC vs 0.99x MS.

Backtest

Historical performance

Rule-based outcomes over the lookback window.

Backtest reality check

Historical trade outcomes using the entry/exit rules.

Trades (lookback)3

Trades / year3.0

Win rate100%

Median hold18.0d

Avg return (gross)4.28%

Avg return (net)4.28%

Max drawdown3.23%

Profit factor∞

Sharpe2.44

Best / worst6.12% / 0.78%

Backtest trades

Showing 3 of 3

Entry	Exit	Side	Hold	Net
2026-05-13	2026-05-20	Long BAC / Short MS	7d	+0.78%
2026-02-06	2026-02-26	Short BAC / Long MS	20d	+6.12%
2026-01-15	2026-02-02	Long BAC / Short MS	18d	+5.95%

Charts

Behavior over time

Price, spread, and hedged path context.

Z-score

Z-score trajectory with entry/exit bands.

Chart window: 90d

Entry ±2.0Exit ±0.5

Leg prices (normalized)

Relative move of each leg across the window.

Chart window: 90d

Normalized to 100 at window start.

Hedged position

Hedged spread with entry-zone shading.

Chart window: 90d

Spread = A - (alpha + gamma · B)

Model diagnostics

Spread mechanics

Helpful for validation and monitoring.

Raw spread?Raw spread = A - γ·B in price space. Positive means A is rich vs B.

-144.4693

Price-space spread

Residual spread?Residual spread = residual(A) - (alpha + gamma · residual(B)). Market-neutralized via index regression.

-0.049034

Market-neutral residual spread

Pair intercept?OLS intercept for the pair regression. Closer to 0 is cleaner.

0.0385

OLS intercept on residualized returns

Rolling corr std (21d)?Rolling correlation variability. Lower values indicate more stable pairs.

0.125

Stability (21d rolling)

Mean corr?Average rolling correlation. Higher is better for stable pairs.0.728

Std dev?Standard deviation of rolling correlation. Lower means more stable.0.125

Min / Max?Range of rolling correlation. Higher minimum indicates stronger stability.0.275 / 0.907

Below 0.70?Count of 21d windows where correlation dropped below the minimum threshold. Lower is better.74

Window 252d

Z-score distribution

Percentile?Position of current z-score within the window. Near 0 or 100 indicates extremes.4%

Min / Max?Historical extremes of z-score in the chart window.-2.83 / +2.17

Mean reversions?Count of times z crossed from entry zone back to exit zone. More events imply more opportunities.2

Entry |z| ≥ 2.0 · Exit |z| ≤ 0.5

Risk & invalidation

MAE (median)0.00z

MAE (max)0.00z

Stop suggestionz > 3.5

Regime min corr0.275

Rolling corr min 0.275 → regime risk high

Z-score context

Spread mean (mu)-0.000000

Spread std (sigma)0.028475

Robust Z (MAD)Off

Z = (S - mu) / sigma | Window 252d

Quality score

Composite of cointegration, stability, and mean reversion signals.

F34/100

Cointegration (ADF)Pass

Stability (corr std)Volatile

Mean reversionFast

LiquidityUnknown

Regime riskHigh

Model transparency

Regression uses OLS on market-neutral residual returns. ADF test is applied to the residual spread series.

Window 252d · Lookback 10y

Z-score window: 252d trading days

Correlation window: 252d trading days

Spread formula: S = A - (alpha + gamma * B) | Raw spread: A - gamma * B

Entry |z| ≥ 2.0 · Exit |z| ≤ 0.5

Min correlation filter: 0.70