Pair detail

MSFT / AAPL

Market: US | As of Sep 02, 2026 | Source: mock

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	MSFT	Microsoft Corp.	Technology · Software - Infrastructure	3.0T	$425.17	0.70%
Short	AAPL	Apple Inc.	Technology · Consumer Electronics	2.9T	$189.04	0.50%

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.

-1.82

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

1.040

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

0.91

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

14.2

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

0.040

Quality62/100

C+Grade

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 = -1.82?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.0.18

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 MSFT, long AAPL. If z <= -2.0: long MSFT, short AAPL. Size: 1x MSFT vs 1.04x AAPL.

Backtest

Historical performance

Rule-based outcomes over the lookback window.

Backtest reality check

Historical trade outcomes using the entry/exit rules.

Trades (lookback)8

Trades / year1.6

Win rate58%

Median hold7.0d

Avg return (gross)1.20%

Avg return (net)1.12%

Max drawdown8.00%

Profit factor1.40

Sharpe1.10

Best / worst5.00% / -3.00%

Backtest trades

Showing 8 of 8

Entry	Exit	Side	Hold	Net
2026-08-03	2026-08-09	Short MSFT / Long AAPL	6d	+0.90%
2026-07-04	2026-07-10	Long MSFT / Short AAPL	6d	+1.50%
2026-06-04	2026-06-12	Short MSFT / Long AAPL	8d	+1.20%
2026-05-05	2026-05-13	Long MSFT / Short AAPL	8d	+1.00%
2026-04-05	2026-04-15	Short MSFT / Long AAPL	10d	+0.80%
2026-03-01	2026-03-10	Long MSFT / Short AAPL	9d	+1.10%
2026-02-04	2026-02-11	Short MSFT / Long AAPL	7d	+1.30%
2026-01-05	2026-01-12	Long MSFT / Short AAPL	7d	+1.70%

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.

-0.3840

Price-space spread

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

-0.320000

Market-neutral residual spread

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

0.0012

OLS intercept on residualized returns

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

0.050

Stability (21d rolling)

Mean corr?Average rolling correlation. Higher is better for stable pairs.0.910

Std dev?Standard deviation of rolling correlation. Lower means more stable.0.050

Min / Max?Range of rolling correlation. Higher minimum indicates stronger stability.0.840 / 0.970

Below 0.70?Count of 21d windows where correlation dropped below the minimum threshold. Lower is better.2

Window 252d

Z-score distribution

Percentile?Position of current z-score within the window. Near 0 or 100 indicates extremes.37%

Min / Max?Historical extremes of z-score in the chart window.-2.36 / -1.36

Mean reversions?Count of times z crossed from entry zone back to exit zone. More events imply more opportunities.0

Entry |z| ≥ 2.0 · Exit |z| ≤ 0.5

Risk & invalidation

MAE (median)0.60z

MAE (max)1.20z

Stop suggestionz > 3.5

Regime min corr0.720

Z-score context

Spread mean (mu)-0.032000

Spread std (sigma)0.120000

Robust Z (MAD)Off

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

Quality score

Composite of cointegration, stability, and mean reversion signals.

C+62/100

Cointegration (ADF)Pass

Stability (corr std)Stable

Mean reversionFast

LiquidityUnknown

Regime riskNormal

Model transparency

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

Window 252d · Lookback 5y

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