Multiple Spread Trading
A multivariate mean-reversion framework that extends classical pair trading to groups of N ≥ 3 cointegrated assets, validated across 5 asset classes with a fixed-parameter walk-forward protocol.
Academic Publication
Multiple Spread Trading: A Multivariate Mean-Reversion Framework Based on PCA Disalignment Detection Across Asset Classes
Abstract
We introduce Multiple Spread Trading (MST), a multivariate mean-reversion framework that extends pair trading to groups of N ≥ 3 cointegrated assets. The central signal — the Temporary Disalignment Index (TDI)— is constructed via PCA projection of z-scores of log-ratio changes across all C(N,2) pairs, followed by normalization to the 98th asymmetric percentile.
Unlike Gaussian standardization, the TDI imposes no distributional assumptions and is robust to heavy tails and regime shifts. The optimal mean-reversion window scales monotonically with the physical rebalancing cycle of the asset class (63 → 252 days, forex to metals).
A 6-strategy portfolio yields an OOS Sharpe ratio of 2.092at 1× leverage (CAGR +7.6%, MDD −3.3%, Calmar = 2.28), with Diversification Ratio = 2.28. Statistical significance is confirmed by the N-independent z-test (z = 2.354, p = 9.29×10−3) and DSR > 0.97 for N ≤ 18.
The TDI Construction Pipeline
The Temporary Disalignment Index is computed in four sequential steps, each strictly backward-looking with zero look-ahead bias (verified via 26 regression tests, 0 failures).
Log-Ratio Changes
For each pair (i,j), compute the change in log(Pi/Pj) over the fast window τf. Captures relative momentum, stationary by construction.
RCᵢⱼ(t) = Δlog(Pᵢ/Pⱼ)Z-Score Normalization
Each RC is standardized using its moving mean and σ over the slow window τs. Prevents pairs with larger spreads from dominating PCA.
Zᵢⱼ = (RC − μ) / σPCA Projection
Project the K-dimensional Z vector onto the first eigenvector v₁ of the covariance matrix. Captures the dominant collective misalignment.
φ(t) = Z(t)ᵀ · v₁(t)Percentile Normalization
Normalize φ using the 98th/2nd asymmetric percentile. Non-parametric, robust to fat tails, regime shifts, and asymmetry.
TDI = (φ − median) / Q₉₈P(t) → RC(t) → Z(t) → φ(t) → TDI(t)TDI Properties
Stationarity
Oscillates around zero by construction. Moving median centers the indicator; z-score removes secular drift.
Non-Parametric Robustness
Percentile scaling (not σ) makes TDI invariant under monotonic tail transformations. Handles kurtosis κ > 5.
No Look-Ahead Bias
All statistics computed over [t−τs, t]. Verified with 26 regression tests and randomized date shuffling (0 failures).
Adaptive Equilibrium
Moving windows (μ, σ, Qp) update every bar. Equilibrium adapts to structural changes without explicit regime switching.
Leverage Invariance
Sharpe ratio is leverage-invariant (ΔSh ≈ 0 from 1× to 3×). Performance scales linearly with capital allocation.
Cointegration Link
First PCA direction of Z(t) converges to Johansen's first cointegrating vector as T → ∞ under r=1.
Trading Logic & Exit Rules
Entry
LONG when TDI(t) < −E (bottom 2% of distribution)
SHORT when TDI(t) > +E (top 2% of distribution)
Entry threshold E ∈ {1.0, 1.2, 1.5} calibrated per asset class
Exit Conditions (sequential priority)
MR — Mean-reversion: |TDI| < X (convergence to zero) — 79%
OS — Overshoot: TDI crosses −E in long (±E in short) — 11%
HS — Hard Stop: unrealized loss > risk budget (ATR-based)
TS — TDI Stop: |TDI| ≥ 2.5 (structural misalignment)
TO — Time Stop: trade exceeds τ_stop bars
Key Results (OOS, Paper Portfolio)
Sharpe (1×)
2.092
CAGR (1×)
+7.6%
MDD (1×)
−3.3%
Calmar
2.28
Div. Ratio
2.28
Max |ρ|
0.049
z-test
z=2.354
p-value
9.29×10⁻³
Paper portfolio: 6 strategies, 5 asset classes, 4-year OOS window. Fixed parameters, no re-optimization. See the full paper for methodology details.
V8 Production Deployment
BEST_8 FX Pure Play Portfolio
The production system deploys 8 FX clusters selected from the paper's validated universe. Dual-timeframe execution (M30 TDI + M1 TP) with unified capital pool, RPT = 0.30.
Sharpe OOS
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CAGR OOS
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Max Drawdown
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Profit Factor
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Win Rate
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Sortino
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Calmar
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Avg P&L
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Total Trades
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OOS Period
Feb 2022 → Mar 2026
Differential Latency Hypothesis
The paper proposes the Differential Latency Hypothesis as the microeconomic foundation for the TDI: the signal captures differential information propagation speeds across cluster assets.
When a macro shock arrives (e.g., a change in USD interest rate expectations), it propagates to EURUSD, GBPUSD, USDJPY, and AUDUSD at different speeds due to liquidity differentials, timezone effects, and market microstructure. This creates a temporary PCA disalignment that the TDI detects and that mean-reverts as arbitrageurs equalize the information.
This mechanism is consistent with the empirical findings of Hong and Stein (1999) and Cohen and Frazzini (2008) on slow diffusion of information among economically linked assets.
Proprietary V8 Implementation
The production V8 engine extends the paper's framework with dual-timeframe execution (M30 + M1), 4-level risk management, news filtering, and real-time MT5 integration. Implementation details are proprietary.
The full academic methodology is available in the published paper.