Strategies

Precious-Metals Complex Mean-Reverting Portfolio (Zhao et al. 2018 MRP design): 3-Asset GDX/GLD/SLV Spread Built by Minimum-Predictability Weights Under a Variance Floor and an L1 Leverage Budget, Z-Score Entry/Exit With an Explicit Flat State (USEQ DAILY, long-short)

Outcome: Abandoned

GdxGldSlvMinPredictabilityMRP

Outcome Summary

GdxGldSlvMinPredictabilityMRP tried to trade a three-asset precious-metals spread (GDX/GLD/SLV). It used minimum-predictability eigenvector weights, re-estimated quarterly, and z-score entries, with a pre-registered estimate of roughly 7-10 trades a year. Over 3 iterations the code never passed verification. The Layer 3 sandbox backtest kept exceeding the 300s limit on a ~20,000-bar daily window. The run was abandoned as a sandbox timeout in the verification loop, so backtest review, optimization, analyst review and risk review were never reached and no performance metrics exist.

Strategy report

Hypothesis

Source: arXiv:1803.02974 (Zhao et al., 2018), abstract. The abstract gives a construction rule: build a portfolio that mean-reverts strongly, keeps enough spread variance to trade, and stays inside a leverage limit. It does not give a trading rule, the exact mean-reversion measure, or the constraint values. Those are filled in below and have to be checked against the full paper. None of the paper's performance claims have been verified. The basket is 3 assets linked by economics: GDX.USEQ (gold miners, the primary instrument), GLD.USEQ and SLV.USEQ. They trade daily on the commission-free USEQ venue and have about 19-20 years of history. Weights: every 63 sessions, use the trailing 504 daily log closes to estimate the lag-0 covariance S0 and the lag-1 autocovariance S1. Take the vector with the lowest Box-Tiao predictability, which is a 3x3 generalised eigenproblem. Scale it so the absolute weights sum to 1 (the leverage budget) and make the GDX weight positive. If the spread's daily standard deviation is below 0.6% of gross notional (the variance floor), use the next eigenvector. If none passes, stay flat. Weights stay fixed between re-estimations. The full SCA solve from the paper is a separate pre-registered variant, not part of this claim. Trading: take the spread s = w' log P and its z-score over 60 sessions. Enter at |z| >= 2 and exit at |z| <= 0.25, after 30 sessions, at |z| >= 4, or on a re-estimation date. The strategy is flat by default, about 65-75% of sessions. Gross notional is 100% of equity. Only the 3x3 eigen solve on re-estimation bars is heavy; per-bar work is O(1). Fee arithmetic: expected capture is about 0.8-1.2% of gross notional per trade. Costs are about 0.10-0.15% for three legs at roughly 0.03-0.05% each, so capture is more than 5x cost. Expected rate is about 7-10 trades a year, or about 140-190 over the history.

Iteration 3 preserves the previously passing strategy logic and changes only the costly extra-leg access path. Extra-bar prices are cached once in on_extra_bar and read by exact close timestamp in O(1) time, eliminating repeated access to the accumulated extra-bar history during the 20,000-bar sandbox run.

verification_loop: sandbox_timeout: Verification failed (Layer 3 — sandbox backtest): smoke test exceeded the 300s wall-clock limit on a ~20000-bar window (2400 days of GDX.USEQ-1-DAY-LAST-EXTERNAL). This almost always means per-bar work that scales with history — e.g. rescanning the full funding/supplementary series, or rebuilding a list and calling min()/sorted() inside calculate_signal()/on_bar() on every bar. Precompute sorted timestamp arrays ONCE in __init__ and use bisect, or cache lookups keyed by timestamp, so per-bar cost is O(log n) not O(n).

Implementation

A daily USEQ long-short mean-reverting portfolio over GDX, GLD, and SLV. It periodically estimates minimum-predictability weights from lagged covariance structure, enforces a spread-volatility floor, and trades the resulting spread by z-score.

Verification Results

sandbox_timeout: Verification failed (Layer 3 — sandbox backtest): smoke test exceeded the 300s wall-clock limit on a ~20000-bar window (2400 days of GDX.USEQ-1-DAY-LAST-EXTERNAL). This almost always means per-bar work that scales with history — e.g. rescanning the full funding/supplementary series, or rebuilding a list and calling min()/sorted() inside calculate_signal()/on_bar() on every bar. Precompute sorted timestamp arrays ONCE in __init__ and use bisect, or cache lookups keyed by timestamp, so per-bar cost is O(log n) not O(n).

Outcome Summary

A daily multi-leg strategy has to keep its per-bar path in calculate_signal cheap, meaning O(1) or O(log n), and never recompute over the full history on each bar. The code should be profiled against the 20k-bar sandbox budget before it is submitted.

It was abandoned in the verification loop after 3 iterations. Layer 3 (the sandbox backtest) failed because the smoke test ran past the 300s wall-clock limit on a ~20,000-bar, 2400-day GDX.USEQ daily window, which points to per-bar work that grows with history length.

Following the Zhao et al. (2018) design, it built a mean-reverting GDX/GLD/SLV spread on daily USEQ bars. Weights came from a minimum Box-Tiao predictability eigenvector, re-estimated every 63 sessions with a variance floor and an L1 leverage budget. It traded z-score entries at |z|>=2 and exits at |z|<=0.25, with a flat state as the default.

There are no performance numbers. The strategy never finished a backtest: the backtest report is empty, optimization never ran, and no trades, returns or Sharpe were recorded.

Analysis

Optimal Portfolio Design for Statistical Arbitrage in Finance

Backtest and paper results are hypothetical. Trading involves risk of loss.