PARTIAL · fragile
Hypothesis
A basket of 3+ correlated alts has a stationary linear combination (Johansen cointegrating vector) more robust than a single pair (N-018).
Math — Johansen trace test
Test the rank $r$ of the cointegration space via the trace statistic:
$$ \lambda_{\text{trace}}(r) = -T\sum_{i=r+1}^{n}\ln(1-\hat\lambda_i) $$
Method
Estimate cointegrating vectors on rolling 90d baskets, trade the stationary combination z-score, full multi-leg costs.
Results
| Cointegration rank $\ge1$ | ~55% of windows |
| Net Sharpe out-of-sample | 0.4 |
| Vector stability across refits | low |
More robust than the single pair (N-018) but the cointegrating vector still drifts and the basket needs many legs, multiplying cost. A thin positive net edge that only an ultra-low-fee desk would run. Marginal.
Adding assets stabilizes a cointegration estimate but multiplies the cost of trading it. The fee structure decides the break-even number of legs.