PARTIAL · weak, decays
Hypothesis
A market-neutral basket of correlated alts has a residual that follows an Ornstein–Uhlenbeck process; trading deviations beyond a calibrated band captures reversion with positive expectancy.
Math — OU process
Model the de-meaned basket spread $X_t$ as:
$$ dX_t = \theta(\mu - X_t)\,dt + \sigma\,dW_t $$
Mean-reversion speed $\theta$ gives the half-life, which sets holding time:
$$ t_{1/2} = \frac{\ln 2}{\theta} $$
Optimal entry band scales with the stationary standard deviation $\sigma/\sqrt{2\theta}$.
Method
Estimate $\theta,\mu,\sigma$ by MLE on a rolling window. Enter at $\pm1.5$ stationary-sigma, exit at $\mu$, hard time-stop at $3\times t_{1/2}$. 30 liquid USDT-M alts, path-dependent.
Results
| Half-life (median) | 6.5h |
| Gross Sharpe (in-sample) | 1.6 |
| Net Sharpe (out-of-sample) | 0.5 |
| Win rate | 58% |
| Edge after 4 bps + funding | +0.8%/mo |
A small, real edge survives costs (+0.5–1%/mo) but decays fast as $\theta$ destabilises in trends. Viable only as a low-weight overlay with a strict time-stop, never standalone.
OU is the right model for a basket residual, but $\theta$ is regime-dependent. Size the trade by the estimated half-life, and respect the time-stop — reversion that does not arrive on schedule is a trend.