Rolling correlation, and what it reveals about regimes

A single correlation hides its own instability. Recomputing it on a window that slides forward one period at a time exposes the instability, and introduces a second artefact that has to be read around.

Run a six-month window across lesson 11's twelve months, one step at a time. The seven readings are 0.2010, 0.8110, 0.8591, 0.8485, 0.8541, 0.8738 and 0.2337. The two lowest are the first and the last. Those are the only two windows that sit entirely inside one regime. The five high readings are precisely the windows that straddle the break between the rising stretch and the falling one.

So a rolling correlation does not report high co-movement when co-movement rises. It reports high co-movement when its window contains a level shift, for exactly the reason lesson 11 computed. The rolling series is a regime detector: the shape of it tells you when the relationship changed, and the level it prints while changing is contaminated by the change itself.

Two further readings are worth taking. The move from 0.8738 to 0.2337 came from dropping one month and adding one — a 0.64 swing from a two-observation change, and a measured 0.8738 on six observations carries a 95 percent interval of roughly 0.21 to 0.99. The window length is also a choice with a cost either way: shorter windows detect a change sooner and are noisier, longer ones are steadier and place the change late.

For a pledged portfolio the consequence is specific. A lender re-estimating on a rolling window sees correlations rise at the start of a drawdown for both reasons at once — the genuine convergence lesson 13 measures, and the pooling artefact. Both push the same way, so a grouping decision taken on a rolling estimate in the first weeks of a drawdown is more conservative than the underlying co-movement alone justifies.