Why the window length changes the answer

A volatility figure is usually quoted as though the asset produced it. The window produced a large part of it, and the window is a choice made by whoever is doing the measuring.

Take an illustrative series of thirty sessions with a regime change in the middle. The first fifteen returns are small — the largest is 1.18 percent — and their standard deviation annualises to 12.38 percent. The last fifteen are large, running to 4.13 percent, and annualise to 40.68 percent. Nothing about this is exotic; it is what Track 4 lesson 3 described when it named regimes.

Now measure the same series three ways on the final session. The last ten returns give 42.41 percent. The last twenty give 35.63 percent. All thirty give 29.66 percent. Three figures, one series, one day, and a spread of 12.75 percentage points that contains no information about the asset at all.

The trade-off is unavoidable rather than a flaw. A short window responds quickly to a change in regime but is built on few observations, so it is noisy. A long window is steady but carries the old regime inside it long after the regime has gone. There is no window that is both responsive and stable, and choosing one is choosing which error to make.

That choice reaches a borrower directly. Feed these two figures into the collateral model this track uses — a coverage multiple of 3.5 and an assumed exit of 22 sessions — and the thirty-session estimate produces a 30.67 percent haircut while the ten-session estimate produces 43.86 percent. Switching windows moves the advance rate by 13.19 percentage points on an unchanged holding.