A fixed full-sample beta or hedge ratio assumes the relationship never changed. A rolling one assumes it changes constantly. Reality is in between, and the window length is the knob that decides which error you prefer.
Short windows adapt quickly to structural change but jitter, causing unnecessary turnover when used to set hedge sizes. Long windows are stable but slow to notice that a relationship has broken. Sixty to 250 days are common choices for daily data.
Do not optimise this window on the same data you evaluate on. The rolling window is a parameter and deserves the same out-of-sample treatment as any other, including a check that nearby values give similar results.
Related: beta-estimation, rolling-window, hedge-ratio, parameter-sensitivity