Rolling vs Exponentially Weighted Betas

A stock's beta — its sensitivity to the market — isn't constant; it drifts as a company's leverage, business mix, or the market's composition changes. Estimating beta from the full available return history assumes it never changes at all, which is rarely true, so practitioners instead estimate it over a moving window of recent data and let the window itself roll forward through time.

The simplest approach is a rolling window: take the most recent, say, 252 trading days, run an ordinary regression of stock returns on market returns, and repeat that regression fresh each day as the window slides forward one day at a time, dropping the oldest observation and adding the newest. Every observation inside the window gets equal weight, and the estimate jumps noticeably whenever an old, extreme observation exits the window and a new one enters — a mechanical "window effect" that has nothing to do with any real change in the stock. An exponentially weighted estimate instead uses the entire available history but down-weights older observations geometrically, controlled by a decay parameter, so recent data dominates smoothly without a hard cutoff and without the abrupt jumps a rolling window produces when data ages out.

The trade-off is that a rolling window is easier to explain and reason about but reacts sluggishly to genuine regime changes until enough new data accumulates in the window, while an exponentially weighted estimate reacts faster to real changes but requires choosing a decay parameter that itself trades off responsiveness against noise.