How Beta Is Calculated from Historical Returns
The regression method computes beta as the slope of the best-fit line when you plot stock returns (Y-axis) against market returns (X-axis). Mathematically, beta equals the covariance of stock and market returns divided by the variance of market returns: β = Cov(Rₛ, Rₘ) / Var(Rₘ).
Most financial databases use 60 months (5 years) of monthly returns against the S&P 500, though Bloomberg defaults to 2 years of weekly data. The choice matters: shorter windows capture recent behavior but introduce more noise; longer windows are more stable but may include outdated regimes. For example, a tech company that pivoted from hardware to SaaS might have a meaningfully different beta today than its 5-year average suggests.
The R-squared of the regression tells you how much of the stock's movement is explained by the market — an R² of 0.30 means 70% of the stock's volatility comes from firm-specific (idiosyncratic) factors, making beta less reliable as a predictor.