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CAPM (Capital Asset Pricing Model)

Expected return as risk-free rate plus beta times market premium.

CAPM prices an asset by its systematic risk (beta) alone: investors are only compensated for non-diversifiable risk. It defines the Security Market Line and is the standard cost-of-equity model, despite empirical weaknesses that motivated multi-factor models.

E(Rᵢ) = R_f + βᵢ · (E(R_m) − R_f)

import statsmodels.api as sm
X = sm.add_constant(mkt_excess)            # market risk premium
fit = sm.OLS(stock_excess, X).fit()
alpha, beta = fit.params
exp_return = rf + beta * (mkt_ret.mean() - rf)