CAPM and Beta¶
One-line definition¶
The Capital Asset Pricing Model prices a stock's required return as the risk-free rate plus its beta (systematic risk relative to the market) times the equity risk premium.
Formula¶
beta = Cov(r_stock, r_market) / Var(r_market)
E[r] = r_f + beta * (E[r_market] - r_f)
Jensen's alpha: realized return minus what CAPM predicted — the standard risk-adjusted skill measure.
Why PMs care¶
Beta is the equity analog of duration: a single number summarizing how much of the market's risk a position carries. CAPM's expected return is the standard required-return input into the DDM and justified-P/E formulas elsewhere in this folder, and Jensen's alpha is a first-pass "did this manager add value beyond just taking market risk" check.
Common mistakes¶
- confusing beta (systematic risk only) with total volatility — a
high-beta stock can have lower total vol than a low-beta,
high-idiosyncratic-vol stock (see
factor_model_covarianceinsrc/pm/factors.pyfor the systematic/specific split) - estimating beta over an unstable or too-short window and then treating it as fixed going forward
Limitations¶
beta() here is a plain OLS regression coefficient over whatever return
series you pass in — no shrinkage toward 1.0 (as Bloomberg-style adjusted
betas do), no multi-factor decomposition. See equity_factor_investing.md
for the fuller multi-factor picture CAPM is a special (one-factor) case
of.