Beta & Alpha

Beta & Alpha (CAPM)

The Capital Asset Pricing Model (CAPM) decomposes an asset's return into market exposure and excess return:

$r_{asset} = \alpha + \beta \cdot r_{market} + \epsilon$

Beta measures systematic risk — how much the asset moves with the market: $\beta = \frac{\text{Cov}(r_{asset}, r_{market})}{\text{Var}(r_{market})}$

• $\beta > 1$: more volatile than market (amplifies moves)
• $\beta < 1$: less volatile than market (dampens moves)
• $\beta < 0$: moves opposite to market (hedge)

Alpha is the excess return not explained by market exposure: $\alpha = \bar{r}_{asset} - r_f - \beta (\bar{r}_{market} - r_f)$

A positive alpha means the asset outperformed the CAPM prediction — the manager "added value."

Your Task

Implement:

• beta(asset_returns, market_returns) — CAPM beta
• alpha(asset_returns, market_returns, rf=0.0) — CAPM alpha