CAPM Beta & Expected Return

CAPM: Capital Asset Pricing Model

The Capital Asset Pricing Model (CAPM) provides a framework for pricing individual assets based on their systematic risk.

Beta

Beta (β) measures an asset's sensitivity to market movements:

$\beta_i = \frac{\text{Cov}(R_i, R_m)}{\text{Var}(R_m)}$

• β = 1: asset moves in lockstep with the market
• β > 1: asset amplifies market movements (aggressive)
• β < 1: asset dampens market movements (defensive)

CAPM Expected Return

The CAPM predicts an asset's expected return based on its beta:

$E[R_i] = r_f + \beta_i (E[R_m] - r_f)$

where (E[R_m] − r_f) is the market risk premium.

Your Task

Implement:

• capm_return(rf, beta, mu_m) — returns the CAPM expected return for an asset
• capm_beta(cov_im, var_m) — returns beta given the covariance of the asset with the market and the market variance