04 // Interactive Formula Compendium // FINANCEE(R_i) = R_f + β_i · [ E(R_m) − R_f ]
Capital Asset Pricing Model (CAPM) — Beta, Alpha & Cost of Equity Sheet
The Capital Asset Pricing Model (CAPM) calculates the required return on equity E(R_i) = R_f + β_i(E(R_m) − R_f), compensating investors only for non-diversifiable systematic market risk measured by β_i.
Formula Reference
Main Formula
E(R_i) = R_f + β_i · [ E(R_m) − R_f ]
Rearranged Forms
β_i = Cov(R_i, R_m) / Var(R_m) = ρ_{i,m} · (σ_i / σ_m) (Asset Beta)
α_i = R_i − [ R_f + β_i (R_m − R_f) ] (Jensen's Alpha)
ERP = E(R_m) − R_f (Equity Market Risk Premium)
Variables & Units
| Symbol | Name | Unit |
|---|---|---|
| E(R_i) | Expected / Required Return on Equity (%) | % |
| Rf | Risk-Free Rate R_f (%) | % |
| beta | Systematic Beta Coefficient (β_i) | 1 |
| Rm | Expected Market Return E(R_m) (%) | % |
Inputs & Parameters
[%]
[1]
[%]
Calculated Result (Expected / Required Return on Equity (%))
E(R_i) =11.725%
Formula Notes & Background
- In Markowitz mean-variance portfolio theory, adding a marginal weight w_i of asset i to the market portfolio M changes portfolio variance by 2 w_i Cov(R_i, R_m).
- In equilibrium, every asset must offer the same marginal excess return per unit of marginal portfolio risk as the market portfolio itself: [E(R_i) − R_f] / Cov(R_i, R_m) = [E(R_m) − R_f] / Var(R_m).
- Defining β_i = Cov(R_i, R_m) / Var(R_m) and rearranging yields the Security Market Line E(R_i) = R_f + β_i[E(R_m) − R_f].
Step-by-Step Examples
#1: Compute the cost of equity for a technology stock with β = 1.30 when the 10-year Treasury yield is 4.25% and expected S&P 500 return is 10.0%.
R_f = 4.25%β = 1.30E(R_m) = 10.0% (ERP = 5.75%)
E(R_i) = 4.25% + 1.30 × (10.0% − 4.25%) = 4.25% + 7.475%
→ E(R_i) = 11.725%
#2: Calculate Jensen's Alpha if the stock above actually returned 14.5% during a year when the market returned 10.0%.
Actual R_i = 14.5%CAPM Expected = 11.725%
α = 14.5% − 11.725%
→ α = +2.775% (277.5 bps outperformance)
Was this tool helpful?
Frequently Asked Questions
Why doesn't CAPM reward investors for high idiosyncratic (company-specific) volatility?+
Because company-specific risk can be eliminated at zero cost by holding a diversified portfolio, the market only prices systematic covariance with the broader economy (β).
What does a beta of β = 0, β = 1, or β < 0 indicate?+
β = 1 moves 1-for-1 with the market; β = 0 is uncorrelated with market swings (e.g. cash/T-bills); β < 0 moves inversely to the market (e.g. tail-risk hedges).
How do you unlever and relever Beta when capital structure changes (Hamada equation)?+
Unlevered asset beta is β_U = β_L / [1 + (1 − T_c)(D/E)], and relevered equity beta is β_L = β_U × [1 + (1 − T_c)(D/E)].