Under the Capital Asset Pricing Model (CAPM), what is the formula for the Expected Return on an equity security ($E(R_i)$) with Beta $\beta_i$, Risk-Free Rate $R_f$, and Market Return $R_m$?

[ A ]E(R_i) = (R_m - R_f) / β_i

[ B ]E(R_i) = R_f * β_i + (R_m - R_f)

[ C ]E(R_i) = R_f + β_i * (R_m - R_f)[ CORRECT ]

[ D ]E(R_i) = R_m + β_i * R_f

Takeaway

CAPM states expected return equals the risk-free rate plus beta times the market risk premium: E(R_i) = R_f + β_i x (R_m - R_f).

Derivation

CAPM decomposes expected return into two building blocks: compensation for waiting (the risk-free rate R_f) and compensation for bearing systematic (non-diversifiable) risk, measured as beta multiplied by the market risk premium (R_m - R_f). A stock with β_i = 1 should earn exactly the market return; a higher-beta stock is expected to earn proportionally more of the market's excess return over the risk-free rate, and a beta below 1 proportionally less. This linear relationship, plotted as the Security Market Line, is the backbone of modern portfolio pricing theory, and candidates are commonly tricked into misplacing where beta multiplies — it scales the risk premium (R_m - R_f), not the risk-free rate itself.

Why the others fail

A — E(R_i) = (R_m - R_f) / β_i

This inverts the structure of the Treynor Ratio (excess return divided by beta) rather than representing CAPM's additive expected-return formula.

B — E(R_i) = R_f * β_i + (R_m - R_f)

Multiplying the risk-free rate by beta is mathematically wrong — beta is meant to scale only the market risk premium (R_m - R_f), not the risk-free component.

D — E(R_i) = R_m + β_i * R_f

Adding beta directly to the market return has no basis in CAPM; beta must multiply the excess return over the risk-free rate, not be summed with R_m.