In CAPM, what is the formula for Ke?

In CAPM, what is the formula for Ke?

• A. Ke = rf + Beta/(rm - rf)
• B. Ke = rf - Beta*(rm - rf)
• C. Ke = rf*(1+Beta) + (rm - rf)
• D. Ke = rf + Beta*(rm - rf)

Answer: (D)

CAPM links the expected return on equity to the amount of systematic risk you’re taking. Ke is the required return on equity, and it is computed as the risk-free rate plus the asset’s beta times the market risk premium. The market risk premium is the extra return investors demand for taking on market risk, which is (rm − rf). So the correct form is Ke = rf + Beta × (rm − rf). This makes intuitive sense: if beta is zero, the expected return stays at the risk-free rate; if beta is one, you earn the market return; higher beta increases Ke above the market return, and lower beta keeps Ke closer to rf. The other forms mix up the relationship—dividing by the market premium, subtracting the premium, or adding terms in a way that doesn’t reflect how risk is priced in CAPM—so they don’t align with the fundamental pricing of systematic risk.

CAPM links the expected return on equity to the amount of systematic risk you’re taking. Ke is the required return on equity, and it is computed as the risk-free rate plus the asset’s beta times the market risk premium. The market risk premium is the extra return investors demand for taking on market risk, which is (rm − rf). So the correct form is Ke = rf + Beta × (rm − rf). This makes intuitive sense: if beta is zero, the expected return stays at the risk-free rate; if beta is one, you earn the market return; higher beta increases Ke above the market return, and lower beta keeps Ke closer to rf. The other forms mix up the relationship—dividing by the market premium, subtracting the premium, or adding terms in a way that doesn’t reflect how risk is priced in CAPM—so they don’t align with the fundamental pricing of systematic risk.