In CAPM, which equation correctly defines the cost of equity Ke?

In CAPM, which equation correctly defines the cost of equity Ke?

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

Answer: (D)

In CAPM, the cost of equity is the risk-free rate plus the market risk premium scaled by the stock’s beta. The market risk premium is (rm − rf), so the correct formula is Ke = rf + Beta(rm − rf). This shows that investors get rf as a baseline for a risk-free investment, plus additional compensation for bearing systematic risk, proportional to how sensitive the stock is to market moves (beta). If beta = 1, Ke = rm; if beta < 1, Ke is between rf and rm; if beta > 1, Ke exceeds rm. The other forms misprice risk: subtracting the premium would imply higher risk reduces required return; multiplying rf by (1 + Beta) ignores the market premium; and using rm + Beta(rf − rm) flips the sign of the premium and mismatches the intercept.

In CAPM, the cost of equity is the risk-free rate plus the market risk premium scaled by the stock’s beta. The market risk premium is (rm − rf), so the correct formula is Ke = rf + Beta(rm − rf). This shows that investors get rf as a baseline for a risk-free investment, plus additional compensation for bearing systematic risk, proportional to how sensitive the stock is to market moves (beta). If beta = 1, Ke = rm; if beta < 1, Ke is between rf and rm; if beta > 1, Ke exceeds rm. The other forms misprice risk: subtracting the premium would imply higher risk reduces required return; multiplying rf by (1 + Beta) ignores the market premium; and using rm + Beta(rf − rm) flips the sign of the premium and mismatches the intercept.