In the context of the Capital Asset Pricing Model (CAPM), what is the expected return on a security with a beta of 1?

• A. It equals the expected return of the market portfolio.
• B. It is higher than the expected return of the market portfolio.
• C. It is independent of the market return.
• D. It is lower than the risk-free rate.

Answer: (A)

Verified step by step guidance

1. Recall the Capital Asset Pricing Model (CAPM) formula for the expected return on a security: \[\text{E}(R_i) = R_f + \beta_i \times (\text{E}(R_m) - R_f)\] where \(\text{E}(R_i)\) is the expected return on security \(i\), \(R_f\) is the risk-free rate, \(\beta_i\) is the beta of the security, and \(\text{E}(R_m)\) is the expected return of the market portfolio.
2. Understand the meaning of beta (\(\beta\)): it measures the sensitivity of the security's returns to the returns of the market portfolio. A beta of 1 means the security moves exactly in line with the market.
3. Substitute \(\beta = 1\) into the CAPM formula: \[\text{E}(R_i) = R_f + 1 \times (\text{E}(R_m) - R_f)\]
4. Simplify the expression: \[\text{E}(R_i) = R_f + \text{E}(R_m) - R_f = \text{E}(R_m)\] This shows that the expected return on a security with beta 1 equals the expected return of the market portfolio.
5. Interpret the result conceptually: since the security has the same systematic risk as the market, its expected return compensates exactly for that risk, matching the market's expected return.