Which of the following is an implication of the CAPM in equilibrium?

Question

BlackTom AI · Accepted Answer

The CAPM equilibrium relation is E[R_i] = R_f + β_i (E[R_m] − R_f), so every asset’s expected return is a linear function of its beta and must lie on the Security Market Line (SML).

1) Relevant knowledge points and concepts
- CAPM formula: E[R_i] = R_f + β_i (E[R_m] − R_f).
- β_i measures systematic (market) risk; unsystematic risk is diversifiable and not priced.
- The SML graphs expected return versus beta; its intercept is R_f and slope is the market risk premium (E[R_m] − R_f).
- In equilibrium, no arbitrage means assets must price so expected returns satisfy CAPM.

2) Step-by-step reasoning
- Start from CAPM: E[R_i] = R_f + β_i (E[R_m] − R_f).
- For any security i, its expected return equals the risk-free rate plus its beta times the market risk premium.
- Plotting E[R_i] on the vertical axis and β_i on the horizontal axis yields a straight line given by the CAPM equation — the SML.
- If any security lay off the SML, investors would arbitrage: buy underpriced (above-SML expected return for given beta) and sell overpriced assets until prices adjust back onto the SML.

3) Intermediate calculation examples
- If β = 1: E[R] = R_f + 1·(E[R_m] − R_f) = E[R_m] (market portfolio).
- If β = 0: E[R] = R_f (risk-free asset).
These plug-ins illustrate that different betas produce different expected returns along the same line.

4) Why the correct answer is correct
Because CAPM explicitly gives a linear relation between expected return and beta, every security’s expected return in equilibrium must satisfy that relation and thus lie on the SML.

5) Why other options are incorrect
- “All securities have the same expected return”: false—expected returns differ by beta.
- “The risk-free rate is equal to the market return”: false—only true if market risk premium is zero, which is not required.
- “The beta of every security is zero”: false—betas vary; β=0 only for risk-free asset.

6) Conclusion
Therefore, the correct implication of CAPM in equilibrium is: All securities lie on the Security Market Line (SML), which matches the provided answer.

Which of the following is an implication of the CAPM in equilibrium?单项选择题

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