Practice Problem – CAPM Beta and Expected Return

Practice Question

Intro to Finance
Capital Asset Pricing Model (CAPM)
Beta
Short Answer

A portfolio is invested in a risk-free asset and the market index. The portfolio has a 7% expected return, and its standard deviation equals 10%. Standard deviation of the market index is 22%. If the risk-free rate is 4% and CAPM holds, what would be the expected return of a security with a beta of 1.55?

Answer +
14.23%
Explanation +

Step 1: Identify Known Inputs
Risk-free rate = 4%, Portfolio return = 7%, σportfolio = 10%, σmarket = 22%, β = 1.55

Step 2: Estimate Market Return Using Portfolio Relationship
0.07 = (1 - 10/22)(0.04) + (10/22) × E(Rm)
0.07 = 0.02182 + 0.4545 × E(Rm)
Solving: E(Rm) ≈ 10.67%

Step 3: Use CAPM to Estimate Expected Return
E(R) = Rf + β × (E(Rm) - Rf)
E(R) = 0.04 + 1.55 × (0.1067 - 0.04) = 0.04 + 0.1038 = 0.1438

Conclusion:
The expected return of a security with a beta of 1.55 is approximately 14.23%.