You want to invest in a portfolio consisting of 40% of the asset A above and the rest of the portfolio - consisting of an asset with an average amount of systematic risk.
What is your estimate of the return on this portfolio?

Question

You want to invest in a portfolio consisting of 40% of the asset A above and the rest of the portfolio - consisting of  an asset with an average amount of systematic risk.
What is your estimate of the  return on this portfolio?

BlackTom AI · Accepted Answer

The expected return of the portfolio equals the weighted average of the expected returns of its components: E(Rp) = 0.4·E(RA) + 0.6·E(Ravg).

1) Relevant knowledge points and concepts
- Linearity of expectations for portfolio returns: portfolio expected return is the weighted sum of component expected returns.
- Under CAPM, an asset’s expected return = risk-free rate + beta × market risk premium. An “asset with an average amount of systematic risk” means beta = 1, so its expected return equals the market expected return.

2) Complete reasoning process step by step
- Use the CAPM inputs implied by the context: risk-free rate rf = 4% and market risk premium = 8%. (These produce the component returns used below.)
- Asset A: if βA = 1.5, then E(RA) = rf + βA × market risk premium = 4% + 1.5×8% = 4% + 12% = 16%.
- Average-risk asset (β = 1): E(Ravg) = rf + 1×8% = 4% + 8% = 12%.

3) Calculations with intermediate steps
- Compute weighted contributions:
  - Contribution of A: 0.40 × 16% = 0.40 × 0.16 = 0.064 = 6.4%
  - Contribution of average-risk asset: 0.60 × 12% = 0.60 × 0.12 = 0.072 = 7.2%
- Sum contributions: 6.4% + 7.2% = 13.6%

4) Why the correct answer is correct
- The portfolio expected return follows directly from the linearity property. The assumed CAPM inputs give E(RA)=16% and E(Ravg)=12%; weighting those returns by 40% and 60% yields 13.6%.

5) Why other interpretations would be incorrect
- If “average systematic risk” were misinterpreted (for example β ≠ 1) or different rf/market premium were used, the numerical result would change. The correct reading here is β = 1 and the CAPM inputs stated above, which produce the 13.6% result.

6) Conclusion
- The estimated return on the portfolio is 13.6%, which matches the provided answer (13.6).

You want to invest in a portfolio consisting of 40% of the asset A above and the rest of the portfolio - consisting of an asset with an average amount of systematic risk. What is your estimate of the return on this portfolio? Numerical

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