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? 数值题

类似问题

You own a bond that pays $64 in interest annually. The face value is $1,000 and the current market price is $1,021.61. The bond matures in 11 years. What is the yield to maturity?

Which of the following statements is CORRECT?

It will cost $9,600 to acquire an ice cream cart that is expected to produce cash inflows of $3,600 a year for three years. After the three years, the cart is expected to be worthless. What is the payback period?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单