You have $10,000 to invest. You invested $3,500 in Firm 1 and the remaining amount in Firm 2. The return on these firms is 20% and 15%, respectively. The return on your portfolio is:

Question

BlackTom AI · Accepted Answer

Weighted average return is the appropriate concept: the portfolio return equals the sum of each asset’s return weighted by the fraction of total capital invested in that asset.

1) Relevant knowledge points and concepts
- Portfolio return = w1*r1 + w2*r2, where wi = amount in firm i / total amount, and ri = return (as decimal).
- The portfolio return must lie between the individual returns (15% and 20%) and depends on investment proportions.

2) Step-by-step reasoning and calculations
- Total capital = $10,000.
- Amount in Firm 1 = $3,500 → weight w1 = 3500 / 10000 = 0.35.
- Amount in Firm 2 = 10000 − 3500 = $6,500 → weight w2 = 6500 / 10000 = 0.65.
- Returns as decimals: r1 = 20% = 0.20, r2 = 15% = 0.15.

3) All intermediate arithmetic
- Contribution from Firm 1 = w1 * r1 = 0.35 * 0.20 = 0.07 (7.00%).
- Contribution from Firm 2 = w2 * r2 = 0.65 * 0.15 = 0.0975 (9.75%).
- Portfolio return = 0.07 + 0.0975 = 0.1675 = 16.75%.
Or equivalently, dollar returns: Firm 1 gives $3,500 * 0.20 = $700; Firm 2 gives $6,500 * 0.15 = $975; total return = $1,675; divide by $10,000 → 0.1675 = 16.75%.

4) Why the correct answer is correct
- Because the return is a weighted average of 20% and 15% with weights 0.35 and 0.65 respectively, giving 16.75%.

5) Why the other options are incorrect
- 13.50% is impossible here: it lies below both individual returns, so no convex combination of 15% and 20% can produce it.
- 17.50% would result from a 50/50 allocation (0.5*20% + 0.5*15% = 17.5%), not the given 35/65 split.
- 18.25% would require 65% invested in Firm 1 (0.65*20% + 0.35*15% = 18.25%), which is the reverse of our actual allocation.

6) Conclusion
The computed portfolio return is 16.75%, which matches the provided correct answer.

You have $10,000 to invest. You invested $3,500 in Firm 1 and the remaining amount in Firm 2. The return on these firms is 20% and 15%, respectively. The return on your portfolio is:单项选择题

类似问题

The 60/40 equity-bond portfolio over time has become 75/25. How much of your portfolio will be lost if the equity market drops by 50%?

American Corporation has 40% of holdings in the US and 60% of holdings in Europe. If the US holdings appreciated 30% over the last year and European holdings appreciated 25%, what is the portfolio return of the American Corporation?

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