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:Single choice

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