You purchased $100 each of three different stocks in January. Stock A increased 30% in value. Stock B increased 15% in value. Stock C lost 20% of its original value. What was the overall net percentage of gain in the three stocks? (Round to the nearest percent.)
The correct answer and explanation is:
Let’s break down the problem step-by-step:
Given:
- You purchased $100 each of three different stocks: A, B, and C.
- Stock A increased by 30%.
- Stock B increased by 15%.
- Stock C lost 20%.
Step 1: Calculate the final value of each stock
- Stock A:
- Original value = $100
- Increase = 30% of $100 = $30
- Final value = $100 + $30 = $130
- Stock B:
- Original value = $100
- Increase = 15% of $100 = $15
- Final value = $100 + $15 = $115
- Stock C:
- Original value = $100
- Loss = 20% of $100 = $20
- Final value = $100 – $20 = $80
Step 2: Calculate the total initial investment and total final value
- Total initial investment = $100 + $100 + $100 = $300
- Total final value = $130 + $115 + $80 = $325
Step 3: Calculate the overall gain
- Gain = Total final value – Total initial investment
- Gain = $325 – $300 = $25
Step 4: Calculate the net percentage gain
Net percentage gain=(GainInitial investment)×100=(25300)×100=8.33%\text{Net percentage gain} = \left(\frac{\text{Gain}}{\text{Initial investment}}\right) \times 100 = \left(\frac{25}{300}\right) \times 100 = 8.33\%
Rounded to the nearest percent, the overall net percentage gain is 8%.
Explanation (300 words):
When you invest equal amounts of money in multiple stocks, each stock’s individual gain or loss contributes to your overall portfolio’s performance. In this problem, you invested $100 in each of three stocks, so your total initial investment was $300.
Stock A increased by 30%, meaning it gained $30 on the $100 investment, making its final value $130. Stock B’s 15% increase added $15 to the original $100, ending at $115. However, Stock C lost 20%, which means you lost $20 from the original $100, resulting in a final value of $80.
To find the overall gain or loss in your portfolio, you combine the final values of all stocks: $130 + $115 + $80 = $325. Compared to your total initial investment of $300, your portfolio increased by $25.
The net percentage gain is calculated by dividing this gain by your original total investment and converting it to a percentage. The $25 gain over $300 investment is approximately 8.33%, which rounds to 8%.
This calculation shows that even though one stock experienced a loss, the gains in the other two stocks were enough to create a positive return on the overall portfolio. The overall net percentage gain is not just the average of the individual gains and losses because the dollar amounts are combined first, then the percentage gain is calculated on the total investment.
This method is essential in portfolio management to understand the true overall return on investment rather than simply averaging the percentage changes of individual assets. It reflects the real-world scenario where different assets contribute differently to the total value of your investments.