A stock portfolio consists of four stocks. Stock A represents 20% of the portfolio and has a return of 6%. Stock B represents 30% of the portfolio and has a return of 8%. Stock C represents 20% of the portfolio and has a return of 4%. Stock D represents the remaining 30% of the portfolio and has a negative return of 5%. What is the average return of the portfolio?
2.9%
Solution: Average Return of the Portfolio
Step 1: Formula for Portfolio Return
The formula for the portfolio return is:
Rportfolio = Σ (wi × ri)
Where:
- wi: Weight (proportion) of stock i in the portfolio.
- ri: Return of stock i.
Step 2: Identify Weights and Returns
From the problem, we know:
- Stock A: wA = 20% = 0.2, rA = 6% = 0.06
- Stock B: wB = 30% = 0.3, rB = 8% = 0.08
- Stock C: wC = 20% = 0.2, rC = 4% = 0.04
- Stock D: wD = 30% = 0.3, rD = -5% = -0.05
Step 3: Apply the Formula
Substitute the weights and returns into the formula:
Rportfolio = (wA × rA) + (wB × rB) + (wC × rC) + (wD × rD)
Step 4: Calculate Each Term
- Stock A: wA × rA = 0.2 × 0.06 = 0.012
- Stock B: wB × rB = 0.3 × 0.08 = 0.024
- Stock C: wC × rC = 0.2 × 0.04 = 0.008
- Stock D: wD × rD = 0.3 × (-0.05) = -0.015
Step 5: Sum the Results
Add the results:
Rportfolio = 0.012 + 0.024 + 0.008 - 0.015 = 0.029
Step 6: Convert to Percentage
Convert the result to a percentage:
Rportfolio = 0.029 × 100 = 2.9%
Final Answer
The average return of the portfolio is: 2.9%
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