What is the beta of a 3-stock portfolio including 35% of stock A with a beta of 0.80, 20% of stock B with a beta of 1.06, and 45% of stock C with a beta of 1.74?
Multiple Choice:
A 0.93,
B 1.09,
C 1.25
D 1.28
The correct answer and explanation is :
To calculate the beta of a 3-stock portfolio, we use the formula for the weighted average beta of the portfolio. The beta of a portfolio is the sum of the weighted betas of each individual stock within the portfolio.
Formula:
[
\beta_{\text{portfolio}} = w_A \cdot \beta_A + w_B \cdot \beta_B + w_C \cdot \beta_C
]
Where:
- (w_A), (w_B), and (w_C) are the weights of stocks A, B, and C in the portfolio.
- (\beta_A), (\beta_B), and (\beta_C) are the betas of stocks A, B, and C.
Given:
- Stock A: weight = 35%, (\beta_A = 0.80)
- Stock B: weight = 20%, (\beta_B = 1.06)
- Stock C: weight = 45%, (\beta_C = 1.74)
Step-by-Step Calculation:
- Multiply the weight of each stock by its corresponding beta:
- For Stock A: ( 0.35 \times 0.80 = 0.28 )
- For Stock B: ( 0.20 \times 1.06 = 0.212 )
- For Stock C: ( 0.45 \times 1.74 = 0.783 )
- Add up these weighted betas:
[
\beta_{\text{portfolio}} = 0.28 + 0.212 + 0.783 = 1.275
]
Thus, the beta of the portfolio is 1.275.
Conclusion:
The beta of the portfolio is closest to 1.28. Therefore, the correct answer is:
D. 1.28
Explanation:
The beta of a stock represents its volatility relative to the market. A beta of 1 means the stock moves in line with the market. A beta higher than 1 indicates more volatility than the market, while a beta lower than 1 means less volatility. The portfolio’s beta is a weighted average of the individual stock betas, reflecting the overall risk profile of the portfolio compared to the market. In this case, the portfolio is more volatile than the market (beta > 1), mainly because of the high beta of stock C.