Let's calculate the portfolio’s beta by considering the weighted average of the beta values of each stock in Megan Ross’s portfolio. Here’s the step-by-step process:
1. Determine the total investment in the portfolio:
- Stock A: \[tex]$150,000
- Stock B: \$[/tex]50,000
- Stock C: \[tex]$100,000
- Stock D: -\$[/tex]75,000
- Total Investment = \[tex]$150,000 + \$[/tex]50,000 + \[tex]$100,000 - \$[/tex]75,000 = \$375,000
2. Calculate the weight of each stock in the portfolio:
- Weight of Stock A: [tex]\( \frac{150,000}{375,000} = 0.4 \)[/tex]
- Weight of Stock B: [tex]\( \frac{50,000}{375,000} = 0.1333 \)[/tex]
- Weight of Stock C: [tex]\( \frac{100,000}{375,000} = 0.2667 \)[/tex]
- Weight of Stock D: [tex]\( \frac{-75,000}{375,000} = -0.2 \)[/tex]
3. Determine the individual weighted betas:
- Weighted Beta of Stock A: [tex]\( 0.4 \times 1.40 = 0.56 \)[/tex]
- Weighted Beta of Stock B: [tex]\( 0.1333 \times 0.80 = 0.1067 \)[/tex]
- Weighted Beta of Stock C: [tex]\( 0.2667 \times 1.00 = 0.2667 \)[/tex]
- Weighted Beta of Stock D: [tex]\( -0.2 \times 1.20 = -0.24 \)[/tex]
4. Summarize the individual weighted betas to find the portfolio beta:
- Portfolio Beta = [tex]\( 0.56 + 0.1067 + 0.2667 - 0.24 = 0.6933 \)[/tex]
Therefore, the portfolio's beta is approximately [tex]\( \beta_p = 0.6933 \)[/tex].
Given the choices:
1. 1.06
2. 1.17
3. 1.29
4. 1.42
5. 1.56
None of these options matches the calculated portfolio beta. The correct portfolio beta based on the calculations is [tex]\( \beta_p = 0.6933 \)[/tex], which doesn't align with the choices provided. This indicates either an error in the provided choices or a potential miscalculation elsewhere. According to the correct process and calculations, [tex]\( \beta_p = 0.6933 \)[/tex] is the appropriate portfolio beta.
