You invest $600 in a security with a beta of 1.2 and $400 in another security with a beta of 0.90. The beta of the resulting portfolio is a. 1.04b. 1c. 0.98d. 1.70
Question
You invest 400 in another security with a beta of 0.90. The beta of the resulting portfolio is a. 1.04b. 1c. 0.98d. 1.70
Solution
To calculate the beta of the resulting portfolio, you need to take into account the proportion of the total investment that each security represents and their respective betas.
Here are the steps:
- Calculate the total investment: 400 = $1000
- Calculate the proportion of the total investment that each security represents:
- For the first security: 1000 = 0.6
- For the second security: 1000 = 0.4
- Multiply the beta of each security by the proportion of the total investment it represents and add these values together to get the beta of the portfolio:
- (0.6 * 1.2) + (0.4 * 0.90) = 0.72 + 0.36 = 1.08
So, the beta of the resulting portfolio is not listed in the options you provided. The closest option is a. 1.04, but the correct answer is 1.08.
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