Math Problem Statement
You own a portfolio equally invested in a risk-free asset and two stocks. One of the stocks has a beta of 1.16 and the total portfolio is equally as risky as the market. What must the beta be for the other stock in your portfolio?
Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.
Solution
To determine the beta for the other stock, we use the fact that the total portfolio beta is equally as risky as the market (beta = 1). Here's how to solve:
Key Points:
- Portfolio is equally invested in:
- Risk-free asset (beta = 0)
- Stock A (beta = 1.16)
- Stock B (unknown beta = )
- The weights of the three components are equal, i.e., for each.
- Total portfolio beta is the weighted average of the betas of its components.
Portfolio Beta Formula:
Substitute the values:
Simplify:
Final Answer:
The beta for the other stock in your portfolio is 1.84.
Do you want further details or have any questions? Here are 5 related questions for further exploration:
- How does the beta of a portfolio change if weights shift between the assets?
- What is the significance of a beta being greater than 1 or less than 1?
- How does adding more risk-free assets affect the portfolio's beta?
- Can a portfolio have a negative beta? Under what conditions?
- How would diversification impact the overall risk of this portfolio?
Tip: Always verify weights and beta contributions to ensure proper calculation of portfolio risk.
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Math Problem Analysis
Mathematical Concepts
Portfolio Theory
Weighted Averages
Risk Metrics
Formulas
Portfolio Beta Formula: β_portfolio = w1 * β1 + w2 * β2 + w3 * β3
Theorems
Portfolio Theory: Weighted average of betas
Suitable Grade Level
Undergraduate (Finance/Investment Basics)