Math Problem Statement
The expected return and volatility for the market portfolio are 0.12 and 0.18, respectively. The current T-Bill rate is 0.03. What is the beta of a portfolio consisting of $20,000 in the market portfolio and $44,000 in T-Bills? Keep 4 decimal places in intermediate steps and show 2 decimal places in your final answer.
Solution
To determine the beta of a portfolio that combines the market portfolio and T-Bills, we can use the following steps:
1. Calculate the Portfolio Weights
Given:
- Total investment =
- Weight in the market portfolio
- Weight in T-Bills
2. Recall the Beta for Each Component
- Beta of the market portfolio (since it's the benchmark)
- Beta of T-Bills (since T-Bills are risk-free and have no market sensitivity)
3. Calculate the Portfolio Beta
The beta of the portfolio () is a weighted average of the betas of the components:
Substitute the values:
Answer
The beta of the portfolio is:
Let me know if you'd like further details, or if you have any other questions!
Here are some related questions for further understanding:
- How would the portfolio beta change if more money was allocated to the market portfolio?
- What would happen to the portfolio beta if the market portfolio’s beta were higher?
- How does portfolio beta affect the expected return of the portfolio?
- What is the significance of a portfolio beta of zero?
- How could you use the Capital Asset Pricing Model (CAPM) to calculate the expected return of this portfolio?
Tip: Portfolio beta provides a measure of market risk; a portfolio beta of 1 matches market risk, while a beta less than 1 indicates lower market sensitivity.
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Math Problem Analysis
Mathematical Concepts
Portfolio Theory
Beta
Weighted Averages
Formulas
Beta of portfolio = (Weight in market portfolio * Beta of market portfolio) + (Weight in T-Bills * Beta of T-Bills)
Theorems
Capital Asset Pricing Model (CAPM)
Suitable Grade Level
Grades 11-12
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