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.

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 = $ 20,000 + 44,000 = 64,000 $
- Weight in the market portfolio $ (W_m) = \frac{20,000}{64,000} = 0.3125 $
- Weight in T-Bills $ (W_f) = \frac{44,000}{64,000} = 0.6875 $

### 2. Recall the Beta for Each Component

- **Beta of the market portfolio** $ \beta_m = 1 $ (since it's the benchmark)
- **Beta of T-Bills** $ \beta_f = 0 $ (since T-Bills are risk-free and have no market sensitivity)

### 3. Calculate the Portfolio Beta

The beta of the portfolio ($ \beta_p $) is a weighted average of the betas of the components:

\[
\beta_p = W_m \cdot \beta_m + W_f \cdot \beta_f
\]

Substitute the values:

\[
\beta_p = (0.3125 \times 1) + (0.6875 \times 0)
\]

\[
\beta_p = 0.3125
\]

### Answer

The beta of the portfolio is:
\[
\beta_p = 0.31
\]

Let me know if you'd like further details, or if you have any other questions!

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Here are some related questions for further understanding:

1. How would the portfolio beta change if more money was allocated to the market portfolio?
2. What would happen to the portfolio beta if the market portfolio’s beta were higher?
3. How does portfolio beta affect the expected return of the portfolio?
4. What is the significance of a portfolio beta of zero?
5. 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.

Learn how to calculate the beta of a portfolio consisting of a market portfolio and T-Bills. Given a market portfolio return of 0.12, volatility of 0.18, and a T-Bill rate of 0.03, this problem explains the steps to calculate the portfolio beta. Suitable for students in Grades 11-12 studying portfolio theory and beta.

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