An investor plans to invest funds in the following stocks:

Stock	Beta	Amount Invested
A	1.31	$1,780.00
B	1.24	$2,689.00
C	0.74	$1,129.00


The risk-free rate is currently 3.00%, while the market risk premium is 7.00%.

What is the beta of this portfolio?

To find the beta of the portfolio, we can use the weighted average of the individual stock betas based on the amount invested in each stock. The formula for the portfolio beta ($\beta_{\text{portfolio}}$) is:

\[
\beta_{\text{portfolio}} = \frac{(W_A \cdot \beta_A) + (W_B \cdot \beta_B) + (W_C \cdot \beta_C)}{W_A + W_B + W_C}
\]

Where:
- $W_A$, $W_B$, and $W_C$ are the amounts invested in stocks A, B, and C, respectively.
- $\beta_A$, $\beta_B$, and $\beta_C$ are the betas of stocks A, B, and C, respectively.

Now, applying the values from the problem:
- Stock A: Beta = 1.31, Amount Invested = \$1,780.00
- Stock B: Beta = 1.24, Amount Invested = \$2,689.00
- Stock C: Beta = 0.74, Amount Invested = \$1,129.00

First, we sum up the total amount invested:

\[
\text{Total Investment} = 1,780 + 2,689 + 1,129 = 5,598
\]

Next, we calculate the weighted betas for each stock:

1. **Stock A's weighted beta:**
   \[
   \frac{1,780}{5,598} \times 1.31 = 0.4163
   \]

2. **Stock B's weighted beta:**
   \[
   \frac{2,689}{5,598} \times 1.24 = 0.5962
   \]

3. **Stock C's weighted beta:**
   \[
   \frac{1,129}{5,598} \times 0.74 = 0.1493
   \]

Finally, sum these weighted betas to get the portfolio beta:

\[
\beta_{\text{portfolio}} = 0.4163 + 0.5962 + 0.1493 = 1.1618
\]

So, the beta of the portfolio is approximately **1.16**.

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. How does a higher portfolio beta affect expected returns?
2. How can diversification influence a portfolio's beta?
3. What role does the market risk premium play in portfolio returns?
4. How would adding a stock with a beta of 0.5 change this portfolio's beta?
5. What is the significance of the risk-free rate in portfolio management?

**Tip:** A portfolio beta higher than 1 suggests more risk and potential return compared to the overall market.

An investor plans to invest funds in the following stocks:

Stock	Beta	Amount Invested
A	1.31	$1,780.00
B	1.24	$2,689.00
C	0.74	$1,129.00

The risk-free rate is currently 3.00%, while the market risk premium is 7.00%.

What is the beta of this portfolio?

This guide explains how to calculate the beta of a portfolio containing three stocks: A (β = 1.31), B (β = 1.24), and C (β = 0.74). Using the weighted average method, we provide a step-by-step solution to find the portfolio beta, which reflects the overall risk relative to the market. Suitable for students and investors learning finance concepts.

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