Tahmina constructs a portfolio with two securities:

Security Weight

Security SD (%)

Beta

Security

(%)

CSL Limited (CSL:AX)

20.0

9

0.18

Macquarie Group Limited

80.0

17

1.14

(MQG:AX)

The correlation of returns between the two securities is -0.1516. Tahmina estimates the expected market return as 12.0% p.a. and a risk-free rate of 4.0%.

Part A: What is the portfolio's beta? (1 mark)

(Please answer to 3 decimal places)

Part B: What is the portfolio's expected return? (2 marks)

(Please answer to 3 decimal places)

Part C: What is the portfolio's expected standard deviation? (2 marks)

%

Let's go through each part step by step to calculate the portfolio's beta, expected return, and expected standard deviation.

### Part A: Portfolio Beta

The portfolio beta (\(\beta_p\)) is calculated as the weighted average of the betas of the individual securities:

\[
\beta_p = w_1 \times \beta_1 + w_2 \times \beta_2
\]

Where:
- \(w_1 = 0.20\) (Weight of CSL Limited)
- \(w_2 = 0.80\) (Weight of Macquarie Group Limited)
- \(\beta_1 = 0.18\) (Beta of CSL Limited)
- \(\beta_2 = 1.14\) (Beta of Macquarie Group Limited)

Substituting the values:

\[
\beta_p = 0.20 \times 0.18 + 0.80 \times 1.14
\]

Let's calculate it:

\[
\beta_p = 0.036 + 0.912 = 0.948
\]

The portfolio's beta is **0.948**.

### Part B: Portfolio's Expected Return

The portfolio's expected return (\(E(R_p)\)) can be calculated using the **Capital Asset Pricing

Learn how to calculate a portfolio's beta, expected return, and expected standard deviation using weighted averages and correlation coefficients. Example problem involving CSL Limited and Macquarie Group Limited securities with specific weights, standard deviations, and correlation.

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