Math Problem Statement

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)

%

Solution

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 (βp\beta_p) is calculated as the weighted average of the betas of the individual securities:

βp=w1×β1+w2×β2\beta_p = w_1 \times \beta_1 + w_2 \times \beta_2

Where:

  • w1=0.20w_1 = 0.20 (Weight of CSL Limited)
  • w2=0.80w_2 = 0.80 (Weight of Macquarie Group Limited)
  • β1=0.18\beta_1 = 0.18 (Beta of CSL Limited)
  • β2=1.14\beta_2 = 1.14 (Beta of Macquarie Group Limited)

Substituting the values:

βp=0.20×0.18+0.80×1.14\beta_p = 0.20 \times 0.18 + 0.80 \times 1.14

Let's calculate it:

βp=0.036+0.912=0.948\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(Rp)E(R_p)) can be calculated using the **Capital Asset Pricing

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Math Problem Analysis

Mathematical Concepts

Portfolio Theory
Beta Calculation
Expected Return
Expected Standard Deviation

Formulas

Portfolio Beta: \(\beta_p = w_1 \times \beta_1 + w_2 \times \beta_2\)
Expected Return: \(E(R_p) = w_1 \times R_1 + w_2 \times R_2\)
Expected Standard Deviation: \(\sigma_p = \sqrt{w_1^2 \times \sigma_1^2 + w_2^2 \times \sigma_2^2 + 2 \times w_1 \times w_2 \times \rho_{12} \times \sigma_1 \times \sigma_2}\)

Theorems

-

Suitable Grade Level

College

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