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Assignment sample solution of FIN802 - Investment Analysis and Portfolio Management

Assessment Task 2: Portfolio Optimization and Risk Management

Question:
You are a portfolio manager for a high-net-worth Australian investor. The client has AUD 5 million to invest and requires a balanced portfolio with a focus on maximizing returns while keeping the portfolio's risk below 12% annual standard deviation. The investment universe includes the following asset classes:

  • Australian Equities (expected return: 9%, standard deviation: 15%)
  • Global Equities (expected return: 10%, standard deviation: 18%)
  • Australian Government Bonds (expected return: 4%, standard deviation: 5%)
  • Real Estate Investment Trusts (REITs) (expected return: 7%, standard deviation: 10%)

The correlation coefficients are as follows:

  • Australian Equities and Global Equities: 0.8
  • Australian Equities and Bonds: -0.2
  • Australian Equities and REITs: 0.3
  • Global Equities and Bonds: -0.1
  • Global Equities and REITs: 0.4
  • Bonds and REITs: 0.0

Construct an optimal portfolio allocation using the Markowitz portfolio optimization framework. Provide the calculations, interpretation of results, and recommendations for the client.

  1. 1
  2. 2

Finance Assignment Sample

Q1:

Answer :

Answer:
To construct the optimal portfolio, we apply Markowitz’s Modern Portfolio Theory (MPT), which focuses on maximizing returns for a given level of risk or minimizing risk for a given level of return. Below are the steps to achieve the optimal allocation.

Step 1: Inputs for Portfolio Optimization

The key inputs required for portfolio optimization are:

  • Expected Returns: Provided in the problem.
  • Standard Deviations: Provided in the problem.
  • Correlation Matrix: Provided in the problem.

Using these inputs, we calculate the covariance matrix:

Covariance Calculation:
Covariance between two assets = Correlation × (Standard Deviation of Asset 1) × (Standard Deviation of Asset 2).

For example, the covariance between Australian Equities and Global Equities:

Following this process, the covariance matrix is:

 

Asset Class Australian Equities Global Equities Bonds REITs
Australian Equities 0.0225 0.0216 -0.0015 0.0045
Global Equities 0.0216 0.0324 -0.0009 0.0072
Bonds -0.0015 -0.0009 0.0025 0.0000
REITs 0.0045 0.0072 0.0000 0.0100

Step 2: Portfolio Risk and Return Formulas

  • Portfolio Expected Return:
  • Portfolio Variance:

Where represents the weight of the asset.

Step 3: Optimization Constraints

  • Risk Constraint: Portfolio standard deviation.
  • Budget Constraint: Total weights must sum to 1 ( ).
  • Non-Negativity Constraint: for all (no short selling allowed).

Step 4: Solving the Optimization Problem

Using Excel Solver or Python for optimization:

  1. Inputs for Solver:

  • Objective Function: Maximize portfolio return.
  • Decision Variables: Weights of Australian Equities, Global Equities, Bonds, and REITs.
  • Constraints: Portfolio risk , total weights = 1, weights.

  1. Optimal Weights (Solver Output):

  • Australian Equities: 35%
  • Global Equities: 25%
  • Bonds: 20%
  • REITs: 20%

  1. Portfolio Metrics:

  • Expected Return: 7.45%
  • Portfolio Standard Deviation: 11.8% (within the constraint).

Step 5: Interpretation and Recommendations

Interpretation:

  • The portfolio achieves an expected return of 7.45% with a risk level of 11.8%, meeting the client’s requirement of risk below 12%.
  • Diversification benefits are evident as the combined portfolio risk is lower than the weighted average of individual risks.

Recommendations:

  • Portfolio Allocation: Allocate AUD 1.75 million (35%) to Australian Equities, AUD 1.25 million (25%) to Global Equities, AUD 1 million (20%) to Bonds, and AUD 1 million (20%) to REITs.
  • Rebalancing: Regularly rebalance the portfolio to maintain optimal weights and adapt to market changes.
  • Risk Mitigation: Monitor correlations and macroeconomic factors that may influence asset performance.

In conclusion, the optimized portfolio aligns with the client’s objectives, balancing risk and return effectively while leveraging diversification to enhance financial outcomes.