Portfolio Management

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The objective of the assignment is to give the students a realistic portfolio management experience by carrying out asset allocation and performance evaluation. By conducting quantitative analysis on actual market data using Matlab, the students will gain knowledge on portfolio optimisation theories and their implementation issues, and acquire Matlab programming skills.
All the relevant data will be provided in the separate excel file, ‘summative assignment data.xlsx’.
You are encouraged to use Matlab for quantitative analysis, but you can also choose another program provided you have a good reason to do so. The source codes, e.g., Matlab m-files, should be included as appendix in the report. The words in the source code will not be counted.
You may employ quantitative methods other than those covered in the class. Whatever method you choose, a proper reason should be given.
Assessment will not be based on the performance of your portfolio but on the analysis and discussion throughout the portfolio management process.
Your report must address the points below.

Write a report including the following:
1. Calculate monthly return of each asset in the investment pool and the benchmark index, S&P 500, during the sample period. The data will be provided in the excel file.
2. Carry out initial inspection on the return time series. This may include visual inspection of the time series data, test of autocorrelation, etc.
3. Refine the investment pool: You may want to eliminate some stocks based on the initial inspection and/or some other reasons such as ethical reasons.
4. Estimate expected return and covariance matrix of the stocks.
5. Construct an optimal risky portfolio (tangent portfolio). Explain why you choose the particular objective function, constraints, and/or optimisation algorithm. You should provide the details of implementation such as, but not limited to, objective function and constraints.
6. Construct an optimal portfolio by mixing the tangent portfolio with a risk-free asset.
7. Repeat 4-6 using different methods to obtain 4 optimal portfolios to compare. Different methods may mean any of the followings:
Different constraints, different sampling schemes (in sample period, etc), different optimisation methods (Classical Mean-Variance, Robust optimisation), different input parameter estimation methods (Sample mean/covariance, Black-Litterman, Bayes-Stein).
Just imagine that youre a portfolio manager and want to test several methods to determine the final model for your data. What is important is to justify why you choose those methods. Using more advanced methods will guarantee extra credits.
8. Evaluate the portfolios and compare them with one another and also with the benchmark. Discuss the results. Choose the final model and explain why it is your choice of model.
9. Reflect on the modern portfolio theory based on your experience through this assignment.
Overall word limit: 2,500 words maximum.