Choose ?ve risky assets and give reasons for your choice. Download historical price information from Yahoo Finance (use ‘adjusted close' prices for the basis of the computation).
· Compute the sample mean, variance, and standard deviation of these shares (in annual terms).
· Compute the variance-covariance matrix V .
· Plot the daily share prices and daily returns for each individual asset.
· Perform linear regression on your data using an appropriate index as proxy for the market porfolio, and ?nd the alpha, beta, and noise coefficients.
Choose appropriate starting time points for the investment period and use previous data to
· compute the efficient frontier and plot it.
· use utility functions u(µ, σ) = µ-ασ2 and u(µ, σ) = µ/σ2 to select the ‘optimal' portfolio.
Use subsequent data to
· compare the investment performance of your constructed portfolios against the index performance at some chosen future time points (say, every 20 trading days);
· study if asset protection would have been useful, using the following approach: if you purchase an asset, but the corresponding Black-Scholes priced put option for the intended time period, if you short an asset, buy the corresponding Black-Scholes priced Call option for the intended time period.
In all steps, discuss the asset allocations and other ?ndings, and draw conclusions of your studies.
Where applicable try to include additional, more advanced concepts (e.g. short selling constraints, detection of outliers, robust optimisation etc.) and observe and discuss how this acects the portfolio selection.
Checklist:
1. Your assignment should have: a title-page, an abstract, an introduction, a main body, a conclusion, appendix and a list of references (if applicable).
2. You can use MATLAB and Excel (or other computing tools), please do explain how you get the numbers by writing the formulas which you are using, and include Matlab code listings in an appendix.
3. Number of words: 3000 words (excluding references, code listings).
4. The assignment should typically be typed (use 1.5 line spacing). LTEX is recommended (but not compulsory) as a typesetting system, especially if your assignment contains a large number of mathematical formulas, but you may opt for a "word editor" instead of a typesetting system, such as Libre Office or some of its commercial equivalents, such as Microsoft's Word.
5. Figures and tables are not considered part of the text for word count purposes, but the ?gure/table captions are. Make sure you put explanatory captions to tables and ?gures, and discuss ?ndings from ?gures/tables in the text. The total pages of ?gures and tables should not exceed the total of pages with text.
6. Handwritten assignments (though not recommended) will be accepted on the condition that they are neatly written, pages numbered, legible and all tables and ?gures are clearly labeled and cross referenced correctly.