Choose ﬁve 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, standard deviation, skewness and kurtosis of these shares. Then annualise sample mean, variance and standard deviation. • Plot the daily share prices and daily returns for each individual asset. • Plot the histogram of returns and compare it with the Gaussian ﬁt. • Compute the variance-covariance matrix V . • Perform linear regression on your data using an appropriate index as proxy for the market portfolio, and ﬁnd 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);
In all steps, discuss the asset allocations and other ﬁndings, 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 aﬀects the portfolio selection.
1. Your dissertation 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 dissertation should typically be typed (use 1.5 line spacing). L ATEX is recommended (but not compulsory) as a typesetting system, especially if your dissertation 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 ﬁgure/table captions are. Make sure you put explanatory captions to tables and ﬁgures, and discuss ﬁndings from ﬁgures/tables in the text. The total pages of ﬁgures and tables should not exceed the total of pages with text.
6. Handwritten dissertations (though not recommended) will be accepted on the condition that they are neatly written, pages numbered, legible and all tables and ﬁgures are clearly labeled and cross referenced correctly.
7. Do not forget to spell-check your dissertation
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