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, 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 find the alpha, beta, and noise coefficients.
• Perform the two tests suggested in the lecture notes to assess whether returns are indeed
(at least approximately) market invariants. Discuss your findings.
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, e.g. using the following approach: if you
purchase an asset, buy 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 findings, and draw conclusions of your studies.
Where applicable try to include additional, more advanced concepts, for example
• short selling constraints,
• detection of outliers,
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• robust optimisation,
• Black-Litterman model,
• …
Observe and discuss how these affect the portfolio selection.
Checklist:

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 be typed (use 1.5 line spacing). LATEX 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 LibreOffice or some of its commercial equivalents, such as Microsoft 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. The
   total pages of figures and tables should not exceed the total of pages with text.
6. Do not use screenshots, but create high quality figures as separate files (e.g. as png) which
   are then inserted in the dissertation. Similarly any tables should be properly created in
   LATEX or LibreOffice/Word, and not inserted as screenshots from other sources.
7. Ensure that graphs/plots have axes labels and units, and curves and labels are clearly
   legible.
8. Explain and discuss your results in the text, discuss what can be gathered from figures and
   tables you present.
9. Use itemization and lists to make the discussion clear and easy to read.
10. Do not forget to spell-check your dissertation.