# Financial Mathematics (Modern Portfolio Theory)

Assessment Requirements

Choose 5 assets between 01/Mar/2009 to 01/Oct/2010 by giving
?adjusted close? Prices for the basis of computation.

NOTE:

1) Calculate the equivalent mean, variance and standard deviation of
these shares (adjusted close prices) annually.
2) Calculate the covariance matrix V.
3) Plot the daily share prices and daily returns for each individual company.
4) Analyse the covariance and share price behaviour over some chosen
sub time intervals to verify the theory of positive covariance and
negative covariance imply that share prices move in the same and
different directions.
Choose some appropriate starting time points, using previous data to
5) Calculate the efficient frontier and plot it explicitly
6) Use utility functions F(μ, σ) = μ ? α σ2 and F(μ, σ) = μ / σ2 to
find the ?optimal? investment portfolio at the beginning of these time
period.
7) Study the methodology of constructing indices or ETF funds,
construct an ETF fund using these 5 assets at the beginning of time
periods.
Use subsequent data to
8) Compare the investment performance of each asset, the constructed
ETF fund and your optimal portfolios at some chosen future time points
(say after every twenty trading days).
9) Study if asset protections have been useful by using options under
the following scenarios:
Purchase suitable BS priced options instead of assets (if weight isl
real asset portfolio.
If you purchase an asset, buy the corresponding BS priced put optionl
for the intended time period, if you short an asset, buy the
corresponding BS priced call option for the intended time period.

Remark:

1) Please select the following assets from yahoo finance: Tesco,
Sainsbury, Morrisons, Asda, Wesfarmers.
2) Computations have to be detailed enough, the appropriate formulas
have to be used so that the mathematical reasoning is clear.
3) The problems have to be included in a single Word document
4) If you use Excel for computations, please provide that file as well.
5) Please check the results to make sure they are correct, and please
let me know what software you used (Excel, Matlab, etc.)

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