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
• 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,