You need to estimate a number of portfolios for two different investors and discuss the implications for diversification. Key information on portfolio construction is as follows:

• Investor utility is based on monthly values and is represented by: U = E(R) - 1/2A2. There are two investors with different risk aversion coefficients (A). Taylor has a risk aversion coefficient of 5 and Travis has a risk aversion coefficient of 10.
• The expected returns per month to be used throughout the report are in the following table. Do not use historical average returns as expected returns.
• The covariance matrix needs to be estimated using all of the historical data provided to construct portfolios for each investor using the Markowitz approach.
• Both investors are able to short-sell each industry throughout the report (i.e. they can have a negative portfolio weight).
• Investors are unable to borrow or lend at the risk-free rate
• Set the initial weights to be equal weights when conducting your optimisation (i.e. weights = 9.09%).

Calculate the expected utility for both investors if they invest 100% of their wealth solely in each industry. Which industry does each investor prefer? What are the reasons for their preference?

Calculate the optimal portfolio for both investors that consists of all eleven industries. Compare this to the other portfolios you have already estimated in terms of diversification benefits. What do you observe? Contrast the differences in what you observe between the two investors.