Calculate expected returns (use arithmetic mean if you have short investment horizon, and geometric mean if you have long investment horizon; e.g. 1 month versus 20 years) and volatility (use standard deviation) of the monthly returns on the assets you selected above and organize this information in a table to be included in the Word file.

2. Create a correlation matrix. Include it in your Word file.

3. Investment opportunity set:

(a) Using the expected returns and volatility numbers from previous question, plot your assets on the expected return-risk space.

(b) Use Solver in Excel to find 5 portfolios on the minimum-variance frontier. Start by finding the global minimum variance portfolio. Next, find 3 portfolios on the efficient frontier (expected return higher than expected return on global minimum variance portfolio) and 1 portfolio with expected return below expected return on global minimum variance portfolio. You are using solver to find 5 different sets of weights (i.e. portfolios) in the four ETFs you selected that will minimize volatility for 5 different levels of expected returns. Include a table that consists of the weights, expected return, volatility, and Sharpe ratio for the 5 different portfolios on the minimum-variance frontier in the Word file.

(c) Add the minimum-variance frontier to your risk-return plot. Include this plot in the Word document.

4. Find the optimal portfolio:

(a) Use Solver in Excel to find the Optimal Risky Portfolio (assume you have access to risk free security, 30-day treasury bills, with zero risk). Include the weights, expected return, volatility, 1 and Sharpe ratio of this optimal portfolio in a table to be included in the Word file. You can assume the monthly risk free rate is 0.10%.

(b) Add the capital allocation line (line connecting risk-free asset to optimal portfolio) on top of the plot in question 3.

(c) Discuss the optimal portfolio and the capital allocation line and what they represent. Is the capital allocation line the most efficient place for investors?

5. Run a Fama-French three-factor regression on the returns of the optimal risky portfolio. You may download the Fama-French factors from Ken Frenchs website or BB: LINK. Make sure to convert the factors from percentages to decimals (the factors you download from Frenchs website are in percentages; e.g. 1.20 is 1.20% or 0.012 in decimals). To calculate returns on your optimal risky portfolio (i.e. the dependent variable in your regression), assume you invested in the four assets you picked according to the optimal weights (from question 4) since the beginning of your sample and rebalanced your portfolio each period. Also, make sure to use excess returns (or return net of risk-free rate).

(a) Include the regression coefficients, p-values, and adjusted R-squared in a table in the Word file.

(b) What factors drive your portfolio returns? What is the (alpha or risk-adjusted performance)? Did the portfolio outperform or underperform? What is the loading on the market risk factor? Does the portfolio have higher or lower risk compared to market? Does the portfolio have a size or value tilt? Which direction? Does the model explain the returns on the portfolio well?