PART A: (10% of course grade)

Analysis of risk and return, portfolio diversification

Here you will apply what you have learned about portfolio theory. Use the monthly-adjusted closing prices for IBM, MSFT, And the S&P500 during the five-year period from January 2013 – December 2017 in the file “Stock Project Stock Prices” posted on Canvas. Calculate returns for each month for each of these three assets (Stock 1; Stock 2; S&P 500).

Exercise 1:

Calculate the following for each asset (in Excel, using the statistical functions given in parentheses): average return (AVERAGE), standard deviation of returns (STDEV.S), and variance of returns (VAR.S). What is the covariance (COVAR.S) and correlation (CORREL) between the returns of stock 1 and stock 2?

Exercise 2:

Calculate the return and standard deviation of a portfolio that holds these two stocks in the following weights: 0%-100%; 10%-90%; 20%-80%; 30%-70%; 40%-60%; 50%-50%; 60%-40%; 70%-30%; 80%-20%; 90%-10%, 100%-0%. Plot these portfolio return / standard deviation combinations. Make sure return is on the vertical axis and standard deviation is on the horizontal axis. (Important: use a scatterplot) (You may use excel for this part)

Exercise 3

1. Which specific combination would deliver the least amount of risk? Use the formula for the minimum variance portfolio (show your work) to get the exact weights, calculate its return, standard deviation and Sharpe ratio (show your work), and mark it by hand on your plot printout.The monthly risk free rate is 0.15%.

2. Draw in the CAL (by hand) that gives you the best risk-return combinations, given that the monthly risk free rate is 0.15%. Mark the optimal risky portfolio. Calculate the optimal risky portfolio’s weights (show your work) in the two stocks (using the book’s formula 6.10). For this optimal portfolio, calculate the average return, standard deviation, and Sharpe ratio (show your work).

3. Mark the spot on your return / standard deviation plot where the market index (i.e. S&P 500) falls.

4. For a moment, assume the correlation between the two stocks equals exactly 1. Graph the investment opportunity set. (Hint: This does not require any additional excel work or calculations)

5. Now assume the correlation between the two stocks equals exactly –1. Again, graph the investment opportunity set. Make sure to be precise, and provide your calculations. If you would like, you can perform steps 4 and 5 on the same graph.

What to hand in: A hard copy of your plot, results, and detailed analysis — this means you should clearly show all of your work! Write out all equations that you use, with the exception of those that are functions in excel such as AVG, COVAR, VAR, etc. For example, you need to write out the equations for portfolio return, portfolio standard deviation, and show all your calculations in determining the MVP and ORP.