Consider two hypothetical stocks, X and Y. The expected return on stock X is equal to 9% and the expected return on stock Y is equal to 15%. Standard deviation of stock X and Y are 19% and 27%, respectively. Correlation between the two stocks is 0.487. Risk free rate is 2.5%.

Consider portfolio P which is invested 30% in stock X and 70% in stock Y.

What is the expected return of portfolio P? (3 points)

What is the standard deviation of portfolio P? (6 points)

How much would you allocate (i.e., what are the weights) to portfolio P and risk-free asset to create a portfolio with expected return of 7%? (4 points)

What would be the standard deviation of the combined portfolio (portfolio P and risk-free asset) found in part c? Show all steps. (4 points)

Which has the highest Sharpe ratio, Stock X, Stock Y or portfolio P? Calculate Sharpe ratio of each to reach your decision. (6 points)

What is the expected return and volatility of a portfolio that is created by borrowing 21% at the risk-free rate, and investing 121% in the portfolio P? (5 points)

Question 2 Suppose you and your spouse are thinking of combining your investment portfolios. Both portfolios have two assets (A and B). Variance of the asset A and B are 0.09 and 0.04, respectively, and covariance between the assets is 0.03.

The expected return of asset A is 10% and the expected return of asset B is 7%. Suppose the riskless asset has an expected return of 3%. You have 75% invested in asset A, while your spouse has 55% invested in asset A. Value of your portfolio is $35,000 and value of your spouse’s portfolio is $30,000.

What is the value of investments in both assets after combining the assets? (6 points)

What is the expected return and the standard deviation of the combined portfolio? Use matrix multiplication method to answer this part. Show all steps. (12 Points)

What is the correlation between assets A and B? (2 points)

Question 3. Use adjusted prices for General Dynamics (GD), Kimberly-Clark Corporation (KMB), Halliburton (HAL), and Abbott Laboratories (ABT) from December 31, 1984 to December 31, 2014 to answer the following question. You can find the prices on Yahoo Finance. Use yearly returns to answer the following. Assume risk-free rate to be 2.50%.

Find yearly returns for years 1985 to 2014 (Hint: Use adjusted price on Dec 31 for 2 consecutive year to find yearly return.). (10 points)

Find mean annual returns. (2 points)

Find the variance-covariance matrix for the 4 assets using the matrix multiplication approach. (6 points)

Use solver for 10 (or more) different expected returns to find the weights of the 4 assets on the min-variance frontier. (16 points)

Draw min-variance frontier using the portfolios found in part iv. Clearly label the axis. (4 points)

Find the optimal portfolio by maximizing the Sharpe ratio of all feasible portfolios. (4 points)