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# Business Finance 310 Fall 2013 Assignment #2 Portfolio Choice Due Date: The topics correspond to Lectures 4 to 6. You will need to use a spreadsheet...

Help me make sense out of Part 1 and part 2, where do I start? How would I solve them?

Part 2: Markowitz Model and Optimal Portfolios For this part of the assignment, use the data in hw2data.xls. 1. Generating some summary statistics: (a) Report the mean and standard deviation of monthly returns for each of the six stocks. (b) Report the covariance matrix of returns (6 by 6). Are the covariances between returns on these stocks generally positive or negative? Are the signs of the co- variances surprising? 2. Solving the Markowitz Problem: Take the means above as the expected returns and the estimated covariance matrix above as your best estimate of the covariance between the returns of the six stocks. (a) Suppose that the target return is 0.8%. What are the portfolio weights for a portfolio with this return and the minimum possible variance? (b) Repeat for target returns of 0.9%, 1%, 1.1%, all the way to 1.8%. Report a table of portfolio weights, expected returns, and volatilities. Plot a graph of the expected return (y-axis) versus the volatility (x-axis) of the optimal portfolios. (c) Would an investor who likes higher expected returns and dislikes volatility ever invest in the portfolio constructed in (a)? Why or why not? 3. Now suppose that the risk-free rate is 0.4167%. (a) What is the optimal risky portfolio? (b) What is the expected return if we invest 50% in the optimal risky portfolio and 50% in the risk-free asset? What about 150% in the optimal risky portfolio and -50% in the risk-free asset? (c) For an investor with a utility function of E ( r ) - 1 2 2 r and a coeﬃcient of risk aversion of 4, what is the optimal asset allocation? Part 3: Diversiﬁcation Start with asset A which has an expected return of 10% and a volatility of 30%. 1. Suppose that we introduce asset B with an expected return of 10% and a volatility of 30%. The correlation between the two asset returns is 0.9. What is the optimal combination of A and B? What is the volatility of this portfolio? [Hint: The expected return of any combination is 10%, so you want to minimize the portfolio volatility.] 2. Now suppose that we introduce asset C with an expected return of 10% and a volatility of 30%. The returns of asset C are uncorrelated with both the returns of asset A and of asset B. What is the optimal combination of A, B, and C? What is the volatility of this portfolio? 3. Did the introduction of B or C have a greater eﬀect in decreasing the portfolio volatility? Why is this the case? 2
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