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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?

Business Finance 310 Fall 2013 Assignment #2 Portfolio Choice Due Date: October 04 5pm, 2013 The focus of this assignment is to construct portfolios. The topics correspond to Lectures 4 to 6. You will need to use a spreadsheet posted on Carmen called hw2data.xls. This dataset contains the historical monthly returns of six stocks: Coca-Cola (KO), Eastman Kodak (EK), General Electric (GE), Dow Chemical (DOW), Johnson & Johnson (JNJ), and 3M (MMM). Please work in a group of 1 - 4 people. Each group should hand in one copy of their answers. Please show your work and provide explanations where relevant. However, you do not need to print out entire spreadsheets. Your answers should be summarized in a write-up with relevant details of calculations, tables and charts (if applicable), and explanations. The assignment can be turned in during class or via e-mail ([email protected]). If you do submit your assignment via e-mail, please submit it either as a Word document or as a PDF file. In particular, please do not e-mail an Excel spreadsheet – if you feel that the Excel spreadsheet is relevant to providing details of your work, please copy and paste the relevant portions into your Word document. Part 1: Preferences and the Equity Premium Puzzle Suppose that you use a quadratic utility function, U = E ( r ) - 1 2 2 , to make your financial decisions. The average historical return for large US stocks is 11.63% with a standard deviation of 20.56%. Suppose that you also use this for your estimates of E ( r ) and σ . 1. Suppose that in choosing a portfolio consisting of a risk-free asset (where r f = 3%) and large US stocks, you invest 60% of your money in large US stocks (and the rest in the risk-free asset). What does this imply about your risk aversion coefficient, A? 2. If your preferences are consistent (i.e. you use the same utility function, including the same A as above), which would you prefer? (a) an asset which has E ( r ) = 5% and σ = 0 (b) an asset with E ( r ) = 10% and σ = 20% Assume that you are only investing in (a) or (b) and not mixing the two assets into a portfolio. 3. Suppose that we interview a group of investors who chose to invest 60% of their portfolio in large US stocks and 40% in the risk-free asset. We then ask them which asset from (2) that they prefer. Most answer that they prefer (b). If we believe that the investors in the group are consistent in their choices, what does this imply about the quadratic utility function? If we believe that the quadratic utility function is the correct utility function, what does this imply about the consistency of investors’ preferences? 1
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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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DATE KO EK GE DOW JNJ MMM 19620731 0.120915 0.093838 0.115546 0.025714 -0.038647 0.085333 19620831 -0.007289 0.046607 0.032015 0.08078 -0.048576 0.065356 19620928 -0.070778 -0.056581 -0.060219 0.018557 -0.033569 -0.101852 19621031 0.012739 -0.011734 0.060665 0.058673 -0.005484 -0.025773 19621130 0.092453 0.140106 0.103321 0.118072 0.106618 0.157672 19621231 -0.011594 0.016336 0.033445 -0.034052 -0.023333 -0.027523 19630131 0.058651 0.047072 0.019544 0.062921 0.102389 0.134434 19630228 -0.00277 -0.008333 -0.070288 -0.052854 0.019814 -0.031601 19630329 0.046389 0.021111 0.032646 0.095446 0.003049 0.006466 19630430 -0.010695 0.010881 0.055276 0.096234 0.012158 0.051392 19630531 0.005405 -0.004952 0.066667 -0.045802 0.051051 -0.030957 19630628 0.015323 -0.047826 -0.053571 -0.0296 0 -0.035865 19630731 0.018667 -0.009132 -0.011076 -0.020747 -0.002865 0.039387 19630830 0.070681 0.018894 0.0432 0.038136 0.097701 0.064842 19630930 0.004156 0.020455-0.019939 -0.04245 -0.034121 -0.031746 19631031 0.014706 0.008909 0.055118 0.062232 0.160326 0.088115 19631129 0.019807 0.021634 -0.014925 0.026263 0.002342 -0.009793 19631231 0.102503 0.05915 0.062727 0.092913 -0.0445 -0.013359 19640131 0.021622 0.026998 0.008608 -0.001812 0.031863 0.067698 19640228 0.003175 0.068349 -0.025605 -0.009074 0.096912 -0.021739 19640331 0.067511 0.006299 0.025401 0.03956 -0.069565 -0.039033 19640430 0.005964 0.007859 -0.055874 -0.012411 -0.070093 -0.03675 19640528 0.009881 0.054971 -0.016692 0.028725 0.012563 -0.040161 19640630 0.034247 -0.012987 -0.008642 0.009773 0.00995 -0.012605 19640731 0.050428 -0.021617 0.045455 -0.003478 -0.002463 0.021277 19640831 -0.009058 -0.016907 0.007496 -0.054101 -0.017284 -0.0375 19640930 -0.007313 0.050049 0.070536 0.098893 0.020151 -0.015217 19641030 -0.033333 0.024299 -0.020979 0.04223 0.037037 0.059603 19641130 0.032567 0.026277 0.058571 0.029173 0.059524 -0.0375 19641231 0.050373 -0.005386 0.012686 -0.030551 0.006757 -0.036957 19650129 0.094139 0.112816 0.065684 0.044118 0.082774 0.151242 19650226 0.022727 -0.000811 0.005031 0.037559 0.031405 -0.034902 19650331 -0.062857 -0.030195 0.001752 -0.03457 -0.002012 0 19650430 0.074957 0.107563 0.047739 -0.038462 0.040323 0 19650528 -0.001585 -0.010622 -0.008393 -0.015 0.039147 -0.017959 19650630 -0.018413 -0.017178 -0.067231 -0.037902 -0.071028 -0.037578 19650730 0.001626 0.068966 0.046936 -0.031858 0.113682 -0.052061 19650831 0.019481 0.11261 0.042341 0 0.086179 0.009611 19650930 0.005414 0.066138 0.124492 0.101645 0.093333 0.082005 19651029 -0.015924 0.088089 0.010684 0.011686 -0.082317 0.056842 19651130 0.057282 -0.02577 -0.038055 -0.023102 0.098339 0.066135 19651231 0.058462 0.107311 0.043077 0.048311 0.043939 0.020638 19660131 -0.002907 0.031949 -0.027542 -0.01945 0.085631 0.014706 19660228 -0.072886 -0.031992 -0.050109 -0.028099 0.016578 -0.021014 19660331 0.062579 0.049893 0.01055 -0.022109 -0.021108 -0.018587 19660429 -0.071429 0.10998 0.049087 0.068301 0.010782 0.132576 19660531 0.016026 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