Question;Portfolio ChoiceThe focus of this assignment is to construct portfolios. The topics correspond to Lectures4 to 6. You will need to use a spreadsheet posted on Carmen called hw2data.xls. Thisdataset contains the historical monthly returns of six stocks: Coca-Cola (KO), EastmanKodak (EK), General Electric (GE), Dow Chemical (DOW), Johnson & Johnson (JNJ), and3M (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 needto print out entire spreadsheets. Your answers should be summarized in a write-up withrelevant details of calculations, tables and charts (if applicable), and explanations.The assignment can be turned in during class or via e-mail (chabi-yo firstname.lastname@example.org). Ifyou do submit your assignment via e-mail, please submit it either as a Word document oras a PDF le. In particular, please do not e-mail an Excel spreadsheet if you feel that theExcel spreadsheet is relevant to providing details of your work, please copy and paste therelevant portions into your Word document.Part 1: Preferences and the Equity Premium Puzzle1Suppose that you use a quadratic utility function, U = E (r) 2 A 2, to make your nancialdecisions. The average historical return for large US stocks is 11.63% with a standarddeviation of 20.56%. Suppose that you also use this for your estimates of E (r) and.1. Suppose that in choosing a portfolio consisting of a risk-free asset (where rf = 3%)and large US stocks, you invest 60% of your money in large US stocks (and the rest inthe risk-free asset). What does this imply about your risk aversion coecient, A?2. If your preferences are consistent (i.e. you use the same utility function, including thesame A as above), which would you prefer?(a) an asset which has E (r) = 5% and = 0(b) an asset with E (r) = 10% and = 20%Assume that you are only investing in (a) or (b) and not mixing the two assets into aportfolio.3. Suppose that we interview a group of investors who chose to invest 60% of their portfolioin 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 investorsin the group are consistent in their choices, what does this imply about the quadraticutility function? If we believe that the quadratic utility function is the correct utilityfunction, what does this imply about the consistency of investors preferences?Part 3: DiversicationStart 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 volatilityof 30%. The correlation between the two asset returns is 0.9. What is the optimalcombination of A and B? What is the volatility of this portfolio? [Hint: The expectedreturn 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 volatilityof 30%. The returns of asset C are uncorrelated with both the returns of asset A andof asset B. What is the optimal combination of A, B, and C? What is the volatility ofthis portfolio?3. Did the introduction of B or C have a greater eect in decreasing the portfolio volatility?Why is this the case?
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