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Unformatted text preview: UNIVERSITY OF NORTH CAROLINA KENAN-FLAGLER BUSINESS SCHOOL BUSI 580: INVESTMENTS PART I: PORTFOLIO THEORY AND ASSET PRICING Prof. Günter Strobl Spring 2010 Problem Set 1 For the following set of questions you will need to use the returns data contained in the Excel spreadsheet PS1_data.xls. Please download this file from the course website. The file contains monthly returns for three indexes (VW = value-weighted index of stocks listed on the NYSE, AMEX, and NASDAQ including distributions, EW = equallyweighted index including distributions, S&P = S&P 500 index excluding dividends) and one-month risk-free rates (RF) over the period from January 1959 to December 2008. You also need to obtain monthly holding period returns (including dividends) for the following five stocks from CRSP for the same 50-year period: General Motors (ticker: GM), IBM, Merck (MRK), Coca Cola (KO), and Eastman Kodak (EK). You can access the CRSP database through the Wharton Research Data Service ( A. Empirical Properties of Stock Returns 1. Calculate the largest and smallest returns for each of the three indexes and five stocks over the entire period. Did anything happen on or around these dates to explain such extreme returns? Are these clustered in time? Why or why not? 2. Compute the mean returns and standard deviations of each of the indexes and individual stocks over the entire period. Are any of the mean returns significantly different from 1%? Can the returns be modeled as normally distributed random variables? 3. Compute the correlation matrix for the indexes and individual stocks for the entire sample. Which index is most highly correlated with the S&P 500 (VW or EW) and why? Which of the five stock returns is most highly correlated with the S&P 500 and why? Are the correlations among the five stocks unusual in any way or are they as you expected them to be? Why or why not? 1 B. Mean-Variance Portfolio Optimization 4. Using the entire sample of monthly returns on the 5 stocks in the data set, calculate and plot the mean-variance efficient frontier in mean-standard deviation space. Plot the position of each stock in mean-standard deviation space. 1 5. If you are restricted to invest in the 5 individual stocks, what is the minimum level of risk you have to bear? How would the minimum variance portfolio look like if you cannot sell stocks short? 6. Compute the optimal tangency portfolio using the average T-bill rate. Plot it on the graph you created in (4). What is the Sharpe ratio of the optimal tangency portfolio? 7. Suppose your desired rate of return is 1.5% per month. Which portfolio (consisting of the five stocks and T-bills) would you optimally choose? 1 Hint: There are several ways to determine the efficient frontier. Probably the easiest way is to use Excel’s solver to minimize the variance at two possible values of expected portfolio returns. Then use the fact that the entire efficient frontier can be constructed as a linear combination of any two frontier portfolios once you know the coordinates of and covariance between these two portfolios. 2 ...
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This note was uploaded on 04/06/2010 for the course BUSI 580 taught by Professor Strobl during the Fall '09 term at UNC.

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