1. Assume that you have a job as a portfolio manager and you are looking at your portfolio’s returns vs. some German index. The historical information you have is: Year Portfolio return German index return 2002 54% 50% 2003 24% 10% 2004 6% 10% 2005 24% 60% 2006 6% 20% 2007 54% 80% (a) Wow, you had some good years as a portfolio manager! But, now looking at the German index return could you have received higher returns for the same level of risk by putting some money in the German index fund? Hint: Find expected returns and standard deviations and the covariance. Then compare the correlation coefficient, ?(your,Ger) , with the ratio of std. deviations. (b) Is it possible to reduce your portfolio’s risk below its current level by investing some in the German index? (c) How much of the variation in the German stocks can be explained by the variation in your portfolio’s returns? Hint: Use R squared. Rsquared = (?(your,Ger)) 2 (d) Is this a violation of CAPM? 2. There is a portfolio of three stocks, where equal amounts are allocated to all three stocks. All have independent distributions such that: (cov(rj , ri) = 0 for all i, j and k and each stock has the same total risk (standard deviation). What fraction of each stock’s risk is diversified away by including it in the portfolio? Document Preview:

Masters of Financial Economics, ADEC 73601Dr. Danielle ZanzalariProblem Set 42018Please follow the instructions listed on your syllabus regarding problem sets. I do not acceptlate work. Email me with any questions you have.1. Assume that you have a job as a portfolio manager and you are looking at your portfolio’sreturns vs. some German index. The historical information you have is:Year Portfolio return German index return2002 54% 50%2003 24% 10%2004 6% 10%2005 24% 60%2006 6% 20%2007 54% 80%(a) Wow, you had some good years as a portfolio manager! But, now looking at theGerman index return could you have received higher returns for the same level ofrisk by putting some money in the German index fund? Hint: Find expected returnsand standard deviations and the covariance. Then compare the correlation coecient, , with the ratio of std. deviations.(your;Ger)(b) Is it possible to reduce your portfolio’s risk below its current level by investing somein the German index?(c) How much of the variation in the German stocks can be explained by the variation in2your portfolio’s returns? Hint: Use R squared. Rsquared = ( )(your;Ger)(d) Is this a violation of CAPM?2. There is a portfolio of three stocks, where equal amounts are allocated to all three stocks.All have independent distributions such that: (cov(r ;r ) = 0 for all i, j and k and each stockj ihas the same total risk (standard deviation). What fraction of each stock’s risk is diversiedaway by including it in the portfolio?13. Below are some stocks with high and low betas found on Yahoo Finance.Stock BetaGoogle 0.94Apple 1.43Exxon 0.90Willamette Valley Vineyards 0.66Nintendo 0.53Yahoo 2.15Marathon Oil 2.37If the risk free rate is r = 1% and the expected return on the market portfolio is 6%,fthen using CAPM calculate the expected returns on each of the stocks.4. Based on forecasts, you see that interest rates for period 1, 2 and 3, in the futureare: r = 0:0989;r = 0:1027…

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