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FIN 5620 Quantitative Problem Set #3

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Question;Q1;Index Models;Download 61 months;(November 2009 to November 2014) of monthly data for the S&P 500 index;(symbol = ^GSPC). Download 61 months (November 2009 to November 2014) of Apple;Inc. data and 61 months (November 2009 to November 2014) of Exxon Mobil;Corporation data. Download 60 months (December 2009 to November 2014) of the 13;week T-bill rate (symbol = ^IRX). Be sure to use end-of-month data!;Construct the following on a spreadsheet;1. Calculate 60;months of returns for the S&P 500 index, Apple and Exxon. (Please compute;simple monthly returns not continuously compounded returns.) Use December 2009 to November 2014. Note this;means you need price data for November 2009.;On the answer sheet report the average monthly returns for the S&P;500 index, Apple and Exxon, as well as the average monthly risk-free rate.;2. Calculate excess;returns for the S&P 500 index, Apple and Exxon. Note you must divide the;annualized risk-free rate (^IRX) by 1200 to approximate the monthly rate in in;decimal form. On the answer sheet report;the average monthly excess returns for the S&P 500 index, Apple and Exxon.;3. Regress excess;Apple returns on the excess S&P 500 index returns and report, on the answer;sheet,?,?, the r-square and whether? and? are different from zero at the;10% level of significance. Briefly explain your inference.;4. Use equation 8.10;to decompose total risk for Apple into systematic risk and firm-specific risk.;That is, calculate total risk, systematic risk and firm-specific risk for;Apple.;5. Regress excess;Exxon returns on the excess S&P 500 index returns and report, on the answer;sheet,?,?, the r-square and whether?,? are different from zero at the 10%;level of significance. Briefly explain;your inference.;6. Use equation 8.10;to decompose total risk for Exxon into systematic risk and firm-specific risk.;That is, calculate total risk, systematic risk and firm-specific risk for;Exxon.;7. Use equation 8.10;to estimate the covariance and correlation of Apple and Exxon excess returns.;? Q2: CAPM and APT;1. The expected rate of return on the market;portfolio is 8.25% and the risk?free rate of return is 1.50%. The standard deviation of the market;portfolio is 18%. What is the;representative investor?s average degree of risk aversion?;2. Stock A has a beta of 1.75 and a standard;deviation of return of 32%. Stock B has;a beta of 2.95 and a standard deviation of return of 56%. Assume that you form a portfolio that is 60%;invested in Stock A and 40% invested in Stock B. Using the information in question 1;according to CAPM, what is the expected rate of return on your portfolio?;3. Using the information in questions 1 and 2;what is your best estimate of the correlation between stocks A and B?;4. Your forecasting model projects an expected;return of 14.50% for Stock A and an expected return of 26.50% for Stock B. Using the information in questions 1 and 2;and your forecasted expected returns, what is your best estimate of the alpha;of your portfolio when using CAPM to determine a fair level of expected return?;5. A different analyst uses a two?factor APT;model to evaluate expected returns and risk.;The risk premiums on the factor 1 and factor 2 portfolios are 4.50% and;2.95%, respectively, while the risk?free rate of return remains at 1.50%. According to this APT analyst, your portfolio;formed in question 2 has a beta on factor 1 of 2.35 and a beta on factor 2 of;3.50. According to APT, what is the;expected return on your portfolio if no arbitrage opportunities exist?;6. Now assume that your forecasting model of;question 4 accurately projects the expected return of Stocks A and B and;therefore your portfolio, and that the APT model of question 5 describes the;fair rate of return for your portfolio.;Do any arbitrage opportunities exist?;If yes, would you invest long or short in your portfolio constructed in;question 2?

 

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