Index Models: Version A

Index Models:  Version A:

Download 61 months (September 2011 to September 2016) of monthly data for the SPDR S&P 500 Index ETF (symbol = SPY). Download 61 months (September 2011 to September 2016) of Apple Inc. data (symbol = AAPL) and 61 months (September 2011 to September 2016) of Berkshire Hathaway Inc. data (symbol = BRK-B). Download 61 months (September 2011 to September 2016) of iShares 1–3 Year Treasury Bond ETF data (symbol = SHY). Be sure to use end-of-month data! Construct the following on a spreadsheet:

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1. Calculate 60 months of returns for the SPDR S&P 500 Index ETF, Apple, Berkshire Hathaway, and the iShares 1–3 Year Treasury Bond ETF. (Please compute simple monthly returns not continuously compounded returns.)  Use October 2011 to September 2016. Note this means you need price data for September 2011.  On the answer sheet report the average monthly returns for the SPDR S&P 500 Index ETF, Apple, Berkshire Hathaway, and the iShares 1–3 Year Treasury Bond ETF.

2. Calculate excess returns for the SPDR S&P 500 Index ETF, Apple and Berkshire Hathaway. Use the monthly returns on the iShares 1–3 Year Treasury Bond ETF as your monthly risk–free return.  On the answer sheet report the average monthly excess returns for the SPDR S&P 500 Index ETF, Apple and Berkshire Hathaway.

3. Regress excess Apple returns on the excess SPDR S&P 500 Index ETF returns and report, on the answer sheet, α, β, the r-square and whether α and β 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 Berkshire Hathaway returns on the excess SPDR S&P 500 Index ETF returns and report, on the answer sheet, α, β, the r-square and whether α and β are different from zero at the 10% level of significance. Briefly explain your inference.

6. Use equation 8.10 to decompose total risk for Berkshire Hathaway into systematic risk and firm-specific risk. That is, calculate total risk, systematic risk and firm-specific risk for Berkshire Hathaway.

7. Use equation 8.10 to estimate the covariance and correlation of Apple and Berkshire Hathaway excess returns.

Q2:  CAPM and APT:

1. The expected rate of return on the market portfolio is 9.25% and the risk–free rate of return is 0.75%.  The standard deviation of the market portfolio is 18.50%.  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 38%.  Stock B has a beta of 4.50 and a standard deviation of return of 79%.  Assume that you form a portfolio that is 65% invested in Stock A and 35% 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 16.25% for Stock A and an expected return of 32.75% 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 3.75% and 2.75%, respectively, while the risk–free rate of return remains at 0.75%.  According to this APT analyst, your portfolio formed in question 2 has a beta on factor 1 of 3.50 and a beta on factor 2 of 2.50.  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?

Answer both questions. Both questions are attached. Upload your completed Excel answer sheet which is what will be graded. Also, upload your file of supportive computations which may be Excel, Word, or a scan (pdf) of your handwritten calculations. So, you should upload two files: one completed answer sheet and one file of supportive computations for the 2 quantitative problems. If your calculations are done in Excel, then you can upload one file with both your answer sheet and calculations in labeled worksheet tabs.