Reference no: EM132443130

Quantitative Problem Set 3

Question 1

Index Models

Download 61 months (November 2010 to November 2015) of monthly data for the SPDR S&P 500 Index ETF (symbol = SPY). Download 61 months (November 2010 to November 2015) of Microsoft Corporation data (symbol = MSFT) and 61 months (November 2010 to November 2015) of Wells Fargo & Company data (symbol = WFC). Download 61 months (November 2010 to November 2015) 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:

1. Calculate 60 months of returns for the SPDR S&P 500 Index ETF, Microsoft, Wells Fargo, and the iShares 1-3 Year Treasury Bond ETF. (Please compute simple monthly returns not continuously compounded returns.)  Use December 2010 to November 2015. Note this means you need price data for November 2010.  On the answer sheet report the average monthly returns for the SPDR S&P 500 Index ETF, Microsoft, Wells Fargo, and the iShares 1-3 Year Treasury Bond ETF.

2. Calculate excess returns for the SPDR S&P 500 Index ETF, Microsoft and Wells Fargo. 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, Microsoft and Wells Fargo.

3. Regress excess Microsoft 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 Microsoft into systematic risk and firm-specific risk. That is, calculate total risk, systematic risk and firm-specific risk for Microsoft.

5. Regress excess Wells Fargo 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 Wells Fargo into systematic risk and firm-specific risk. That is, calculate total risk, systematic risk and firm-specific risk for Wells Fargo.

7. Use equation 8.10 to estimate the covariance and correlation of Microsoft and Wells Fargo excess returns.

Question 2

CAPM and APT

1. The expected rate of return on the market portfolio is 11.50% and the risk-free rate of return is 2.00%.  The standard deviation of the market portfolio is 19.75%.  What is the representative investor's average degree of risk aversion? 

2. Stock A has a beta of 1.50 and a standard deviation of return of 32%.  Stock B has a beta of 3.50 and a standard deviation of return of 58%.  Assume that you form a portfolio that is 45% invested in Stock A and 55% 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 17.25% for Stock A and an expected return of 33.75% 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 3.25% and 2.48%, respectively, while the risk-free rate of return remains at 2.00%.  According to this APT analyst, your portfolio formed in question 2 has a beta on factor 1 of 3.95 and a beta on factor 2 of 3.25.  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?