5. Download the Excel file “PS3 Data” It contains the (actual) monthly returns on EXXON and American Express over the past 5 years (2010-2014). It also has the corresponding returns on the S&P500 and the monthly risk-free rates. (Assume throughout that the S&P500 is the appropriate market index.) Also, note that the risk-free rate is listed in the month for which it is relevant. In other words, in the row Jan-10 are the returns for January 2010 and the risk-free rate that was known at the beginning of that month.
a. Estimate the betas of EXXON and American Express using the 5 years of monthly data (60 observations). (The easiest way is to use the =SLOPE function. This function returns the slope coefficient from a linear regression. Alternatively you can use the regression 3 package in the data analysis tool kit. Under the “Data” tab see Data Analysis/Regression.) Why are the numbers (slightly) different from those reported in Lecture 9?
b. Calculate the monthly returns of a portfolio constructed to have a beta = 1.0 from the returns on EXXON and American Express. Calculate the beta and alpha of this portfolio. To what extent does this represent a profit opportunity? (The easiest way is to use the =SLOPE and =INTERCEPT function. The INTERCEPT function returns the constant coefficient, i.e., intercept, from a linear regression. If you used the regression package, it returns the slope, intercept, and many other outputs.)
c. Based on the 5 years of data, what percentage of the (monthly) variance of EXXOM, American Express and the beta=1 portfolio is systematic? What percentage is idiosyncratic? (If you use the regression package, the output, specifically the R-squared of the regression, might be useful for answering this question. Otherwise you will need to calculate these quantities directly.)
d. Assuming the CAPM holds, using the beta estimates from above, and assuming an annual risk-free rate of 2% (rf = 2%), and an annual market risk premium of 8% (E[rM]- rf = 8%), what are the annual expected/required returns on EXXON and American Express?
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