In this exercise you will familiarize yourself with index models, beta and CAPM estimation. Download the spreadsheet data_question3.xlsx from Sakai and use the data contained therein to answer Question 3. Spreadsheet data_question3.xlsx contains monthly stock returns for AT&T, Ford, Google and Exxon Mobile. Additionally, it contains monthly returns on Treasury securities and a broad market index. Be careful to calculate monthly excess returns over Treasuries as this is what you will need for estimating single index models.
a) In class we have discussed how index models can be used to separate firm-specific risk and market risk inherent in a firm's expected returns. What is the analytical formula to separate a security's risk into market risk and firm specific risk?
b) Using excess returns over Treasuries, estimate the beta coefficients for AT&T, Ford, Google and Exxon Mobile without running a regression model. Additionally, using your result from part (a) estimate the standard deviation for each firm's expected return and estimate each firm's market risk component and firm-specific risk component. (Again use excess returns over Treasuries) Use the Excel functions STDEV.S and COVARIANCE.S for this exercise. Tabulate your results in the write-up as follows:
c) Describe and interpret your results in the single-index model sense. i.e. how each stock moves with the overall market and which stock is the riskiest for a diversified investor? How does beta relate to the market risk component and how does it relate to the firm specific component?
d) Suppose you want to construct a portfolio consisting of AT&T, Ford, Google and Exxon that exhibits minimal movement with the overall market, i.e. = 0. Using Microsoft Excel Solver calculate the weights such that is minimized under the constraint
β = 0. (Use excess returns over Treasuries for your calculations). Break up into market risk and firm-specific risk. Would you have eliminated all risk by only holding this portfolio of stocks?