The purpose of this assignment is to help you gain hands-on experience with the Capital Asset Pricing Model (CAPM) we developed in class, using ordinary least squares (OLS) techniques. The CAPM of modern portfolio theory in its risk-premium can be expressed as ri - rf = σi /σm (rm - rf ), (1) where ri - rf is the risk premium of security i, rm - rf is the risk premium of the market (the market is usually represented by the S&P500), and σi/σm is the fraction of security i's risk in relation to market risk, a measure of systematic risk (risk that cannot be eliminated through diversification).
For empirical purposes, (1) can be estimated via OLS and is written as ri - rf = αi + βi (rm - rf ) + ei . (2) If CAPM holds, αi is expected to be zero. βi is the estimate of σi/σm, which, as stated above, measures the extent to which the ith security's return moves with the market.
1. Using the MARKET variable, plot returns for the last 36 months in the data series, from January 1985 through December 1987.
(a) Using the entire 120-month time span, construct the risk premium measure for the MARKET and the risk premium measure for MOBIL.
(b) Plot MOBIL's market risk premium along with the MARKET's risk premium for the 1 time period between from January 1985 through December 1987. Do you think that MOBIL's β during this time period will be greater or less than unity?
(c) Calculate the standard deviation for the MOBIL and MARKET variables, along with the correlation coefficient between them.
2. From the list of industries in the data file, choose one industry that you think is risky and another that you think is safe.
(a) Estimate via OLS the parameters αi and βi from Equation (2) for one firm in each of these two industries. Do the estimates of β correspond well with your beliefs?
(b) For one of these companies, make a time plot for the time period between January 1985 through December 1987, of the company risk premium, the company risk premium predicted by the regression, and the associated residuals. Are there any dates that appear to correspond with unusually large residuals?
(c) For each of the two companies in 2(a) compute the proportion of total risk that is systematic risk.
3. Choose one industry that you think is relatively safe and another you think is relatively risky. Choose two companies from the safe industry and two from the riskier industry.
(a) Calculate the mean and standard deviations of the returns for each of the four companies over the January 1983 - December 1987 time period.
(b) Construct three alternative (one million dollars total) portfolios as follows: Portfolio I: 50% in a company in the safe industry and 50% in the company from the risky industry.
Portfolio II: 50% in each of the two companies in the safe industry.
Portfolio III: 50% in each of the two companies in the risky industry.
(c) Calculate the sample correlation coefficient between the two company returns in each of the three portfolios. Comment on the size and interpretation of these correlations.
(d) For each of the three portfolios, calculate the means and standard deviations for returns over the January 1983 - December 1987 time period. Does anything stand out?
(e) Which of the three alternative portfolios is most justifiable in terms of reducing unsystematic risk of investment? Why?
(f) Estimate the CAPM equation (2) for each of the portfolios over the same January 1983 - December 1987 time span. Report and explain your results.
(g) Based on the regression model, which of the alternative portfolios has the smallest proportion of unsystematic risk? Do these results match those from question 3(e)?