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The data for this question are available from the website of Robert J. Shiller. First, go to http:/www.econ.yale.edu/-shiller/data.htm, click on long term stock, bond, interest rate and consumption data, and download the excel file. For the period 1871-2012, prepare four data series for the analysis: (i) Real Return on S&P 500 Composite; (ii) Real Stock Price; (iii) Real S&P Dividend; and (iv) Real One-year Interest Rate. Keep in mind that, in the data file, the real one-year interest rate series is gross rate of return, while the return on S&P 500 series is net rate of return. Then, for the period 1889-2009, prepare the data series of Real Per Capita Consumption. (a) For the period 1871-2012, compute the mean and the standard deviation of the equity premium, defined as the return on S&P 500 minus the one-year interest rate. For this period, compute also the mean and the standard deviation of the one- year interest rate. (b) For the two sub-samples, 1871-1945 and 1946-2012, compute the mean and the standard deviation of the equity premium, defined as the return on S&P 500 minus the relatively risk-free one-year interest rate. For the sub-samples, compute also the mean and the standard deviation of the one-year interest rate. (c) For the sample period 1890-2009, compute the per-capita real consumption growth rate as the log difference in per-capita real consumption. Then, compute the mean and the standard deviation of the per-capita real consumption growth. (d) For the two sub-samples, 1890-1945 and 1946-2009, compute the mean and the standard deviation of the per-capita real consumption growth. (e) It is often argued that the economy is more stable in the post-war period than in the pre-war period. Do the results in (b) and (d) support the argument? (f) For the sample period 1871-2012, compute price-dividend as the ratio of real stock price to real S&P dividend. For the period 1872-2012, compute the correlation coefficient between equity premium and the lagged log price-dividend ratio (lagged one year, and in logarithm). The square of the correlation coefficient is the fraction of variation in one variable explainable by the variation of other. What fraction of equity premium could be explained by variation in lagged price- dividend ratio? (g) Based on your finding in (f), devise an investment strategy to improve your expected portfolio return