The price level, earnings, and return data are given in real terms in units of December 31, 2012, dollars) in Exhibit 2. Why is it important to work in real units? The geometric average nominal return of the sample period is 9.9%. How does this compare to the geometric average real return? 2. Plot the price and earnings of the S&P Composite Index over time. What relationship do you observe? Can you suggest an economic interpretation for these results? 3. Exhibit 3 contains the smoothed P/E ratio for each year. The ratio is calculated using the most recent price divided by the average earnings over the previous 10 years. What is the rationale for using the most recent price but then averaging the earnings over such a long time? What was the average smoothed P/E ratio over the entire sample? What was it at the end of 2007 and at the end of 2008? 4. Exhibit 3 also includes the 1-year, 5-year, and 10-year forward-looking geometric average returns. Plot the backward-looking smoothed P/E ratio versus the corresponding 10-year forward-looking returns. What relationship do you observe between price and earnings over time? Can you suggest an economic interpretation for these results? 5. Assuming you can only invest in the S&P Composite Index or 3-month T-bills, give a decision rule for asset allocation based on the smoothed P/E ratio i.e., invest 100% of your portfolio in the S&P Composite Index 3-month T-bills when the smoothed P/E ratio is above/below X). Calculate the return you would earn from such a strategy. How does this compare to the return on the S&P? Is this the correct benchmark for your strategy 6. Analyze the power of the P/E ratio to predict the S&P's future/forward-looking 1., 5., or 10-year returns. To do this, regress the future return of the S&P Composite Index on the S&P smoothed P/E ratio. Does the P/E ratio have predictive power? Can you suggest an economic interpretation for these results? What are the differences in the predictive power for the 1., 5., and 10-year returns? Why do they differ? (For a primer on regression analysis, read the technical note "Regression: Forecasting Using Explanatory Factors.3) 7. In recommending an asset allocation to the board of the Oxcel College endowment, you will need a forecast of the expected return for equities. Using the regression model you developed for the 10- year forward-looking S&P Composite Index returns and a current smoothed P/E ratio of 23,4 what is your forecast of the expected return? Year Real S&P Composite Index Price (Dec 31) Real S&P Composite Dividends (Jan-Dec) Real S&P Composite Earnings (Jan-Dec) 3-Mo. T- Bill Return (Ann) S&P Composite Annual Return (Nominal) Real S&P Composite Annual Return Real Smoothed P/Arg10(E) Real S&P Real S&P 1-Year 5-Year Forward- i Forward- Looking Looking Return Return Real S&P 10-Year Forward- Looking Return 120.91 2.39% 13.01 12.34 16.03 5.17% 26.05% 25.24% 6.62 6.87 7.24 8.42 9.61 10.73 16.09 11.38% 25.68% 20.71% 12.31% 39.38% 48.09% -9.53% 9.93% 6.38% 8.64% 10.31% 2.47% 0.17% 1.49% 2.32% 5.22% 36.57% 46.66% -8.77% -21.88% -42.93% 12.18 -16.83% -8.55% 6.00% 54.87% 12.84 3.40% 11.54 17.14 117.19 140.41 162.26 173.82 232.65 333.79 289.80 227.89 130.53 124.26 183.33 158.66 228.94 288.48 180.33 205.00 201.72 171.79 132.28 137.08 156.37 174.01 227.33 162.43 145.51 146.33 164.22 -7.87% 53.67% 33.07% -31.15% 6.02% 5.00% -0.74% 2.77% 22.17 15.03% 1.69% 3.36% 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 13.14 12.13 8.24 7.20 7.25 7.35 11.11 12.00 7.87 9.56 10.26 9.89 7.54 7.57 7.76 7.83 7.13 7.75 8.33 10.43 -8.78% -8.63% 19.60% 14.73 18.53 21.49 13.83 9.59 7.19 7.65 8.40 12.64 16.73 18.02 10.50 14.76 17.10 17.18 13.99 12.40 12.00 12.11 11.32 15.80 21.82 22.57 26.08 21.14 20.64 21.42 23.82 31.01 28.37 27.24 22.96 26.47 25.19 25.68% 20.71% 12.31% 39.38% 48.09% -9.53% -16.83% 37.40% 1.52% 53.33% -9.50% 48.92% 30.86% -33.33% 18.04% 3.07% -9.75% -17.24% 9.33% 19.59% 16.25% 35.15% -25.41% -5.64% 6.29% 19.35% 26.35% 13.49% 12.86% 1.70% 46.61% 27.87% 3.52% -8.44% 36.86% 5.60% 4.65% 18.05% 23.49% 28.60% 20.41% 11.77% -0.56% -6.67% -6.02% -6.01% 5.60% 22.38% 12.51% 6.78% 9.59% -0.86% -9.54% -0.13% 0.13% 2.57% 11.19% 8.91% 5.75% 3.28% 3.83% 2.44% 11.41% 15.47% 14.46% 19.26% 19.55% 17.37% 12.56% 19.45% 11.86% 7.47% 10.33% 11.33% 3.24% 10.02% 10.97% 0.28% 0.17% 0.17% 0.28% 0.07% 0.05% 0.04% 0.13% 0.34% 0.38% 0.38% 0.38% 0.38% 0.60% 1.05% 1.12% 1.20% 1.52% 1.72% 1.89% 0.94% 1.73% 2.63% 3.23% 1.77% 3.39% 2.88% i -37.40% 1.52% 53.33% -9.50% 48.92% 30.86% -33.33% 18.04% 3.07% -9.75% -17.24% 9.33% 19.59% 16.25% 35.15% -25.41% -5.64% 6.29% 19.35% 26.35% 13.49% 12.86% 1.70% 46.61% 27.87% 3.52% -8.44% 36.86% 5.60% 4.65% 19.24% 38.47% -11.65% 13.79 15.29 16.00 14.40 10.79 10.53 11.42 12.28 15.64 11.22 10.44 10.67 11.06 12.46 12.68 13.30 12.36 3.02% 9.84% 3.20% 6.73% 10.15% 10.50% 8.73% 11.28% 10.66% 14.35% 14.01% 16.93% 15.50% 13.35% 13.79% 11.95% 13.71% 10.94% 9.21% 7.72% 9.95% 194.79 12.70 1 11.49 17.32% 34.36% 20.70% 14.06% 2.79% 45.88% 28.62% i 1 16.56 19.23 209.59 225.13 217.31 306.13 378.24 377.93 332.44 441.88 453.19 460.13 11.40 11.64 12.46 13.21 13.61 13.61 13.08 13.44 14.13 17.53 14.29 6.84% -5.55% 39.52% 7.62% 6.27% 7.12% 18.10 18.48 18.47 i : 4.95% 4.60% | 1961 14.54 24.41 5.1% 3.86 21.29 19.3 | 1962 15.13 19.04 -2.72% 21.01% 27.71 8.58 5.64 13.93 29.87 3.48 6.01% 18.05% 4.18 13.8 % 14.61% 2.23 17.30 | 1963 | 1964 | 1965 | 1966 | 1987 15.92 -4.18% 18.85% 14.61% 5.23% 9.73 12.38% 21.6 23.73 24.35 0.11 12.3 2.77% 3.1 35 3.95 4.363 4.31% 5.34% 6.67 13.47 37.47 13.84 20.81 11.52 -6.43% 16.00 10.60 9.73% 12.38% 21.93 5.43 18.60 18.68 1968 5.43 1.17 3.65% -2.01% -0.42 3.12 3.05% -1.31% -0.36% -2.87 -2.03% 21.82 -13.92% 1.1 | 198 18.10 -8.40 -13.92 17.37 16.57 -1.41 2.56% 2.79% 3.44% -7.26% -2.60 -3.32 -8.68% -2.65 5.03% 17.04 6.39 7.00 9.99 1970 1971 16.13 13.78% 528.62 49138 568.06 33.76 73.19 589.36 643.70 659.96 550.01 539.33 77.08 639.73 477.64 321.00 400.71 40953 333.68 338.16 331.89 353.77 286.46 339.39 38.73 36.10 37.25 5.20 29.59 31.84 34.68 40.55 39.33 32.93 39.10 40.26 17.30 13.63 1.1 9.99% 13.63% 4.33% 4.07% | 1972 16.01 17.69 18.97 15.30 -22.87 13.83 2.01% | 1973 | 1974 | 1973 14.98 9.04 6.01% 14.32 1111 1.92 5.31 7.44% 1976 7.03 7.3% 3.78% 4.97% 5.27% 17.19% | 10.07% 15.03 11.0 -2.41% 16.24 -22.87% -29.56% 29.29% 39 -14.36% 6.19% 2.85 11.24 .14.72% 23.78% -29.66 29.29 5.95% -14.5 6.19% 2.85 11.24% 9.36 5.10 | 1977 | 1978 | 1979 3.43 16.17 41.82 6.90 9.07 -15.99% .20.76% 38.56 11.36% -8.5 16.10 16.36% 25.49% -6.81% 23.87 20.25% 7.66% 25.92% 13.31 6.99 10.51% 1980 15.41 11.4 3.32% 8.60 | 1981 13.23 14.03% -14.72% 18.28 15.20 10.61% 15.37% 11.36% 1982 | 1983 4.48 39.43 37.2 19.74 31.80 36.28 30.8 30.09 34.82 3.70 9.79 377.13 15.11 3.81% 11.29 13.05 11.14% 10.43% 9.89% 10.80 10.23% 1984 15.44 99- 14.1 13.61 11.71 3.38% 23.78% 15.37 3.31 21.05% 29.37% -6.33% 12.62% 17.31% | 1985 | 1986 16.18 31.03% 14.81 8.05% | 1987 16.49 13.76 13.31% 1988 3.31 21.05% 29.37% -6.33% 12.62% 17.31% -6.61 27.4 4.37 3.41% -1.37% 17.33% 22.99 45.27 15.5 10.42% 9.58% 5.78% 15.07% 41.64 17.19 14.33% 17.44 18.92 198 19.11 36.62 -0.70% 15.8 13.28 14.32 19.54 9.85 26.49 30.89 9.52% 7.48% 5.98% 3.78% 6.67% 3.11% 7.49% 5.33% 3.43% 3.00% 4.25% 3.49% 3.01 3.06 4.78% 4.64% 31.58% 7.38% -6.61% 27.45% 4.37% 8.41 13.84 6.70 18.63 34.46 11.37 1985 | 1990 | 1991 | 1992 | 1993 1994 | 1995 | 1996 | 1997 1998 -1.6 374.19 437.33 549.61 498.36 543.82 615.01 558.56 692.77 704.22 744.85 713.57 919.03 1109.24 1371.29 1749.35 1944.84 1756.22 1481.57 1137.01 | 1346.26 19.01 7.80 8.93 -1.65 20.51 21.62 20.55 25.68 29.34 12.46% 16.68% 20.3 24.10% 15.38% 7.29% -2.43 19.40 1.1 35.03% 27.13% 27.75% 31.31% 6.32 20.29 329 31.31 22.90% 25.50% 29.13% 20.75 33.94 3.14 41.09 4.30 21.34 21.42 46.93 50.80 56.07 36.54 52.81 65.72 65.98 32.08 35.02 60.72 31.51% 22.90% 25.50% 29.138 12.40 -3.66% .14.54% -21.96 20.209 19.11% | 1999 15.0 12.40 4.85 3.24 20.19 5.82 -3.66 38.40 -1.23 19.24 -3.32% -4.39% -1.98% 3.33% 9.04. 4.77% 30.44 2000 2001 2002 | 2003 10.27% 5.50 -13.1 .20.02% 22.57% 3.3923 11.60 11.01% 19.18 20.38 -14.34 -21.96% 20.20% 4.23% 23.10 27.12 3.11% 22.06 24.38 2004 | 1446.87 2005 | 1472.42 2006 1611.35 2007 | 1617.01 2008 958.43 2009 1130.57 2010 1300.56 2011 1264.97 2012 1422.29 -2.07% -0.47% -2.70% -0.37% 26.62 28.51 29.16 22.41 23.31 26.89 31.25 70.64 81.59 2.74 72.34 28.57 34.19 31.03 38.46 86.51 1.37% 13.15% 14.73% 4.35% | 1.37% | 0.15% 10.14% | 0.0 0.09% 12.77% 7.02 14.20 6.39 33.75% 29.08% 13.86 2.27% 16.91% 3.45 11.26 2.11% 38.92% 25.52% 12.18% -0.67 14.51 27.68 26.95 27.92 26.234 15.22 19.50 21.90 20.77 21.38 345% 11.26% 2.11% .38.925 25.52% 12.18% -0.67% 14.91%