Saving for Retirement Assume an investor begins saving for retirement at age 25 and retires at age 65. Each year, she contributes $10,000 to her retirement account. To keep things simple, assume that there are 40 annual contributions that occur on the investor's 25-th, 26-th, ...,64-th birthdays, and that the final retirement wealth is determined on the investor's 65-th birthday. Savings are invested as follows: 50% in a broad stock market index and 50% in T-Bills. Your task is to compute the accumulated real retirement savings at age 65 for different return realizations. As explained below, you will generate returns using a Monte Carlo simulation. On Canvas, you can find an Excel file containing historical net returns on the S&P 500 and 3-month T-bills, as well as the consumer price index (CPI) from 1926 to 2017. The return on the CPI serves as measure of inflation. STEPS: 1. Compute the annual real return on the 50/50 portfolio for each year in the sample. The resulting set of 92 portfolio returns represents the empirical distribution. These are the returns investors historically realized when investing in a 50/50 mix of stocks and T-bills over this time period. T-bills Stocks Date 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 1961 3.60% 3.09% 4.44% 4.92% 2.75% 0.71% 0.87% 0.47% 0.33% 0.16% 0.19% 0.44% 0.04% 0.02% 0.02% -0.68% 0.40% 0.41% 0.40% 0.40% 0.38% 0.57% 0.86% 1.14% 1.20% 1.57% 1.91% 2.22% 1.13% 1.60% 2.78% 3.75% 2.05% 3.59% 3.84% 2.52% 9.85% 32.87% 39.14% -15.10% -28.90% -44.39% -7.94% 57.41% 3.18% 45.45% 32.32% -34.60% 28.44% 1.84% -7.51% -10.04% 16.72% 27.97% 21.36% 39.06% -6.42% 3.29% 2.13% 20.11% 30.47% 20.94% 13.33% 0.38% 50.41% 25.41% 8.58% -10.35% 44.78% 12.65% 1.21% 26.96% CPI 0.179 0.177 0.173 0.171 0.172 0.161 0.146 0.131 0.132 0.134 0.138 0.140 0.144 0.140 0.140 0.141 0.155 0.169 0.174 0.178 0.182 0.215 0.234 0.241 0.236 0.250 0.265 0.267 0.269 0.267 0.268 0.276 0.284 0.289 0.294 0.298 0.300 CPI 1973 1978 Date T-bills Stocks 1961 2.52% 26.96% 1962 2.94% -10.31% 1963 3.26% 20.89% 1964 3.77% 16.30% 1965 4.07% 14.39% 1966 5.20% -8.69% 1967 4.74% 28.57% 1968 5.55% 14.17% 1969 6.98% -10.84% 1970 7.83% 0.07% 1971 4.94% 16.20% 1972 4.21% 17.34% 7.15% -18.75% 1974 8.51% -27.94% 1975 6.86% 37.36% 1976 5.68% 26.77% 1977 5.41% -2.98% 7.36% 8.55% 1979 10.60% 24.41% 1980 12.59% 33.24% 1981 16.46% -3.99% 1982 13.20% 20.42% 1983 9.33% 22.64% 1984 11.12% 3.16% 1985 8.53% 31.41% 1986 6.75% 15.56% 1987 6.64% 1.83% 1988 6.86% 17.56% 1989 9.03% 28.43% 1990 8.44% -6.08% 1991 6.39% 33.65% 1992 3.92% 9.07% 1993 3.25% 11.59% 1994 4.28% -0.76% 1995 6.09% 35.68% 1996 5.41% 21.18% 1997 5.49% 30.35% 0.300 0.304 0.309 0.312 0.318 0.329 0.339 0.355 0.377 0.398 0.411 0.425 0.462 0.519 0.555 0.582 0.621 0.677 0.767 0.863 0.940 0.976 1.013 1.053 1.093 1.105 1.154 1.205 1.261 1.338 1.379 1.419 1.458 1.497 1.535 1.586 1.613 Date T-bills Stocks 1997 5.49% 30.35% 1998 5.30% 22.26% 1999 4.92% 25.27% 2000 6.15% -11.16% 2001 4.48% -11.27% 2002 1.80% -20.84% 2003 1.16% 33.13% 2004 1.31% 13.00% 2005 3.08% 7.31% 2006 4.84% 16.21% 2007 5.09% 7.26% 2008 2.04% -38.22% 2009 0.22% 31.29% 2010 0.13% 17.71% 2011 0.10% -1.07% 2012 0.11% 15.76% 2013 0.08% 30.45% 2014 0.05% 10.51% 2015 0.06% -1.68% 2016 0.35% 12.67% 2017 0.89% 20.64% 1.613 1.639 1.683 1.740 1.767 1.809 1.843 1.903 1.968 2.018 2.100 2.102 2.159 2.192 2.257 2.296 2.330 2.348 2.365 2.414 2.465 A Report the mean and standard deviation of the portfolio returns computed in step one. Saving for Retirement Assume an investor begins saving for retirement at age 25 and retires at age 65. Each year, she contributes $10,000 to her retirement account. To keep things simple, assume that there are 40 annual contributions that occur on the investor's 25-th, 26-th, ...,64-th birthdays, and that the final retirement wealth is determined on the investor's 65-th birthday. Savings are invested as follows: 50% in a broad stock market index and 50% in T-Bills. Your task is to compute the accumulated real retirement savings at age 65 for different return realizations. As explained below, you will generate returns using a Monte Carlo simulation. On Canvas, you can find an Excel file containing historical net returns on the S&P 500 and 3-month T-bills, as well as the consumer price index (CPI) from 1926 to 2017. The return on the CPI serves as measure of inflation. STEPS: 1. Compute the annual real return on the 50/50 portfolio for each year in the sample. The resulting set of 92 portfolio returns represents the empirical distribution. These are the returns investors historically realized when investing in a 50/50 mix of stocks and T-bills over this time period. T-bills Stocks Date 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 1961 3.60% 3.09% 4.44% 4.92% 2.75% 0.71% 0.87% 0.47% 0.33% 0.16% 0.19% 0.44% 0.04% 0.02% 0.02% -0.68% 0.40% 0.41% 0.40% 0.40% 0.38% 0.57% 0.86% 1.14% 1.20% 1.57% 1.91% 2.22% 1.13% 1.60% 2.78% 3.75% 2.05% 3.59% 3.84% 2.52% 9.85% 32.87% 39.14% -15.10% -28.90% -44.39% -7.94% 57.41% 3.18% 45.45% 32.32% -34.60% 28.44% 1.84% -7.51% -10.04% 16.72% 27.97% 21.36% 39.06% -6.42% 3.29% 2.13% 20.11% 30.47% 20.94% 13.33% 0.38% 50.41% 25.41% 8.58% -10.35% 44.78% 12.65% 1.21% 26.96% CPI 0.179 0.177 0.173 0.171 0.172 0.161 0.146 0.131 0.132 0.134 0.138 0.140 0.144 0.140 0.140 0.141 0.155 0.169 0.174 0.178 0.182 0.215 0.234 0.241 0.236 0.250 0.265 0.267 0.269 0.267 0.268 0.276 0.284 0.289 0.294 0.298 0.300 CPI 1973 1978 Date T-bills Stocks 1961 2.52% 26.96% 1962 2.94% -10.31% 1963 3.26% 20.89% 1964 3.77% 16.30% 1965 4.07% 14.39% 1966 5.20% -8.69% 1967 4.74% 28.57% 1968 5.55% 14.17% 1969 6.98% -10.84% 1970 7.83% 0.07% 1971 4.94% 16.20% 1972 4.21% 17.34% 7.15% -18.75% 1974 8.51% -27.94% 1975 6.86% 37.36% 1976 5.68% 26.77% 1977 5.41% -2.98% 7.36% 8.55% 1979 10.60% 24.41% 1980 12.59% 33.24% 1981 16.46% -3.99% 1982 13.20% 20.42% 1983 9.33% 22.64% 1984 11.12% 3.16% 1985 8.53% 31.41% 1986 6.75% 15.56% 1987 6.64% 1.83% 1988 6.86% 17.56% 1989 9.03% 28.43% 1990 8.44% -6.08% 1991 6.39% 33.65% 1992 3.92% 9.07% 1993 3.25% 11.59% 1994 4.28% -0.76% 1995 6.09% 35.68% 1996 5.41% 21.18% 1997 5.49% 30.35% 0.300 0.304 0.309 0.312 0.318 0.329 0.339 0.355 0.377 0.398 0.411 0.425 0.462 0.519 0.555 0.582 0.621 0.677 0.767 0.863 0.940 0.976 1.013 1.053 1.093 1.105 1.154 1.205 1.261 1.338 1.379 1.419 1.458 1.497 1.535 1.586 1.613 Date T-bills Stocks 1997 5.49% 30.35% 1998 5.30% 22.26% 1999 4.92% 25.27% 2000 6.15% -11.16% 2001 4.48% -11.27% 2002 1.80% -20.84% 2003 1.16% 33.13% 2004 1.31% 13.00% 2005 3.08% 7.31% 2006 4.84% 16.21% 2007 5.09% 7.26% 2008 2.04% -38.22% 2009 0.22% 31.29% 2010 0.13% 17.71% 2011 0.10% -1.07% 2012 0.11% 15.76% 2013 0.08% 30.45% 2014 0.05% 10.51% 2015 0.06% -1.68% 2016 0.35% 12.67% 2017 0.89% 20.64% 1.613 1.639 1.683 1.740 1.767 1.809 1.843 1.903 1.968 2.018 2.100 2.102 2.159 2.192 2.257 2.296 2.330 2.348 2.365 2.414 2.465 A Report the mean and standard deviation of the portfolio returns computed in step one