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Please use the excel function data on stocks, bonds, bills to start discussion on time value. First question: Using the data and $100 invested in

Please use the excel function data on stocks, bonds, bills to start discussion on time value.

First question:

Using the data and $100 invested in stocks, bonds and bills, confirm the values at 2011.

Terminal value at 2011= $100(1+r1)(1+r2)...(1+r84)

where r1= actual return given for 1928

r2=actual return given for 1929

r84=actual return given for 2011 for stocks, bonds and bills

Second Question:

Investing over 84 years is a little far fetched unless your grandfather was like Donald Trump's G.PA. Now consider dividing 1928-2011 to three sub-period of 1928-56 (28 years), 1956-1984 28 yr) and 1984-2011 (27 yr). Let's see how investment of $100 in stocks, bonds, bills using again the actual returns provided in each asset class (stocks, bonds, bills) perform? Compare, the future value of each investment as if in the second 28 years, and last 27 years you start with $100 investment in stocks, bonds, bills. What are the lessons we learn in this exercise as far as your future contribution to your own 401K is concerned?

Annual returns stocks bonds bills compound value of $100 DATE VALUE GDP growth rate 1929-69 1970-1999 2000-2010 43.81% 0.3458 7.2317E-08
Year Stocks T.Bills T.Bonds Stocks T.Bills T.Bonds skewness 1929 976.1 -0.086159205 -0.086159205 1 -0.086159205 0.060599779 0.010796691 -0.086159205 0.033565385 0.010796691 -8.30% -0.1753 -9.42131E-09
1 1928 43.81% 3.08% 0.84% $143.81 $103.08 $100.84 7.2317E-08 1930 892 -0.064798206 -0.064798206 2 -0.064798206 0.043716203 0.018134509 -0.064798206 0.053135276 0.018134509 -25.12% -0.3435 -7.08836E-08
2 1929 -8.30% 3.16% 4.20% $131.88 $106.34 $105.07 -9.42131E-09 1931 834.2 -0.130664109 -0.130664109 3 -0.130664109 0.057865169 0.025409119 -0.130664109 0.057926698 0.025409119 -43.84% -0.5307 -2.61404E-07
3 1930 -25.12% 4.55% 4.54% $98.75 $111.18 $109.85 -7.08836E-08 1932 725.2 -0.012961942 -0.012961942 4 -0.012961942 0.064200153 0.034681153 -0.012961942 -0.005516203 0.034681153 -8.64% -0.1787 -9.9802E-09
4 1931 -43.84% 2.31% -2.56% $55.46 $113.74 $107.03 -2.61404E-07 1933 715.8 0.108829282 0.108829282 5 0.108829282 0.065178819 0.030709812 0.108829282 -0.002108193 0.030709812 49.98% 0.4075 1.18345E-07
5 1932 -8.64% 1.07% 8.79% $50.66 $114.96 $116.44 -9.9802E-09 1934 793.7 0.088824493 0.088824493 6 0.088824493 0.025272637 0.026578468 0.088824493 0.053636625 0.026578468 -1.19% -0.1042 -1.97865E-09
6 1933 49.98% 0.96% 1.86% $75.99 $116.06 $118.60 1.18345E-07 1935 864.2 0.130525341 0.130525341 7 0.130525341 0.048410845 0.019130301 0.130525341 0.045981039 0.019130301 46.74% 0.3751 9.23011E-08
7 1934 -1.19% 0.32% 7.96% $75.09 $116.44 $128.05 -1.97865E-09 1936 977 0.051279427 0.051279427 8 0.051279427 0.031066128 -0.003369578 0.051279427 0.055777856 -0.003369578 31.94% 0.2271 2.04841E-08
8 1935 46.74% 0.18% 4.47% $110.18 $116.64 $133.78 9.23011E-08 1937 1027.1 -0.034368611 -0.034368611 9 -0.034368611 0.001902212 -0.030694657 -0.034368611 0.031254407 -0.030694657 -35.34% -0.4457 -1.54844E-07
9 1936 31.94% 0.17% 5.02% $145.38 $116.84 $140.49 2.04841E-08 1938 991.8 0.08076225 0.08076225 10 0.08076225 0.033565385 0.023914594 0.08076225 -0.00275209 0.023914594 29.28% 0.2005 1.40964E-08
10 1937 -35.34% 0.30% 1.38% $94.00 $117.19 $142.43 -1.54844E-07 1939 1071.9 0.087694748 0.087694748 11 0.087694748 0.053135276 0.018073949 0.087694748 0.02538567 0.018073949 -1.10% -0.1033 -1.92782E-09
11 1938 29.28% 0.08% 4.21% $121.53 $117.29 $148.43 1.40964E-08 1940 1165.9 0.170769363 0.170769363 12 0.170769363 0.057926698 0.173364361 0.015760396 0.170769363 -0.019424617 0.173364361 0.015760396 -10.67% -0.199 -1.37824E-08
12 1939 -1.10% 0.04% 4.41% $120.20 $117.33 $154.98 -1.92782E-09 1941 1365 0.184468864 0.184468864 13 0.184468864 -0.005516203 0.184468864 0.045176358 -12.77% -0.22 -1.86223E-08
13 1940 -10.67% 0.03% 5.40% $107.37 $117.36 $163.35 -1.37824E-08 1942 1616.8 0.163718456 0.163718456 14 0.163718456 -0.002108193 0.163718456 0.071865468 19.17% 0.0994 1.71761E-09
14 1941 -12.77% 0.08% -2.02% $93.66 $117.46 $160.04 -1.86223E-08 1943 1881.5 0.080786606 0.080786606 15 0.080786606 0.053636625 0.080786606 0.041375637 25.06% 0.1583 6.93759E-09
15 1942 19.17% 0.34% 2.29% $111.61 $117.85 $163.72 1.71761E-09 1944 2033.5 -0.011212196 -0.011212196 16 -0.011212196 0.045981039 -0.011212196 0.034646521 19.03% 0.098 1.64605E-09
16 1943 25.06% 0.38% 2.49% $139.59 $118.30 $167.79 6.93759E-09 1945 2010.7 -0.109414632 -0.109414632 17 -0.109414632 0.055777856 -0.109414632 0.031989266 35.82% 0.2659 3.28792E-08
17 1944 19.03% 0.38% 2.58% $166.15 $118.75 $172.12 1.64605E-09 1946 1790.7 -0.008990897 -0.008990897 18 -0.008990897 0.031254407 -0.008990897 0.041111263 -8.43% -0.1766 -9.63247E-09
18 1945 35.82% 0.38% 3.80% $225.67 $119.20 $178.67 3.28792E-08 1947 1774.6 0.044009918 0.044009918 19 0.044009918 -0.00275209 0.044009918 0.03572837 5.20% -0.0403 -1.14467E-10
19 1946 -8.43% 0.38% 3.13% $206.65 $119.65 $184.26 -9.63247E-09 1948 1852.7 -0.005181627 -0.005181627 20 -0.005181627 0.02538567 -0.005181627 0.018770941 5.70% -0.0353 -7.6929E-11
20 1947 5.20% 0.57% 0.92% $217.39 $120.33 $185.95 -1.14467E-10 1949 1843.1 0.087407086 0.087407086 21 0.087407086 -0.019424617 0.087407086 -0.002342066 18.30% 0.0907 1.30493E-09
21 1948 5.70% 1.02% 1.95% $229.79 $121.56 $189.58 -7.6929E-11 1950 2004.2 0.077387486 0.077387486 22 0.077387486 0.045176358 0.077387486 0.0339273 30.81% 0.2158 1.7576E-08
22 1949 18.30% 1.10% 4.66% $271.85 $122.90 $198.42 1.30493E-09 1951 2159.3 0.038299449 0.038299449 23 0.038299449 0.071865468 0.038299449 0.02852657 23.68% 0.1445 5.27678E-09
23 1950 30.81% 1.17% 0.43% $355.60 $124.34 $199.27 1.7576E-08 1952 2242 0.04603033 0.04603033 24 0.04603033 0.041375637 0.04603033 0.04073413 18.15% 0.0892 1.24125E-09
24 1951 23.68% 1.48% -0.30% $439.80 $126.18 $198.68 5.27678E-09 1953 2345.2 -0.006310762 -0.006310762 25 -0.006310762 0.034646521 -0.006310762 0.025149214 -1.21% -0.1044 -1.99006E-09
25 1952 18.15% 1.67% 2.27% $519.62 $128.29 $203.19 1.24125E-09 1954 2330.4 0.072004806 0.072004806 26 0.072004806 0.031989266 0.072004806 0.037398195 52.56% 0.4333 1.42276E-07
26 1953 -1.21% 1.89% 4.14% $513.35 $130.72 $211.61 -1.99006E-09 1955 2498.2 0.019774237 0.019774237 27 0.019774237 0.041111263 0.019774237 0.044569161 32.60% 0.2337 2.23225E-08
27 1954 52.56% 0.96% 3.29% $783.18 $131.98 $218.57 1.42276E-07 1956 2547.6 0.020097347 0.020097347 28 0.020097347 0.03572837 0.020097347 0.043551123 7.44% -0.0179 -1.00306E-11
28 1955 32.60% 1.66% -1.34% $1,038.47 $134.17 $215.65 2.23225E-08 1957 2598.8 -0.009004156 -0.009004156 29 -0.009004156 0.018770941 -0.009004156 0.048273916 -10.46% -0.1969 -1.33507E-08
29 1956 7.44% 2.56% -2.26% $1,115.73 $137.60 $210.79 -1.00306E-11 1958 2575.4 0.071717015 0.071717015 30 0.071717015 -0.002342066 0.071717015 0.041380783 43.72% 0.3449 7.17539E-08
30 1957 -10.46% 3.23% 6.80% $999.05 $142.04 $225.11 -1.33507E-08 1959 2760.1 0.024781711 0.024781711 31 0.024781711 0.0339273 0.024781711 0.988694005 0.032956467 12.06% 0.0283 3.96392E-11
31 1958 43.72% 1.78% -2.10% $1,435.84 $144.57 $220.39 7.17539E-08 1960 2828.5 0.023298568 0.023298568 32 1.170101873 0.036565684 0.02852657 0.023298568 0.34% -0.0889 -1.22877E-09
32 1959 12.06% 3.26% -2.65% $1,608.95 $149.27 $214.56 3.96392E-11 1961 2894.4 0.060599779 0.060599779 33 0.04073413 0.060599779 26.64% 0.1741 9.22916E-09
33 1960 0.34% 3.05% 11.64% $1,614.37 $153.82 $239.53 -1.22877E-09 1962 3069.8 0.043716203 0.043716203 34 0.025149214 0.043716203 -8.81% -0.1804 -1.02678E-08
34 1961 26.64% 2.27% 2.06% $2,044.40 $157.30 $244.46 9.22916E-09 1963 3204 0.057865169 0.057865169 35 0.037398195 0.057865169 22.61% 0.1338 4.18923E-09
35 1962 -8.81% 2.78% 5.69% $1,864.26 $161.67 $258.38 -1.02678E-08 1964 3389.4 0.064200153 0.064200153 36 0.044569161 0.064200153 16.42% 0.0719 6.50058E-10
36 1963 22.61% 3.11% 1.68% $2,285.80 $166.70 $262.74 4.18923E-09 1965 3607 0.065178819 0.065178819 37 0.043551123 0.065178819 12.40% 0.0317 5.57113E-11
37 1964 16.42% 3.51% 3.73% $2,661.02 $172.54 $272.53 6.50058E-10 1966 3842.1 0.025272637 0.025272637 38 0.048273916 0.025272637 -9.97% -0.192 -1.23785E-08
38 1965 12.40% 3.90% 0.72% $2,990.97 $179.28 $274.49 5.57113E-11 1967 3939.2 0.048410845 0.048410845 39 0.041380783 0.048410845 23.80% 0.1457 5.40934E-09
39 1966 -9.97% 4.84% 2.91% $2,692.74 $187.95 $282.47 -1.23785E-08 1968 4129.9 0.031066128 0.031066128 40 0.010796691 0.031066128 10.81% 0.0158 6.89822E-12
40 1967 23.80% 4.33% -1.58% $3,333.69 $196.10 $278.01 5.40934E-09 1969 4258.2 0.001902212 0.001902212 41 1.39770264 0.035838529 0.001902212 -8.24% -0.1747 -9.32491E-09
41 1968 10.81% 5.26% 3.27% $3,694.23 $206.41 $287.11 6.89822E-12 1970 4266.3 0.033565385 0.033565385 42 1.591612386 0.038819814 3.56% -0.0567 -3.18797E-10
42 1969 -8.24% 6.56% -5.01% $3,389.77 $219.96 $272.71 -9.32491E-09 1971 4409.5 0.053135276 0.053135276 43 14.22% 0.0499 2.17304E-10
43 1970 3.56% 6.69% 16.75% $3,510.49 $234.66 $318.41 -3.18797E-10 1972 4643.8 0.057926698 0.057926698 44 18.76% 0.0953 1.51372E-09
44 1971 14.22% 4.54% 9.79% $4,009.72 $245.32 $349.57 2.17304E-10 1973 4912.8 -0.005516203 -0.005516203 45 -14.31% -0.2354 -2.28131E-08
45 1972 18.76% 3.95% 2.82% $4,761.76 $255.01 $359.42 1.51372E-09 1974 4885.7 -0.002108193 -0.002108193 46 -25.90% -0.3513 -7.58229E-08
46 1973 -14.31% 6.73% 3.66% $4,080.44 $272.16 $372.57 -2.28131E-08 1975 4875.4 0.053636625 0.053636625 47 37.00% 0.2777 3.74536E-08
47 1974 -25.90% 7.78% 1.99% $3,023.54 $293.33 $379.98 -7.58229E-08 1976 5136.9 0.045981039 0.045981039 48 23.83% 0.146 5.44282E-09
48 1975 37.00% 5.99% 3.61% $4,142.10 $310.90 $393.68 3.74536E-08 1977 5373.1 0.055777856 0.055777856 49 -6.98% -0.1621 -7.44929E-09
49 1976 23.83% 4.97% 15.98% $5,129.20 $326.35 $456.61 5.44282E-09 1978 5672.8 0.031254407 0.031254407 50 6.51% -0.0272 -3.51943E-11
50 1977 -6.98% 5.13% 1.29% $4,771.20 $343.09 $462.50 -7.44929E-09 1979 5850.1 -0.00275209 -0.00275209 51 18.52% 0.0929 1.40221E-09
51 1978 6.51% 6.93% -0.78% $5,081.77 $366.87 $458.90 -3.51943E-11 1980 5834 0.02538567 0.02538567 52 31.74% 0.2251 1.99477E-08
52 1979 18.52% 9.94% 0.67% $6,022.89 $403.33 $461.98 1.40221E-09 1981 5982.1 -0.019424617 -0.019424617 53 -4.70% -0.1393 -4.72736E-09
53 1980 31.74% 11.22% -2.99% $7,934.26 $448.58 $448.17 1.99477E-08 1982 5865.9 0.045176358 0.045176358 54 20.42% 0.1119 2.45051E-09
54 1981 -4.70% 14.30% 8.20% $7,561.16 $512.73 $484.91 -4.72736E-09 1983 6130.9 0.071865468 0.071865468 55 22.34% 0.1311 3.9407E-09
55 1982 20.42% 11.01% 32.81% $9,105.08 $569.18 $644.04 2.45051E-09 1984 6571.5 0.041375637 0.041375637 56 6.15% -0.0308 -5.10996E-11
56 1983 22.34% 8.45% 3.20% $11,138.90 $617.26 $664.65 3.9407E-09 1985 6843.4 0.034646521 0.034646521 57 31.24% 0.2201 1.86477E-08
57 1984 6.15% 9.61% 13.73% $11,823.51 $676.60 $755.92 -5.10996E-11 1986 7080.5 0.031989266 0.031989266 58 18.49% 0.0926 1.38867E-09
58 1985 31.24% 7.49% 25.71% $15,516.60 $727.26 $950.29 1.86477E-08 1987 7307 0.041111263 0.041111263 59 5.81% -0.0342 -6.99591E-11
59 1986 18.49% 6.04% 24.28% $18,386.33 $771.15 $1,181.06 1.38867E-09 1988 7607.4 0.03572837 0.03572837 60 16.54% 0.0731 6.83153E-10
60 1987 5.81% 5.72% -4.96% $19,455.08 $815.27 $1,122.47 -6.99591E-11 1989 7879.2 0.018770941 0.018770941 61 31.48% 0.2225 1.92644E-08
61 1988 16.54% 6.45% 8.22% $22,672.40 $867.86 $1,214.78 6.83153E-10 1990 8027.1 -0.002342066 -0.002342066 62 -3.06% -0.1229 -3.24654E-09
62 1989 31.48% 8.11% 17.69% $29,808.58 $938.24 $1,429.72 1.92644E-08 1991 8008.3 0.0339273 0.0339273 63 30.23% 0.21 1.61966E-08
63 1990 -3.06% 7.55% 6.24% $28,895.11 $1,009.08 $1,518.87 -3.24654E-09 1992 8280 0.02852657 0.02852657 64 7.49% -0.0174 -9.21326E-12
64 1991 30.23% 5.61% 15.00% $37,631.51 $1,065.69 $1,746.77 1.61966E-08 1993 8516.2 0.04073413 0.04073413 65 9.97% 0.0074 7.08697E-13
65 1992 7.49% 3.41% 9.36% $40,451.51 $1,101.98 $1,910.30 -9.21326E-12 1994 8863.1 0.025149214 0.025149214 66 1.33% -0.079 -8.62277E-10
66 1993 9.97% 2.98% 14.21% $44,483.33 $1,134.84 $2,181.77 7.08697E-13 1995 9086 0.037398195 0.037398195 67 37.20% 0.2797 3.82686E-08
67 1994 1.33% 3.99% -8.04% $45,073.14 $1,180.07 $2,006.43 -8.62277E-10 1996 9425.8 0.044569161 0.044569161 68 23.82% 0.1459 5.43165E-09
68 1995 37.20% 5.52% 23.48% $61,838.19 $1,245.15 $2,477.55 3.82686E-08 1997 9845.9 0.043551123 0.043551123 69 31.86% 0.2263 2.02684E-08
69 1996 23.82% 5.02% 1.43% $76,566.48 $1,307.68 $2,512.94 5.43165E-09 1998 10274.7 0.048273916 0.048273916 70 28.34% 0.1911 1.22053E-08
70 1997 31.86% 5.05% 9.94% $100,958.71 $1,373.76 $2,762.71 2.02684E-08 1999 10770.7 0.041380783 0.041380783 71 20.89% 0.1166 2.77244E-09
71 1998 28.34% 4.73% 14.92% $129,568.35 $1,438.70 $3,174.95 1.22053E-08 2000 11216.4 0.010796691 0.010796691 72 -9.03% -0.1826 -1.0648E-08
72 1999 20.89% 4.51% -8.25% $156,629.15 $1,503.58 $2,912.88 2.77244E-09 2001 11337.5 0.018134509 0.018134509 73 -11.85% -0.2108 -1.63824E-08
73 2000 -9.03% 5.76% 16.66% $142,482.69 $1,590.23 $3,398.03 -1.0648E-08 2002 11543.1 0.025409119 0.025409119 74 -21.97% -0.312 -5.31165E-08
74 2001 -11.85% 3.67% 5.57% $125,598.83 $1,648.63 $3,587.37 -1.63824E-08 2003 11836.4 0.034681153 0.034681153 75 28.36% 0.1913 1.22436E-08
75 2002 -21.97% 1.66% 15.12% $98,009.73 $1,675.96 $4,129.65 -5.31165E-08 2004 12246.9 0.030709812 0.030709812 76 10.74% 0.0151 6.02139E-12
76 2003 28.36% 1.03% 0.38% $125,801.18 $1,693.22 $4,145.15 1.22436E-08 2005 12623 0.026578468 0.026578468 77 4.83% -0.044 -1.48979E-10
77 2004 10.74% 1.23% 4.49% $139,315.72 $1,714.00 $4,331.30 6.02139E-12 2006 12958.5 0.019130301 0.019130301 78 15.61% 0.0638 4.5418E-10
78 2005 4.83% 3.01% 2.87% $146,050.90 $1,765.59 $4,455.50 -1.48979E-10 2007 13206.4 -0.003369578 -0.003369578 79 5.48% -0.0375 -9.22273E-11
79 2006 15.61% 4.68% 1.96% $168,853.19 $1,848.18 $4,542.87 4.5418E-10 2008 13161.9 -0.030694657 -0.030694657 80 -36.55% -0.4578 -1.678E-07
80 2007 5.48% 4.64% 10.21% $178,114.34 $1,933.98 $5,006.69 -9.22273E-11 2009 12757.9 0.023914594 0.023914594 81 25.94% 0.1671 8.16009E-09
81 2008 -36.55% 1.59% 20.10% $113,009.37 $1,964.64 $6,013.10 -1.678E-07 2010 13063 0.018073949 0.018073949 82 14.82% 0.0559 3.05493E-10
82 2009 25.94% 0.14% -11.12% $142,318.62 $1,967.29 $5,344.65 8.16009E-09 2011 13299.1 2.753670752 0.033581351 2.07% -0.0716 -6.41955E-10
83 2010 14.82% 0.13% 8.46% $163,411.79 $1,969.84 $5,796.96 3.05493E-10 -9.47347E-08
84 2011 2.07% 0.03% 16.04% $166,787.51 $1,970.44 $6,726.52 -6.41955E-10
Risk Premium -9.47347E-08
Arithmetic Average Stocks - T.Bills Stocks - T.Bonds
1928-2011 11.20% 3.66% 5.41% 7.55% 5.79%
1962-2011 10.60% 5.22% 7.24% 5.38% 3.36%
2002-2011 4.93% 1.81% 6.85% 3.12% -1.92%
Risk Premium
Geometric Average Stocks - T.Bills Stocks - T.Bonds
1928-2011 9.23% 3.61% 5.14% 5.62% 4.10%
1962-2011 9.20% 5.19% 6.85% 4.02% 2.35%
2002-2011 2.88% 1.80% 6.49% 1.08% -3.61%

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