Here are some tables for planning during the accumulation stage.
The first set of tables has historical growth multipliers with dollar cost averaging. Multiply the entries by $1000 to find out how much investing $1000 per year for 5, 10, 15, 20, 25 and 30 years into an all-stock portfolio would have returned.
The second set of tables has historical growth multipliers for an account that switches allocations between stocks and TIPS at 2% interest depending upon P/E10. The P/E10 thresholds are 9-12-21-24 and the corresponding stock allocations are 100%-50%-30%-20%-0%. (As examples: if P/E10 equals 14, the stock allocation is 30%. If P/E10 equals 22, the stock allocation is 20%.) Multiply the initial balance by these growth multipliers to determine the balances after 5, 10, 15, 20, 25 and 30 years.
All balances are in real dollars. That is, they are adjusted to compensate for inflation. The very long-term historical return of the stock market is around 6.5% to 7.0% above inflation. A growth multiplier of 2 at ten years corresponds to an annualized real return of 7%+, which is just a little bit higher than the long-term return of stocks overall. At 20 years, a growth multiplier of 4 corresponds to the same annualized real return of 7%+.
[Reference approximation: the rule of 72. The interest rate in percent times the number of years for an investment to double equals 72.]
Switching stock allocations reduces the maximum stock market returns. Switching increases the minimum returns.
In general, one has done best by dollar cost averaging into a 100% stock portfolio over a long time period, typically 25 years or longer. Once an investor has built up some capital, it makes sense for him to protect some of his money. He should take part of his money out of his 100% stock portfolio. He should put it into an account that varies allocations between stocks and TIPS in a gradual manner according to valuations.
Doing this becomes more and more important as the investor approaches his retirement. He can no longer tolerate losses that delay his retirement by a decade or more, which is typical of what can happen with stocks.
With these growth multiplier tables, you can construct historical sequences for such a transition. You would start out with an initial allocation. Normally, this would be zero dollars as you begin by dollar cost averaging into a 100% stock portfolio. At some point later on, you remove money from the account. First, you determine the balance at that time by using the dollar cost averaging growth multipliers. Then you split your money into two [actually, three] separate accounts, one with dollar cost averaging and the other [two] with an initial balance. This is where it gets to be a little tricky.
The money that you remove from the account must be put into a sequence that begins at the right time. For example, if you remove some money from the 1942 sequence after ten years, you need to place the balance at the start of the 1952 historical sequence. Then you look up the 1952 growth multipliers that apply to switching stock allocations.
You need to break off the money that you leave in the dollar cost averaging account and treat it separately. For example, if you withdraw $5000 from the 1942 historical sequence in 1952, you look up the dollar cost averaging growth multiplier after ten years. It is 18.84. Your annual $1000 investment would have grown to $18840. After withdrawing $5000, the remaining balance is $13840. You use a table of growth multipliers for 100% stocks for the $13840 that you leave untouched, beginning from 1952. You now treat the dollar cost averaging account as brand new, but beginning in 1952.
[It is simpler if you remove all of your money from the dollar cost averaging account. Then you do not have to include a 100% stock portfolio without deposits and/or withdrawals.]
This process is difficult to do manually, but it is easy to do with an Excel spreadsheet. You end up with a complete set of Historical Surviving Withdrawal Rates.
Additional material:
Some Accumulation Multipliers and Examples dated Tue Nov 09, 2004.
http://nofeeboards.com/boards/viewtopic.php?t=3067
Annualized Real Total Returns 100% stocks dated Tue Mar 16, 2004.
[These tables have annualized real returns. Let r be the annualized real return expressed as a fraction. Let the number of years equal N. Then to calculate growth multipliers, use this equation: (the growth multiplier at N years) = (1 + r)^N.]
http://nofeeboards.com/boards/viewtopic.php?t=2226
Have fun.
John R.
Additional tables for the accumulation stage
Moderator: hocus2004
The Dollar Cost Averaging Account
The same amount of money is invested annually into a 100% stock portfolio (with all dividends reinvested and with no expenses). Later balances equal the annual investment times the applicable growth multipliers. All amounts are in terms of real dollars.
Year, Growth Multipliers at Year 5, Year 10 and Year 15.
The same amount of money is invested annually into a 100% stock portfolio (with all dividends reinvested and with no expenses). Later balances equal the annual investment times the applicable growth multipliers. All amounts are in terms of real dollars.
Year, Growth Multipliers at Year 20, Year 15 and Year 30.
Remember that all amounts are in real dollars.
Have fun.
John R.
The same amount of money is invested annually into a 100% stock portfolio (with all dividends reinvested and with no expenses). Later balances equal the annual investment times the applicable growth multipliers. All amounts are in terms of real dollars.
Year, Growth Multipliers at Year 5, Year 10 and Year 15.
Code: Select all
1871 7.76 24.87 39.58
1872 6.19 20.86 39.68
1873 7.04 21.28 36.68
1874 8.63 20.65 37.28
1875 9.59 18.43 37.61
1876 10.82 20.87 29.87
1877 10.70 24.91 40.63
1878 9.34 19.95 33.95
1879 6.58 14.76 22.27
1880 6.85 18.02 26.82
1881 7.32 13.49 22.64
1882 8.38 17.53 25.02
1883 7.81 17.02 28.84
1884 8.08 15.63 35.08
1885 7.97 14.92 27.48
1886 6.40 13.73 30.05
1887 7.28 13.29 31.36
1888 7.43 16.09 31.92
1889 6.66 19.11 26.46
1890 6.44 15.02 29.58
1891 6.99 19.04 36.50
1892 6.18 17.98 28.77
1893 8.32 20.31 26.51
1894 9.27 15.59 30.57
1895 7.33 17.55 28.31
1896 8.64 20.25 28.48
1897 8.68 17.10 26.28
1898 7.73 12.66 24.55
1899 5.51 13.71 18.85
1900 7.82 16.03 20.09
1901 8.13 14.71 22.70
1902 6.87 13.64 19.64
1903 5.95 14.80 15.48
1904 7.39 12.73 14.35
1905 7.12 11.43 14.43
1906 6.69 13.30 12.25
1907 7.24 13.41 16.05
1908 6.92 9.19 19.65
1909 5.55 8.32 18.07
1910 5.90 10.02 25.96
1911 7.02 8.67 28.88
1912 6.25 10.02 29.57
1913 4.75 13.52 41.00
1914 5.07 13.92 58.46
1915 5.35 16.84 50.20
1916 4.48 17.80 37.08
1917 5.44 18.56 23.05
1918 7.36 25.10 23.43
1919 7.12 33.65 32.59
1920 9.38 31.75 31.04
Code: Select all
1921 11.22 26.59 46.53
1922 9.90 14.30 47.52
1923 11.00 12.47 28.52
1924 14.17 17.39 30.85
1925 10.23 13.42 27.67
1926 7.64 18.98 23.97
1927 4.70 21.98 18.44
1928 4.52 14.11 19.12
1929 6.56 15.31 21.57
1930 6.56 16.89 26.51
1931 10.32 15.67 35.98
1932 13.04 13.05 26.56
1933 7.42 12.21 20.86
1934 7.16 12.98 20.45
1935 7.15 14.71 23.79
1936 5.65 17.82 26.84
1937 4.77 13.11 29.89
1938 5.90 12.79 34.03
1939 6.82 13.29 32.48
1940 7.64 15.14 43.97
1941 9.23 16.66 48.81
1942 6.92 18.84 48.90
1943 6.16 20.04 41.88
1944 6.21 18.56 51.59
1945 6.97 24.62 49.72
1946 7.08 24.90 41.20
1947 8.58 26.08 48.90
1948 9.52 23.18 45.71
1949 8.75 28.41 48.91
1950 10.09 23.87 44.52
1951 11.00 21.92 43.17
1952 10.03 23.27 35.66
1953 7.97 19.57 35.12
1954 9.75 20.97 33.81
1955 8.40 20.15 25.22
1956 7.61 19.21 22.89
1957 8.28 16.09 23.55
1958 7.57 17.10 25.63
1959 7.79 16.08 18.21
1960 8.18 13.04 12.68
1961 8.27 12.69 16.14
1962 6.80 13.07 16.39
1963 7.22 14.20 13.99
1964 7.01 10.53 14.67
1965 5.75 7.54 14.83
1966 5.72 9.79 16.35
1967 6.34 10.51 14.33
1968 6.85 9.06 17.51
1969 5.21 9.66 19.71
1970 4.09 10.28 20.64
1971 5.59 11.75 24.89
1972 5.93 10.21 30.96
1973 5.03 12.07 27.05
1974 5.65 13.81 29.41
1975 6.30 14.92 34.84
1976 6.62 16.89 30.63
1977 5.63 20.32 36.43
1978 6.89 18.05 35.38
1979 7.21 18.09 34.19
1980 7.13 19.72 31.55
1981 8.08 17.37 38.63
1982 10.04 21.43 45.68
1983 8.09 19.45 50.05
1984 8.12 19.02 57.65
1985 8.51 17.00 57.91
1986 7.19 20.21 47.92
1987 8.04 21.72 35.62
1988 7.87 25.05
1989 7.69 28.57
1990 6.87 28.26
1991 8.65 24.15
1992 9.19 17.83
1993 10.43
1994 11.68
1995 11.37
1996 8.42
1997 6.26
Year, Growth Multipliers at Year 20, Year 15 and Year 30.
Code: Select all
1871 51.98 73.50 131.45
1872 59.05 70.89 138.38
1873 56.62 80.39 133.35
1874 50.97 95.89 111.14
1875 49.76 77.31 128.10
1876 44.49 82.23 133.28
1877 51.58 104.02 140.86
1878 51.18 87.69 96.32
1879 44.49 53.27 88.14
1880 44.60 76.63 104.71
1881 44.69 75.04 88.70
1882 53.57 75.05 96.14
1883 52.25 59.35 95.30
1884 44.38 75.97 86.46
1885 49.54 69.73 71.61
1886 53.01 64.68 80.72
1887 46.13 61.03 70.48
1888 38.07 63.11 52.09
1889 47.59 55.91 49.04
1890 43.73 46.41 44.30
1891 46.73 60.31 41.25
1892 40.03 47.91 42.13
1893 46.32 39.80 63.73
1894 37.75 34.55 57.04
1895 31.68 31.72 64.17
1896 38.96 28.14 76.10
1897 33.46 31.24 77.44
1898 22.62 38.55 100.84
1899 18.70 32.80 121.87
1900 21.96 46.99 126.67
1901 18.04 51.26 97.71
1902 20.24 52.34 59.85
1903 28.99 78.53 67.41
1904 27.30 104.29 91.41
1905 33.31 91.99 79.54
1906 37.11 72.17 109.51
1907 43.77 50.98 145.47
1908 55.52 48.50 94.90
1909 71.78 64.24 97.48
1910 74.01 65.43 114.65
1911 57.68 89.48 94.89
1912 35.31 102.84 70.48
1913 36.79 73.39 78.82
1914 53.78 82.98 91.51
1915 45.69 81.30 99.94
1916 59.44 64.07 116.41
1917 69.28 48.34 79.45
1918 48.02 52.58 73.06
1919 51.79 58.47 74.03
1920 57.21 72.52 94.75
Code: Select all
1921 52.18 98.18 117.80
1922 34.96 59.78 109.58
1923 33.48 48.68 107.70
1924 37.65 49.98 103.50
1925 38.20 52.45 131.91
1926 49.34 62.42 162.02
1927 34.32 66.19 154.15
1928 30.09 69.68 130.78
1929 30.83 66.41 166.34
1930 38.77 100.52 183.58
1931 48.09 127.72 190.84
1932 53.70 127.31 215.87
1933 50.39 96.12 171.04
1934 46.09 117.46 181.53
1935 64.41 119.60 198.59
1936 74.47 113.37 196.87
1937 73.82 127.57 170.60
1938 67.12 121.40 188.06
1939 85.13 133.50 184.33
1940 83.75 141.04 147.63
1941 75.94 133.47 130.12
1942 86.38 116.94 138.30
1943 77.75 122.30 147.18
1944 83.24 116.93 103.59
1945 86.37 92.21 68.36
1946 74.80 74.61 70.64
1947 68.32 82.77 75.71
1948 74.32 91.80 64.71
1949 71.27 65.11 63.56
1950 49.57 38.17 53.32
1951 45.38 45.12 55.06
1952 46.02 44.69 45.23
1953 46.48 35.11 51.17
1954 33.31 35.10 55.60
1955 21.29 32.33 52.19
1956 25.12 33.20 57.77
1957 25.26 27.60 70.44
1958 21.47 33.63 65.04
1959 21.52 36.56 68.73
1960 21.34 36.53 76.31
1961 23.47 43.02 69.76
1962 19.73 52.75 84.71
1963 24.00 48.27 85.06
1964 27.01 52.49 89.18
1965 27.29 58.69 84.08
1966 31.92 53.09 105.17
1967 40.31 66.17 125.69
1968 36.81 66.22 150.78
1969 39.77 68.80 184.57
1970 45.82 66.73 202.73
1971 42.64 85.81 182.37
1972 52.35 100.97 148.36
1973 50.03 115.53
1974 52.16 141.62
1975 51.99 159.68
1976 63.42 136.34
1977 72.29 107.42
1978 83.97
1979 95.58
1980 99.74
1981 85.30
1982 69.72
Have fun.
John R.
The Single Deposit Account
An initial balance is placed into an account with varying stock allocations. Later balances equal the initial balance times the applicable growth multipliers. All amounts are in terms of real dollars.
TIPS at 2% interest .
P/E10 thresholds of 9-12-21-24.
Allocations of 100-50-30-20-0% stocks.
No expenses.
Year, Growth Multipliers at Year 5, Year 10 and Year 15.
An initial balance is placed into an account with varying stock allocations. Later balances equal the initial balance times the applicable growth multipliers. All amounts are in terms of real dollars.
TIPS at 2% interest .
P/E10 thresholds of 9-12-21-24.
Allocations of 100-50-30-20-0% stocks.
No expenses.
Year, Growth Multipliers at Year 20, Year 15 and Year 30.
Remember that all amounts are in real dollars.
Have fun.
John R.
An initial balance is placed into an account with varying stock allocations. Later balances equal the initial balance times the applicable growth multipliers. All amounts are in terms of real dollars.
TIPS at 2% interest .
P/E10 thresholds of 9-12-21-24.
Allocations of 100-50-30-20-0% stocks.
No expenses.
Year, Growth Multipliers at Year 5, Year 10 and Year 15.
Code: Select all
1871 1.23 1.88 2.21
1872 1.14 1.77 2.20
1873 1.19 1.76 2.11
1874 1.35 1.76 2.15
1875 1.43 1.69 2.14
1876 1.52 1.79 2.03
1877 1.55 1.93 2.27
1878 1.47 1.77 2.10
1879 1.31 1.59 1.83
1880 1.18 1.50 1.69
1881 1.18 1.33 1.56
1882 1.24 1.46 1.62
1883 1.20 1.43 1.67
1884 1.22 1.40 1.78
1885 1.27 1.43 1.75
1886 1.13 1.32 1.71
1887 1.18 1.30 1.73
1888 1.19 1.38 1.75
1889 1.15 1.46 1.65
1890 1.13 1.38 1.72
1891 1.17 1.51 1.87
1892 1.11 1.47 1.72
1893 1.16 1.47 1.62
1894 1.27 1.44 1.90
1895 1.22 1.52 1.89
1896 1.29 1.60 1.89
1897 1.33 1.55 1.88
1898 1.27 1.39 1.80
1899 1.13 1.50 1.64
1900 1.25 1.55 1.61
1901 1.24 1.47 1.70
1902 1.17 1.42 1.60
1903 1.10 1.42 1.37
1904 1.32 1.44 1.38
1905 1.24 1.29 1.27
1906 1.18 1.37 1.05
1907 1.21 1.37 1.29
1908 1.29 1.24 1.73
1909 1.09 1.04 1.51
1910 1.04 1.03 1.84
1911 1.16 0.89 1.99
1912 1.13 1.06 2.09
1913 0.96 1.35 2.32
1914 0.95 1.38 2.69
1915 0.99 1.76 2.80
1916 0.77 1.72 2.43
1917 0.94 1.85 2.22
1918 1.40 2.41 2.63
1919 1.45 2.82 3.99
1920 1.79 2.84 3.87
Code: Select all
1921 2.24 3.15 5.48
1922 1.97 2.36 4.93
1923 1.72 1.88 3.67
1924 1.95 2.75 3.82
1925 1.59 2.16 3.14
1926 1.41 2.45 2.78
1927 1.20 2.51 2.49
1928 1.09 2.13 2.35
1929 1.41 1.96 2.25
1930 1.36 1.98 2.40
1931 1.74 1.97 2.87
1932 2.08 2.07 2.94
1933 1.95 2.15 2.81
1934 1.39 1.59 1.98
1935 1.45 1.76 2.23
1936 1.14 1.65 1.99
1937 0.99 1.41 1.96
1938 1.10 1.44 2.15
1939 1.15 1.43 2.06
1940 1.22 1.54 2.31
1941 1.46 1.75 2.57
1942 1.42 1.97 2.73
1943 1.31 1.95 2.54
1944 1.25 1.80 2.59
1945 1.26 1.90 2.45
1946 1.20 1.76 2.13
1947 1.39 1.92 2.42
1948 1.49 1.94 2.50
1949 1.45 2.08 2.54
1950 1.51 1.94 2.40
1951 1.47 1.77 2.21
1952 1.39 1.75 2.08
1953 1.30 1.67 2.07
1954 1.43 1.75 2.08
1955 1.29 1.59 1.79
1956 1.21 1.50 1.67
1957 1.26 1.50 1.70
1958 1.28 1.59 1.81
1959 1.22 1.45 1.52
1960 1.24 1.39 1.37
1961 1.24 1.38 1.72
1962 1.19 1.35 1.67
1963 1.24 1.41 1.56
1964 1.19 1.25 1.51
1965 1.12 1.11 1.48
1966 1.11 1.38 1.59
1967 1.13 1.40 1.47
1968 1.14 1.26 1.73
1969 1.05 1.27 1.93
1970 0.99 1.31 2.01
1971 1.24 1.44 2.19
1972 1.24 1.30 2.42
1973 1.11 1.52 2.29
1974 1.21 1.84 2.54
1975 1.33 2.04 2.91
1976 1.15 1.76 2.25
1977 1.05 1.96 2.38
1978 1.37 2.07 2.59
1979 1.52 2.09 2.60
1980 1.53 2.18 2.58
1981 1.53 1.95 2.56
1982 1.86 2.27 2.77
1983 1.51 1.89 2.29
1984 1.38 1.71 2.04
1985 1.43 1.68 2.02
1986 1.28 1.67 1.85
1987 1.22 1.48 1.64
1988 1.25 1.52
1989 1.24 1.47
1990 1.18 1.41
1991 1.31 1.45
1992 1.22 1.35
1993 1.21
1994 1.19
1995 1.20
1996 1.10
1997 1.10
TIPS at 2% interest .
P/E10 thresholds of 9-12-21-24.
Allocations of 100-50-30-20-0% stocks.
No expenses.
Year, Growth Multipliers at Year 20, Year 15 and Year 30.
Code: Select all
1871 2.50 2.93 3.77
1872 2.59 2.87 3.80
1873 2.51 2.93 3.70
1874 2.46 3.13 3.54
1875 2.43 2.96 3.69
1876 2.37 3.06 3.79
1877 2.51 3.33 3.90
1878 2.45 3.10 3.42
1879 2.32 2.63 3.48
1880 2.07 2.58 3.20
1881 2.01 2.49 2.95
1882 2.15 2.52 3.04
1883 2.11 2.33 2.99
1884 2.01 2.66 2.91
1885 2.18 2.70 2.82
1886 2.11 2.50 2.89
1887 2.03 2.45 2.77
1888 1.93 2.49 2.39
1889 2.18 2.38 2.27
1890 2.13 2.22 2.19
1891 2.21 2.56 1.97
1892 2.08 2.35 2.21
1893 2.09 2.01 2.82
1894 2.08 1.98 2.88
1895 1.97 1.94 3.47
1896 2.19 1.68 3.76
1897 2.13 2.00 3.93
1898 1.73 2.42 4.16
1899 1.56 2.26 4.40
1900 1.59 2.85 4.52
1901 1.31 2.92 4.12
1902 1.51 2.96 3.56
1903 1.91 3.29 3.60
1904 2.00 3.89 5.49
1905 2.28 3.62 4.93
1906 2.36 3.32 5.78
1907 2.53 3.04 6.34
1908 2.98 3.26 6.37
1909 2.94 4.16 5.78
1910 2.92 3.98 5.77
1911 2.81 4.89 5.55
1912 2.51 5.24 5.20
1913 2.53 4.95 5.45
1914 3.80 5.28 6.05
1915 3.82 5.53 6.73
1916 4.22 4.79 6.98
1917 4.63 4.60 6.54
1918 5.14 5.66 7.40
1919 5.54 6.35 7.90
1920 5.62 6.83 8.63
Code: Select all
1921 6.22 9.06 10.89
1922 4.89 6.95 9.64
1923 4.04 5.29 7.91
1924 4.38 5.45 7.89
1925 3.81 4.82 7.25
1926 4.05 4.87 7.15
1927 3.53 4.90 6.80
1928 3.07 4.59 5.98
1929 2.80 4.05 5.82
1930 3.04 4.57 5.89
1931 3.46 5.07 6.13
1932 4.08 5.66 7.12
1933 4.20 5.47 7.02
1934 2.87 4.11 5.03
1935 3.35 4.32 5.34
1936 2.92 3.52 4.39
1937 2.71 3.42 4.06
1938 2.80 3.60 4.45
1939 2.96 3.62 4.30
1940 2.98 3.68 4.14
1941 3.10 3.86 4.28
1942 3.44 4.09 4.63
1943 3.27 4.04 4.60
1944 3.16 3.75 3.94
1945 3.03 3.41 3.36
1946 2.65 2.94 3.66
1947 2.88 3.26 4.04
1948 3.09 3.51 3.89
1949 3.01 3.16 3.84
1950 2.70 2.66 3.54
1951 2.44 3.04 3.51
1952 2.35 2.91 3.05
1953 2.35 2.60 3.57
1954 2.18 2.65 4.02
1955 1.77 2.35 3.60
1956 2.07 2.39 3.65
1957 2.10 2.20 4.11
1958 2.00 2.74 4.14
1959 1.85 2.80 3.87
1960 1.83 2.79 3.98
1961 1.98 3.02 3.86
1962 1.75 3.26 3.97
1963 2.14 3.23 4.04
1964 2.29 3.17 3.93
1965 2.26 3.22 3.81
1966 2.43 3.11 4.07
1967 2.74 3.34 4.07
1968 2.61 3.27 3.96
1969 2.67 3.31 3.93
1970 2.87 3.38 4.05
1971 2.80 3.68 4.06
1972 2.95 3.59 3.97
1973 2.87 3.48
1974 3.15 3.75
1975 3.43 4.11
1976 2.95 3.26
1977 2.90 3.20
1978 3.14
1979 3.09
1980 3.08
1981 2.82
1982 3.05
Have fun.
John R.