Additional tables for the accumulation stage

Research on Safe Withdrawal Rates

Moderator: hocus2004

JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Additional tables for the accumulation stage

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.

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.
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
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.

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       ``````
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.

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       ``````
Remember that all amounts are in real dollars.

Have fun.

John R.
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida
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.

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       ``````
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.

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       ``````
Remember that all amounts are in real dollars.

Have fun.

John R.