CTVR50 versus Earnings Yield

Research on Safe Withdrawal Rates

Moderator: hocus2004

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

CTVR50 versus Earnings Yield

Post by JWR1945 »

This discussion is almost identical to that in CTVR80 versus Earnings Yield. The equation and tables differ.

CTVR50 refers to a portfolio consisting of 50% stocks and 50% commercial paper. It is rebalanced annually. Its expenses are 0.20%. The initial balance was set to $100000. Withdrawals were adjusted to match inflation in accordance with the CPI. I have determined the maximum withdrawal rates (in increments of 0.1%) that would have ended with a final balance of $100000 (in real dollars) or higher after 30 years.

This is similar to the conventional Safe Withdrawal Rate strategy that is investigated most frequently. The difference is that I have required the portfolio's final balance to equal (or exceed) its original value instead of falling to zero. I refer to these withdrawal rates as Constant Terminal Value Rates (CTVR). These are similar to Historical Surviving Withdrawal Rates and Half Failure Withdrawal Rates. The constraint is different.

I have made a (straight line) linear curve fit to the 1923-1972 Constant Terminal Value Rates versus the Percentage Earnings Yield 100E10/P. The equation that it produces is y = 0.3279x+1.4254%, where y is the Constant Terminal Value Rate and x is the Percentage Earnings Yield. R squared was 0.7411%, which is high

It was necessary for me to limit the upper end of the data [for making curve fits] to 1972 because the dummy data in the calculator from 2003-2010 reduces the Constant Terminal Value Rates of later sequences sharply. The dummy data assumes that stock prices and dividends both decrease 20% per year starting in 2003.

I have calculated the confidence limits. They are plus and minus 0.72%. [This is 1.64 times the standard deviation of 0.439% using 48 degrees of freedom.]

I have collected 30-year Constant Terminal Value Rate data for sequences extending through 1980, using dummy data (for 2003-2010) when needed. I have extended the calculations through 2003.

Here are tables.

1923-1980 with 50% stocks: Year, P/E10, 100E10/P, CTVR50, Calculated Withdrawal Rate for a Constant Terminal Value

Code: Select all


1923    8.2    12.2    5.5   5.42
1924    8.1    12.3    5.6   5.47
1925    9.7    10.3    5.5   4.81
1926   11.3     8.8    5.0   4.33
1927   13.2     7.6    4.7   3.91
1928   18.8     5.3    3.7   3.17
1929   27.1     3.7    2.9   2.64
1930   22.3     4.5    3.0   2.90
1931   16.7     6.0    3.1   3.39
1932    9.3    10.8    3.8   4.95
1933    8.7    11.5    4.1   5.19
1934   13.0     7.7    3.3   3.95
1935   11.5     8.7    3.8   4.28
1936   17.1     5.8    3.0   3.34
1937   21.6     4.6    2.4   2.94
1938   13.5     7.4    3.2   3.85
1939   15.6     6.4    3.0   3.53
1940   16.4     6.1    3.0   3.42
1941   13.9     7.2    3.7   3.78
1942   10.1     9.9    4.6   4.67
1943   10.2     9.8    4.6   4.64
1944   11.1     9.0    4.1   4.38
1945   12.0     8.3    3.5   4.16
1946   15.6     6.4    3.6   3.53
1947   11.5     8.7    5.0   4.28
1948   10.4     9.6    5.2   4.58
1949   10.2     9.8    5.1   4.64
1950   10.7     9.3    5.0   4.49
1951   11.9     8.4    4.7   4.18
1952   12.5     8.0    4.2   4.05
1953   13.0     7.7    4.2   3.95
1954   12.0     8.3    4.5   4.16
1955   16.0     6.3    3.5   3.47
1956   18.3     5.5    3.2   3.22
1957   16.7     6.0    3.5   3.39
1958   13.8     7.2    3.8   3.80
1959   18.0     5.6    3.1   3.25
1960   18.3     5.5    3.2   3.22
1961   18.5     5.4    3.1   3.20
1962   21.2     4.7    2.9   2.97
1963   19.3     5.2    3.1   3.12
1964   21.6     4.6    2.8   2.94
1965   23.3     4.3    2.6   2.83
1966   24.1     4.1    2.7   2.79
1967   20.4     4.9    3.1   3.03
1968   21.5     4.7    3.1   2.95
1969   21.2     4.7    3.2   2.97
1970   17.1     5.8    3.7   3.34
1971   16.5     6.1    3.6   3.41
1972   17.3     5.8    3.4   3.32
1973   18.7     5.3    3.2   3.18
1974   13.5     7.4    3.8   3.85
1975    8.9    11.2    4.6   5.11
1976   11.2     8.9    3.6   4.35
1977   11.4     8.8    3.3   4.30
1978    9.2    10.9    3.6   4.99
1979    9.3    10.8    3.2   4.95
1980    8.9    11.2    2.7   5.11
1981-2003 with 50% stocks: Year, P/E10, 100E10/P, Calculated Withdrawal Rate for a Constant Terminal Value

Code: Select all


1981     9.3    10.71    4.94
1982     7.4    13.48    5.85
1983     8.7    11.51    5.20
1984     9.8    10.25    4.79
1985     9.9    10.07    4.73
1986    11.7     8.57    4.24
1987    14.7     6.78    3.65
1988    13.7     7.28    3.81
1989    15.2     6.60    3.59
1990    17.0     5.88    3.35
1991    15.6     6.42    3.53
1992    19.6     5.11    3.10
1993    20.4     4.90    3.03
1994    21.5     4.65    2.95
1995    20.5     4.89    3.03
1996    25.4     3.93    2.71
1997    29.2     3.43    2.55
1998    33.8     2.96    2.40
1999    40.9     2.44    2.23
2000    44.7     2.24    2.16
2001    37.0     2.70    2.31
2002    30.3     3.30    2.51
2003    22.9     4.37    2.86
1923-1980 with 50% stocks:Year, CTVR50, Safe Withdrawal Rate for a Constant Terminal Value, Calculated Withdrawal Rate for a Constant Terminal Value, High Risk Rate for a Constant Terminal Value

Code: Select all


1923   5.5   4.70    5.42    6.14
1924   5.6   4.75    5.47    6.19
1925   5.5   4.09    4.81    5.53
1926   5.0   3.61    4.33    5.05
1927   4.7   3.19    3.91    4.63
1928   3.7   2.45    3.17    3.89
1929   2.9   1.91    2.64    3.36
1930   3.0   2.18    2.90    3.62
1931   3.1   2.67    3.39    4.11
1932   3.8   4.23    4.95    5.67
1933   4.1   4.47    5.19    5.91
1934   3.3   3.23    3.95    4.67
1935   3.8   3.56    4.28    5.00
1936   3.0   2.62    3.34    4.06
1937   2.4   2.22    2.94    3.66
1938   3.2   3.13    3.85    4.57
1939   3.0   2.81    3.53    4.25
1940   3.0   2.70    3.42    4.15
1941   3.7   3.06    3.78    4.50
1942   4.6   3.95    4.67    5.39
1943   4.6   3.92    4.64    5.36
1944   4.1   3.66    4.38    5.10
1945   3.5   3.44    4.16    4.88
1946   3.6   2.81    3.53    4.25
1947   5.0   3.56    4.28    5.00
1948   5.2   3.86    4.58    5.30
1949   5.1   3.92    4.64    5.36
1950   5.0   3.77    4.49    5.21
1951   4.7   3.46    4.18    4.90
1952   4.2   3.33    4.05    4.77
1953   4.2   3.23    3.95    4.67
1954   4.5   3.44    4.16    4.88
1955   3.5   2.75    3.47    4.20
1956   3.2   2.50    3.22    3.94
1957   3.5   2.67    3.39    4.11
1958   3.8   3.08    3.80    4.52
1959   3.1   2.53    3.25    3.97
1960   3.2   2.50    3.22    3.94
1961   3.1   2.48    3.20    3.92
1962   2.9   2.25    2.97    3.69
1963   3.1   2.40    3.12    3.84
1964   2.8   2.22    2.94    3.66
1965   2.6   2.11    2.83    3.55
1966   2.7   2.07    2.79    3.51
1967   3.1   2.31    3.03    3.75
1968   3.1   2.23    2.95    3.67
1969   3.2   2.25    2.97    3.69
1970   3.7   2.62    3.34    4.06
1971   3.6   2.69    3.41    4.13
1972   3.4   2.60    3.32    4.04
1973   3.2   2.46    3.18    3.90
1974   3.8   3.13    3.85    4.57
1975   4.6   4.39    5.11    5.83
1976   3.6   3.63    4.35    5.07
1977   3.3   3.58    4.30    5.02
1978   3.6   4.27    4.99    5.71
1979   3.2   4.23    4.95    5.67
1980   2.7   4.39    5.11    5.83
1981-2003 with 50% stocks:Year, Safe Withdrawal Rate for a Constant Terminal Value, Calculated Withdrawal Rate for a Constant Terminal Value, High Risk Rate for a Constant Terminal Value

Code: Select all


1981    4.22    4.94    5.66
1982    5.13    5.85    6.57
1983    4.48    5.20    5.92
1984    4.07    4.79    5.51
1985    4.01    4.73    5.45
1986    3.51    4.24    4.96
1987    2.93    3.65    4.37
1988    3.09    3.81    4.53
1989    2.87    3.59    4.31
1990    2.63    3.35    4.07
1991    2.81    3.53    4.25
1992    2.38    3.10    3.82
1993    2.31    3.03    3.75
1994    2.23    2.95    3.67
1995    2.31    3.03    3.75
1996    1.99    2.71    3.43
1997    1.83    2.55    3.27
1998    1.68    2.40    3.12
1999    1.51    2.23    2.95
2000    1.44    2.16    2.88
2001    1.59    2.31    3.03
2002    1.79    2.51    3.23
2003    2.14    2.86    3.58
The current value of P/E10 is close to 28. This is similar, but slightly less than, the P/E10 value in 1997. In 1997, the Safe, Calculated and High Risk Rates for a Constant Terminal Value were 1.83%, 2.55% and 3.27% respectively. A person who retires today with a balanced (50% stock) portfolio and who withdraws 2.6% of his initial balance (plus inflation) has about a 50-50 chance of maintaining the full buying power of his portfolio at year 30. If he withdraws 3.3%, he is almost certain to have lost buying power at year 30. If he limits his withdrawals to 1.8%, he is almost certain to have increased his buying power at year 30.

Have fun.

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

Post by JWR1945 »

Users of the conventional methodology would select the smallest of the CTVR50 numbers and claim that it was 100% safe.

The smallest value of CTVR50 occurred in the 1937 sequence. It was 2.4%.

[Before 1923, the lowest value of CTVR50 was 2.9%.]

Those using the conventional methodology would claim that they are certain [place slippery disclaimer here] of maintaining the entire buying power of their portfolios when they withdraw 2.4%. In reality, their odds would be very close to 55-45, only slightly better than 50-50.

Have fun.

John R.
Post Reply