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
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
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
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
Have fun.
John R.