Expanded Baselines
The Value portfolio consists of 80% Large Capitalization Value Stocks and 20% T-Bills, rebalanced annually. The Growth portfolio consists of 80% Large Capitalization Growth Stocks and 20% T-Bills, rebalanced annually.
I set expenses equal to zero. I selected the CPI for inflation adjustments.
Baseline
The baseline is the Value portfolio.
The Value portfolio consists of 80% Large Capitalization Value stocks and 20% T-Bills, rebalanced annually.
Algorithm F Baseline
Algorithm F switches between the Value portfolio and the Growth portfolio. For switching, it replaces P/E10 with the interest rate of Treasury Bonds minus the interest rate of commercial paper.
Algorithm F allocates 100%-80%-0% to the Value portfolio (with the remainder of 0%-20%-100% going to the Growth portfolio) using thresholds (of the Treasury Bond interest rate minus the commercial paper interest rate) of plus and minus two percent.
Algorithm D Baseline
Algorithm D switches between the Value portfolio and the Growth portfolio. For switching, it replaces P/E10 with the interest rate of Treasury Bonds.
Stock allocations: 100%-20%-0%-0%-0%. The programmed part is 20%-0%-0%.
Thresholds: 2% and 6%. The calculator inputs are 2-6-79-80.
Algorithm G Baseline
Algorithm G switches between the Value portfolio and the Growth portfolio. For switching, it replaces P/E10 with the single-year total return of Government Long Bonds minus the single-year total return of T-Bills. The numbers come from Gummy's database.
Lower Threshold = minus 100 percent.
Higher Threshold = plus 300 percent.
Allocations of the Value portfolio: 100%-80%-0%.
30-Year Historical Surviving Withdrawal Rates
Tables
Year 100E10/P Baseline Algorithm F
1928 5.3 4.4 4.9
1929 3.7 3.9 4.1
1930 4.5 3.8 4.1
1931 6.0 5.5 5.6
1932 10.8 10.2 9.6
1933 11.5 12.2 11.6
1934 7.7 7.2 7.2
1935 8.7 9.3 8.8
1936 5.8 7.4 7.0
1937 4.6 5.7 5.5
1938 7.4 8.8 8.4
1939 6.4 7.8 7.3
1940 6.1 9.6 8.6
1941 7.2 11.9 10.7
1942 9.9 14.7 13.3
1943 9.8 13.6 12.5
1944 9.0 11.7 10.9
1945 8.3 9.9 9.4
1946 6.4 9.1 8.8
1947 8.7 11.7 11.3
1948 9.6 12.5 12.0
1949 9.8 13.2 12.7
1950 9.3 14.0 13.3
1951 8.4 11.3 11.1
1952 8.0 11.3 10.9
1953 7.7 10.8 10.5
1954 8.3 12.7 12.0
1955 6.3 8.7 8.4
1956 5.5 7.7 7.4
1957 6.0 8.2 7.8
1958 7.2 11.0 10.2
1959 5.6 7.6 7.2
1960 5.5 7.3 6.9
1961 5.4 8.3 7.8
1962 4.7 7.5 7.0
1963 5.2 8.2 7.7
1964 4.6 6.9 6.6
1965 4.3 6.4 6.1
1966 4.1 5.7 5.5
1967 4.9 6.7 6.5
1968 4.7 5.9 5.7
1969 4.7 5.5 5.4
1970 5.8 6.9 6.6
1971 6.1 6.9 6.5
1972 5.8 6.9 6.4
1973 5.3 6.9 6.4
1974 7.4 8.2 7.7
1975 11.2 11.7 11.0
1976 8.9 9.6 9.0
1977 8.8 8.0 7.7
1978 10.9 9.2 8.9
1979 10.8 10.9 10.3
1980 11.2 11.2 10.3
Year 100E10/P Algorithm D Algorithm G
1928 5.3 4.7 4.7
1929 3.7 4.0 4.0
1930 4.5 4.1 4.1
1931 6.0 5.6 5.6
1932 10.8 9.6 9.6
1933 11.5 11.6 11.5
1934 7.7 7.2 7.2
1935 8.7 8.8 8.8
1936 5.8 7.0 7.0
1937 4.6 5.5 5.5
1938 7.4 8.4 8.4
1939 6.4 7.3 7.3
1940 6.1 8.6 8.6
1941 7.2 10.7 10.7
1942 9.9 13.3 13.2
1943 9.8 12.5 12.4
1944 9.0 10.9 10.9
1945 8.3 9.4 9.4
1946 6.4 8.8 8.8
1947 8.7 11.3 11.2
1948 9.6 12.0 12.0
1949 9.8 12.7 12.6
1950 9.3 13.3 13.2
1951 8.4 11.1 11.0
1952 8.0 10.9 10.8
1953 7.7 10.5 10.4
1954 8.3 12.1 11.9
1955 6.3 8.4 8.3
1956 5.5 7.5 7.3
1957 6.0 7.9 7.7
1958 7.2 10.3 10.3
1959 5.6 7.3 7.2
1960 5.5 7.0 7.0
1961 5.4 7.9 7.8
1962 4.7 7.1 7.0
1963 5.2 7.8 7.8
1964 4.6 6.7 6.6
1965 4.3 6.2 6.1
1966 4.1 5.7 5.6
1967 4.9 6.6 6.5
1968 4.7 5.8 5.7
1969 4.7 5.6 5.3
1970 5.8 7.1 6.5
1971 6.1 7.0 6.4
1972 5.8 6.9 6.3
1973 5.3 6.9 6.3
1974 7.4 8.2 7.6
1975 11.2 11.7 10.8
1976 8.9 9.6 8.9
1977 8.8 8.0 7.7
1978 10.9 9.2 9.0
1979 10.8 10.8 10.6
1980 11.2 11.1 10.8
Graphs
I have put a graph of 30-Year Historical Surviving Withdrawal Rates for these baselines in my Yahoo briefcase. They are available to everybody.
You can find this graph in the Graphs versus Earnings Yield folder. They are stored as pictures in Microsoft Word documents.
Yahoo Briefcase
Regression Equations
These are the regression equations:
Baseline: y = 0.9953x + 1.7753 with R-squared = 0.6607.
Algorithm F Baseline: y = 0.9138x + 1.9237 with R-squared = 0.6782.
Algorithm D Baseline: y = 0.9351x + 1.905 with R-squared = 0.7101.
Algorithm G Baseline: y = 0.9207x + 1.8515 with R-squared = 0.6886.
y is the estimate of the Historical Surviving Withdrawal Rate (in percent).
x is the percentage earnings yield 100E10/P (in percent).
Comparisons
The four baselines are almost identical. All four regression equations start at almost the exact same place at the lowest percentage earnings yields (i.e., at the highest valuations). The standard baseline (Value portfolio by itself) is a little bit better than the others. It has a slightly greater slope.
Data points from the four baselines are clustered together.
Have fun.
John Walter Russell
October 21, 2005