HDBR Switching Results (Initial)

Research on Safe Withdrawal Rates

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JWR1945
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HDBR Switching Results (Initial)

Post by JWR1945 » Wed Oct 22, 2003 10:40 am

HDBR Switching Results (Initial)

I have collected a full set of switching data using the Retire Early Safe Withdrawal [Rate] Calculator (Version 1.61, November 7, 2002). I have presented an abridged, initial summary of results below. This summary compares switching and not switching, albeit imperfectly.

Details

The switching portfolio was run on the Retire Early Safe Withdrawal [Rate] Calculator, version 1.61 dated November 7, 2002, as-is. The portfolio's initial amount was set high ($100000) to reduce round off errors. The time span was 30 years. The stock allocation was 80% when stock valuations were favorable (i.e., whenever the P/E10 was below 12.0) and 20% otherwise. The fixed income alternative to stocks was commercial paper. The expense ratio was 0.20%. The inflation adjustment was the CPI. (The portfolio was re-balanced annually at no cost. Expenses and withdrawal amounts were split in two and then applied equally at the beginning January of each year and at the end of December of each year, which is the default setting.) Historical Database Rates were collected in increments of 0.1%.

For purposes of comparison, I have presented FIRECalc results that I collected for the From Intrinsic Valuations thread. That portfolio consisted of 80% stocks and 20% commercial paper without any switching. I used $1000 for my initial balance (which means that it may have round off errors) and a 30-year portfolio lifespan. Those results were collected in increments of 0.2%. Otherwise, the inputs were the same. FIRECalc does not split withdrawal amounts. It makes only one. (I configured it so that the first withdrawal came at the end of the first year.)

When using switching with the Retire Early Safe Withdrawal [Rate] Calculator, it is important to remember that cells I19 and F20 are not active. The only threshold input that is used is in cell F19. The only stock allocations are those in cells B20 and I20.

Alignment of Data

I have included a column in which I have adjusted the years associated with the Retire Early Safe Withdrawal [Rate] Calculator to line them up with the FIRECalc and with Professor Shiller's P/E10 data. To create that column, I took the year (which corresponds to the FIRECalc and P/E10 data), added one, looked up the Retire Early results for the later year and placed it into the column (back in the original row). I had suspected that such an adjustment would be necessary. I collected comparative data from the Retire Early Safe Withdrawal [Rate] Calculator without switching to confirm my suspicion.

The FIRECalc result (without switching) for 1931 was 5.6%. For 1932 it was 8.0%. The Retire Early Safe Withdrawal [Rate] Calculator results (using my method of data analysis) were 5.0% in 1932 and 6.9% in 1933. The numbers are different because FIRECalc applies expenses and withdrawals only once and the Retire Early calculator applied them in two increments.

I further compared FIRECalc results for 1953, 1964 and 1965 with the Retire Early Safe Withdrawal [Rate] Calculator results of 1954, 1965 and 1966. The comparisons are 8.6% with 8.2%, 4.6% with 4.4% and 4.2% with 4.0%

Notice that an adjustment was necessary to align these data. The jump in the Historical Database Rate from 1931 to 1932 on FIRECalc is dramatic. On the Retire Early Safe Withdrawal [Rate] Calculator, it is seen to occur from 1932 to 1933.

As an aside, the Retire Early Safe Withdrawal [Rate] Calculator does not calculate the results for a retirement that starts in 1871. I think that it could be made to do so by duplicating 1871 column (with its detailed data) and labeling the new column 1870. The reason that 1871 data is not calculated is that the algorithm calculates a stock price increase. There is no data available to use with 1871. A duplicate column would provide the means to make the necessary calculations without modifying the algorithm.

An alternative way to describe the Retire Early Safe Withdrawal [Rate] Calculator is to refer to the 12/31 line. The calculator starts with the initial balance as of 12/31/1871. There is no line for an initial balance as of 12/31/1870, which is needed to make an 1871 calculation.

Tables

These tables show the Year, PE10, Dividend Yield, FIRECalc HDBR for an 80% stock portfolio, RE Safe Withdrawal [Rate] Calculator results for switching between 80% and 20% stock allocations with a P/E10 threshold of 12.0 and the same information with the data aligned to reference the same start years.

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Year  PE10 Yield FIRECalc80% 80/20and12 adjusted RE
1921   5.1   7.11%   11.6%    9.8%   10.6%*
1922   6.2   6.35%   10.2%   10.6%   10.7%
1924   8.0   6.02%    9.4%    9.9%   10.3%
1923   8.1   5.74%    9.0%   10.7%    9.9%
1933   8.7   6.98%    8.4%    7.2%    8.3%*
1980   8.8   5.18%   10.4%    9.2%   not collected
1975   8.9   4.99%    8.2%    6.8%    7.7%*
1978   9.2   5.22%    9.2%    6.9%    8.5%*
1979   9.2   5.12%    9.6%    8.5%    9.2%*
1932   9.3   9.55%    8.0%    7.1%    7.2%*
1925   9.6   5.26%    8.4%   10.3%    9.6%
1942  10.1   7.87%    9.0%    6.8%    7.8%*
1943  10.1   5.90%    9.2%    7.8%    7.4%*
1949  10.2   6.18%   11.0%    7.2%    6.8%*
1948  10.4   5.69%   10.8%    6.9%    7.2%*
1950  10.7   6.84%   10.2%    6.8%    6.8%*
1944  11.0   5.19%    8.6%    7.4%    6.7%*
1976  11.1   3.80%    7.2%    7.7%    6.6%*
1926  11.3   4.82%    7.6%    9.6%    8.5%
1935  11.4   4.85%    7.6%    6.4%    6.9%*


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Year  PE10 Yield FIRECalc80% 80/20and12 adjusted RE
1947   11.4   4.69%   9.4%    5.9%    6.9%*
1977   11.4   3.97%   7.4%    6.6%    6.9%*
1951   11.8   6.98%   9.4%    6.8%    5.8%*
1945   11.9   4.77%   8.2%    6.7%    6.3%*
1954   12.0   5.73%   9.0%    5.2%    5.2%*
1952   12.5   5.86%   9.0%    5.8%    5.2%*
1934   13.0   4.19%   6.2%    8.3%    6.4%
1953   13.0   5.40%   8.6%    5.2%    5.2%*
1927   13.1   5.19%   7.2%    8.5%    8.3%
1938   13.5   7.02%   6.6%    5.1%    5.5%*
1974   13.5   3.53%   5.8%    6.0%    6.8%
1958   13.7   4.33%   7.0%    4.9%    5.1%*
1941   13.9   6.41%   7.0%    5.7%    6.8%*
1939   15.5   4.10%   6.0%    5.5%    5.5%*
1946   15.6   3.70%   6.8%    6.3%    5.9%*
1955   15.9   4.34%   6.8%    5.2%    4.9%*
1940   16.3   5.06%   6.0%    5.5%    5.7%*
1971   16.4   3.35%   6.8%    5.4%    5.5%*
1931   16.7   6.07%   5.6%    7.2%    7.1%
1957   16.7   3.82%   6.0%    4.8%    4.9%*


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Year  PE10 Yield FIRECalc80% 80/20and12 adjusted RE
1936   17.0   3.50%   5.4%    6.9%    5.2%*
1970   17.0   3.50%   4.8%    5.2%    5.4%
1972   17.2   2.98%   4.8%    5.5%    5.7%
1959   17.9   3.15%   5.4%    5.1%    4.9%*
1956   18.2   3.78%   5.8%    4.9%    4.8%*
1960   18.3   3.21%   5.2%    4.9%    4.9%*
1961   18.4   3.26%   5.2%    4.9%    4.9%*
1973   18.7   2.67%   4.6%    5.7%    6.0%
1928   18.8   4.43%   5.8%    8.3%    7.9%
1963   19.2   3.28%   5.0%    4.9%    5.0%
1967   20.4   3.41%   4.4%    4.9%    5.1%
1962   21.1   2.93%   4.8%    4.9%    4.9%
1969   21.1   3.01%   4.2%    5.1%    5.2%
1968   21.6   3.08%   4.2%    5.1%    5.1%
1937   21.6   4.17%   4.6%    5.2%    5.1%
1964   21.6   3.00%   4.6%    5.0%    4.9%
1930   22.3   4.47%   4.8%    7.4%    7.2%
1965   23.2   2.92%   4.2%    4.9%    4.9%
1966   24.0   2.93%   4.0%    4.9%    4.9%
1929   27.0   3.46%   4.2%    7.9%    7.4%


An asterisk has been placed all switching results in the adjusted RE column for which switching reported a higher Historical Database Rate than FIRECalc without switching.

Summary

Switching increases the Historical Database Rates (HDBR) when they are lowest. In the 1921-1980 time frame, the minimum HDBR was increased from 4.0% to 4.8%. (If the full set of data is used, the lowest HDBR with switching is 4.7% and 1911 was the most dangerous year for starting one's retirement. That year becomes 1910 when it is adjusted to correspond to FIRECalc.)

As an aside, the data alignment problem may help explain why the strong correlation between P/E10 and Historical Database Rates was not discovered earlier.

Have fun.

John R.

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