HFWR80 versus Earnings Yield

Research on Safe Withdrawal Rates

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JWR1945
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HFWR80 versus Earnings Yield

Post by JWR1945 »

This is another application of my new Deluxe Calculator V1.0A02.

HFWR80 refers to a portfolio consisting of 80% stocks and 20% 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 kept portfolio balances above $50000 (in real dollars) for an entire 30-year period.

This is similar to the conventional Safe Withdrawal Rate strategy that is investigated most frequently. The difference is that I have limited the portfolio's balance to fall to one half of its original value instead of zero. I refer to such an occurrence as a Half Failure. I refer to these withdrawal rates as Half Failure Withdrawal Rates (HFWR). The corresponding rates when the threshold is zero dollars are the Historical Surviving Withdrawal Rates (also known as the Historical Database Rates).

HFWR80 and HDBR80 are identical except for the threshold. HFWR80 has a threshold of one half of its original balance. HDBR80 has a threshold of zero.

To collect these data I used my latest modification of the Retire Early Safe Withdrawal Calculator, Version V1.61, dated 7 November 2002. I call this update the Deluxe Calculator V1.1A02. [The 02 refers to minor changes including some debugging.] You can download this version from the special SWR Research section of this site.

I have tabulated the 30-year Half Failure Withdrawal Rates along with the percentage earnings yield (100E10/P) for 1871-1980. [E10/P is 1/[P/E10]. P/E10 is Yale Professor Robert Shiller's measure of valuation. He and Dr. Campbell have shown that it has a reasonable amount of capability for predicting long-term stock market returns. P/E10 is the current price of the S&P500 divided by the average of earnings over the previous decade.]

I have made a (straight line) linear curve fit to the 1923-1980 Half Failure Withdrawal Rate data versus the Percentage Earnings Yield 100E10/P. The equation that it produces is y = 0.6822x + 0.5298%, where y is the Half Failure Withdrawal Rate and x is the Percentage Earnings Yield. R squared was 0.6669. I have not calculated confidence limits yet. Using an eyeball estimate, they are likely to be slightly wider than plus and minus 2%.

I wrote the following in From Earnings Yield:
With the 80% stock portfolio, the Historical Database Rate (HDBR80) equation is HDBR80 = 0.6685x+1.6424%, where x = 100*(E10/P) or 100/[P/E10] = the earnings yield in percent and R squared equals 0.7274. The standard deviation of HDBR80 using this formula is 0.9649. The 90% confidence limits are plus and minus 1.58%.
There is a tremendous amount of similarity between these two sets of results. The equations for HFWR80 and HDBR80 have almost identical slopes and values of R squared (a measure of the goodness of fit). Their intercepts differ.

This suggests that previous estimates based upon Historical Surviving Withdrawal Rates are still useful if one wants to set a floor for his portfolio's balance other than zero. To an excellent first approximation, the Half Failure Withdrawal Rate (for an 80% stock portfolio) equals the Historical Surviving Withdrawal Rate minus 1.1% [or, more precisely, the difference of the intercepts: 1.6424% - 0.5298%].

Have fun.

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

Post by JWR1945 »

This table shows the year, P/E10, 100E10/P (the percentage earnings yield) and HFWR80.

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1871   13.3     7.5    9.0
1872   14.5     6.9    8.8
1873   15.3     6.5    8.3
1874   13.9     7.2    8.3
1875   13.6     7.4    8.1
1876   13.3     7.5    8.5
1877   10.6     9.4    8.7
1878    9.7    10.3    8.4
1879   10.7     9.3    9.6
1880   15.3     6.5    7.1
1881   18.5     5.4    6.6
1882   15.7     6.4    6.9
1883   15.3     6.5    6.5
1884   14.4     6.9    6.3
1885   13.1     7.6    6.9
1886   16.7     6.0    5.9
1887   17.5     5.7    5.9
1888   15.4     6.5    5.6
1889   15.8     6.3    5.2
1890   17.2     5.8    5.1
1891   15.4     6.5    5.1
1892   19.0     5.3    4.8
1893   17.7     5.6    4.2
1894   15.7     6.4    5.0
1895   16.5     6.1    5.1
1896   16.6     6.0    4.8
1897   17.0     5.9    5.3
1898   19.2     5.2    4.7
1899   22.9     4.4    4.3
1900   18.7     5.3    4.7
1901   21.0     4.8    3.9
1902   22.3     4.5    3.6
1903   20.3     4.9    3.5
1904   15.9     6.3    4.7
1905   18.5     5.4    3.4
1906   20.1     5.0    2.6
1907   17.2     5.8    2.8
1908   11.9     8.4    4.6
1909   14.8     6.8    3.1
1910   14.5     6.9    2.7
1911   14.0     7.1    2.6
1912   13.8     7.2    2.7
1913   13.1     7.6    2.9
1914   11.6     8.6    3.8
1915   10.4     9.6    5.1
1916   12.5     8.0    3.2
1917   11.0     9.1    4.8
1918    6.6    15.2    8.2
1919    6.1    16.4    9.1
1920    6.0    16.7    8.5

Code: Select all

1921    5.1    19.6    9.2
1922    6.3    15.9    9.2
1923    8.2    12.2    8.3
1924    8.1    12.3    8.5
1925    9.7    10.3    7.9
1926   11.3     8.8    6.8
1927   13.2     7.6    6.6
1928   18.8     5.3    5.1
1929   27.1     3.7    3.4
1930   22.3     4.5    3.7
1931   16.7     6.0    4.5
1932    9.3    10.8    6.5
1933    8.7    11.5    7.6
1934   13.0     7.7    5.7
1935   11.5     8.7    6.7
1936   17.1     5.8    4.6
1937   21.6     4.6    3.2
1938   13.5     7.4    5.6
1939   15.6     6.4    5.2
1940   16.4     6.1    5.3
1941   13.9     7.2    6.8
1942   10.1     9.9    8.5
1943   10.2     9.8    8.2
1944   11.1     9.0    7.5
1945   12.0     8.3    6.8
1946   15.6     6.4    6.4
1947   11.5     8.7    8.7
1948   10.4     9.6    9.2
1949   10.2     9.8    9.1
1950   10.7     9.3    9.2
1951   11.9     8.4    8.1
1952   12.5     8.0    7.2
1953   13.0     7.7    7.0
1954   12.0     8.3    7.4
1955   16.0     6.3    5.5
1956   18.3     5.5    4.6
1957   16.7     6.0    4.8
1958   13.8     7.2    5.6
1959   18.0     5.6    4.1
1960   18.3     5.5    4.0
1961   18.5     5.4    4.0
1962   21.2     4.7    3.4
1963   19.3     5.2    3.9
1964   21.6     4.6    3.2
1965   23.3     4.3    2.7
1966   24.1     4.1    2.4
1967   20.4     4.9    3.1
1968   21.5     4.7    2.7
1969   21.2     4.7    2.6
1970   17.1     5.8    3.6
1971   16.5     6.1    3.7
1972   17.3     5.8    3.4
1973   18.7     5.3    2.9
1974   13.5     7.4    5.1
1975    8.9    11.2    6.8
1976   11.2     8.9    5.4
1977   11.4     8.8    5.2
1978    9.2    10.9    6.0
1979    9.3    10.8    5.7
1980    8.9    11.2    5.2
Have fun.

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

Post by JWR1945 »

These are the same values of HFWR80 from 1871-1980, but separated to make them easier to copy onto your own spreadsheet (or document).
1871-1900

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9.0
8.8
8.3
8.3
8.1
8.5
8.7
8.4
9.6
7.1
6.6
6.9
6.5
6.3
6.9
5.9
5.9
5.6
5.2
5.1
5.1
4.8
4.2
5.0
5.1
4.8
5.3
4.7
4.3
4.7
1901-1920

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3.9
3.6
3.5
4.7
3.4
2.6
2.8
4.6
3.1
2.7
2.6
2.7
2.9
3.8
5.1
3.2
4.8
8.2
9.1
8.5
1921-1950

Code: Select all

9.2
9.2
8.3
8.5
7.9
6.8
6.6
5.1
3.4
3.7
4.5
6.5
7.6
5.7
6.7
4.6
3.2
5.6
5.2
5.3
6.8
8.5
8.2
7.5
6.8
6.4
8.7
9.2
9.1
9.2
1951-1980

Code: Select all

8.1
7.2
7.0
7.4
5.5
4.6
4.8
5.6
4.1
4.0
4.0
3.4
3.9
3.2
2.7
2.4
3.1
2.7
2.6
3.6
3.7
3.4
2.9
5.1
6.8
5.4
5.2
6.0
5.7
5.2
Have fun.

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

Post by JWR1945 »

HFWR80 refers to a portfolio consisting of 80% stocks and 20% 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 kept portfolio balances above $50000 (in real dollars) for an entire 30-year period.

This is similar to the conventional Safe Withdrawal Rate strategy that is investigated most frequently. The difference is that I have limited the portfolio's balance to fall to one half of its original value instead of zero. I refer to such an occurrence as a Half Failure. I refer to these withdrawal rates as Half Failure Withdrawal Rates (HFWR). The corresponding rates when the threshold is zero dollars are the Historical Surviving Withdrawal Rates (also known as the Historical Database Rates).

HFWR80 and HDBR80 are identical except for the threshold. HFWR80 has a threshold of one half of its original balance. HDBR80 has a threshold of zero.
..
I have made a (straight line) linear curve fit to the 1923-1980 Half Failure Withdrawal Rate data versus the Percentage Earnings Yield 100E10/P. The equation that it produces is y = 0.6822x + 0.5298%, where y is the Half Failure Withdrawal Rate and x is the Percentage Earnings Yield. R squared was 0.6669. I have not calculated confidence limits yet. Using an eyeball estimate, they are likely to be slightly wider than plus and minus 2%.

I have calculated the confidence limits. They are plus and minus 1.864%. [This is 1.64 times the standard deviation of 1.1367% using 56 degrees of freedom.]

Here are tables.

Year, P/E10, 100E10/P, HFWR80, Calculated Withdrawal Rate

Code: Select all

1923    8.2    12.2    8.3   8.85
1924    8.1    12.3    8.5   8.95
1925    9.7    10.3    7.9   7.56
1926   11.3     8.8    6.8   6.57
1927   13.2     7.6    6.6   5.70
1928   18.8     5.3    5.1   4.16
1929   27.1     3.7    3.4   3.05
1930   22.3     4.5    3.7   3.59
1931   16.7     6.0    4.5   4.61
1932    9.3    10.8    6.5   7.87
1933    8.7    11.5    7.6   8.37
1934   13.0     7.7    5.7   5.78
1935   11.5     8.7    6.7   6.46
1936   17.1     5.8    4.6   4.52
1937   21.6     4.6    3.2   3.69
1938   13.5     7.4    5.6   5.58
1939   15.6     6.4    5.2   4.90
1940   16.4     6.1    5.3   4.69
1941   13.9     7.2    6.8   5.44
1942   10.1     9.9    8.5   7.28
1943   10.2     9.8    8.2   7.22
1944   11.1     9.0    7.5   6.68
1945   12.0     8.3    6.8   6.21
1946   15.6     6.4    6.4   4.90
1947   11.5     8.7    8.7   6.46
1948   10.4     9.6    9.2   7.09
1949   10.2     9.8    9.1   7.22
1950   10.7     9.3    9.2   6.91
1951   11.9     8.4    8.1   6.26
1952   12.5     8.0    7.2   5.99
1953   13.0     7.7    7.0   5.78
1954   12.0     8.3    7.4   6.21
1955   16.0     6.3    5.5   4.79
1956   18.3     5.5    4.6   4.26
1957   16.7     6.0    4.8   4.61
1958   13.8     7.2    5.6   5.47
1959   18.0     5.6    4.1   4.32
1960   18.3     5.5    4.0   4.26
1961   18.5     5.4    4.0   4.22
1962   21.2     4.7    3.4   3.75
1963   19.3     5.2    3.9   4.06
1964   21.6     4.6    3.2   3.69
1965   23.3     4.3    2.7   3.46
1966   24.1     4.1    2.4   3.36
1967   20.4     4.9    3.1   3.87
1968   21.5     4.7    2.7   3.70
1969   21.2     4.7    2.6   3.75
1970   17.1     5.8    3.6   4.52
1971   16.5     6.1    3.7   4.66
1972   17.3     5.8    3.4   4.47
1973   18.7     5.3    2.9   4.18
1974   13.5     7.4    5.1   5.58
1975    8.9    11.2    6.8   8.19
1976   11.2     8.9    5.4   6.62
1977   11.4     8.8    5.2   6.51
1978    9.2    10.9    6.0   7.95
1979    9.3    10.8    5.7   7.87
1980    8.9    11.2    5.2   8.19
Year, HFWR80, Safe Withdrawal Rate for a Half-Failure, Calculated Withdrawal Rate for a Half-Failure, High Risk Rate for a Half-Failure

Code: Select all

1923   8.3   6.99    8.85   10.71
1924   8.5   7.09    8.95   10.82
1925   7.9   5.70    7.56    9.43
1926   6.8   4.70    6.57    8.43
1927   6.6   3.83    5.70    7.56
1928   5.1   2.29    4.16    6.02
1929   3.4   1.18    3.05    4.91
1930   3.7   1.72    3.59    5.45
1931   4.5   2.75    4.61    6.48
1932   6.5   6.00    7.87    9.73
1933   7.6   6.51    8.37   10.24
1934   5.7   3.91    5.78    7.64
1935   6.7   4.60    6.46    8.33
1936   4.6   2.66    4.52    6.38
1937   3.2   1.82    3.69    5.55
1938   5.6   3.72    5.58    7.45
1939   5.2   3.04    4.90    6.77
1940   5.3   2.83    4.69    6.55
1941   6.8   3.57    5.44    7.30
1942   8.5   5.42    7.28    9.15
1943   8.2   5.35    7.22    9.08
1944   7.5   4.81    6.68    8.54
1945   6.8   4.35    6.21    8.08
1946   6.4   3.04    4.90    6.77
1947   8.7   4.60    6.46    8.33
1948   9.2   5.23    7.09    8.95
1949   9.1   5.35    7.22    9.08
1950   9.2   5.04    6.91    8.77
1951   8.1   4.40    6.26    8.13
1952   7.2   4.12    5.99    7.85
1953   7.0   3.91    5.78    7.64
1954   7.4   4.35    6.21    8.08
1955   5.5   2.93    4.79    6.66
1956   4.6   2.39    4.26    6.12
1957   4.8   2.75    4.61    6.48
1958   5.6   3.61    5.47    7.34
1959   4.1   2.46    4.32    6.18
1960   4.0   2.39    4.26    6.12
1961   4.0   2.35    4.22    6.08
1962   3.4   1.88    3.75    5.61
1963   3.9   2.20    4.06    5.93
1964   3.2   1.82    3.69    5.55
1965   2.7   1.59    3.46    5.32
1966   2.4   1.50    3.36    5.22
1967   3.1   2.01    3.87    5.74
1968   2.7   1.84    3.70    5.57
1969   2.6   1.88    3.75    5.61
1970   3.6   2.66    4.52    6.38
1971   3.7   2.80    4.66    6.53
1972   3.4   2.61    4.47    6.34
1973   2.9   2.31    4.18    6.04
1974   5.1   3.72    5.58    7.45
1975   6.8   6.33    8.19   10.06
1976   5.4   4.76    6.62    8.49
1977   5.2   4.65    6.51    8.38
1978   6.0   6.08    7.95    9.81
1979   5.7   6.00    7.87    9.73
1980   5.2   6.33    8.19   10.06
Have fun.

John R.
hocus2004
Moderator
Posts: 752
Joined: Thu Jun 10, 2004 7:33 am

Post by hocus2004 »

My understanding is that the numbers reported above relate to the criticism of the REHP study raised by FoolMeOnce that I reported on in the "FMO Gets Hocomania!" thread. If a retiree with an 80 percent S&P allocation wants to insure that he will not experience a 50 percent drop in his real portfolio value, he needs to limit his take-out number to the Safe Withdrawal Rate (SWR) for a Half-Failure.

Can you say what the SWR for a half-failure of an 80 percent S&P portfolio was in January 2000 and can you say (roughly) what it is at the valuation level that applies today?
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Post by JWR1945 »

Here are the same calculations for 1981-2003. There are no completed 30-year sequences for HFWR80 after 1980 (even with dummy data).

With 80% stocks: Year, Safe Withdrawal Rate for a Half-Failure, Calculated Withdrawal Rate for a Half-Failure, High Risk Rate for a Half-Failure

Code: Select all

1981    5.97    7.84    9.70
1982    7.86    9.73   11.59
1983    6.52    8.38   10.25
1984    5.66    7.52    9.39
1985    5.54    7.40    9.27
1986    4.51    6.38    8.24
1987    3.29    5.16    7.02
1988    3.63    5.49    7.36
1989    3.17    5.03    6.90
1990    2.68    4.54    6.41
1991    3.05    4.91    6.78
1992    2.15    4.02    5.88
1993    2.01    3.87    5.74
1994    1.84    3.70    5.56
1995    2.00    3.86    5.73
1996    1.35    3.21    5.08
1997    1.00    2.87    4.73
1998    0.69    2.55    4.41
1999    0.33    2.20    4.06
2000    0.19    2.06    3.92
2001    0.51    2.37    4.24
2002    0.92    2.78    4.65
2003    1.65    3.51    5.37
With 80% stocks: Year, P/E10, 100E10/P, Calculated Withdrawal Rate for a Half-Failure

Code: Select all

1981     9.34    10.71    7.84
1982     7.42    13.48    9.73
1983     8.69    11.51    8.38
1984     9.76    10.25    7.52
1985     9.93    10.07    7.40
1986    11.67     8.57    6.38
1987    14.74     6.78    5.16
1988    13.75     7.28    5.49
1989    15.15     6.60    5.03
1990    17.00     5.88    4.54
1991    15.57     6.42    4.91
1992    19.55     5.11    4.02
1993    20.40     4.90    3.87
1994    21.52     4.65    3.70
1995    20.46     4.89    3.86
1996    25.44     3.93    3.21
1997    29.16     3.43    2.87
1998    33.76     2.96    2.55
1999    40.93     2.44    2.20
2000    44.73     2.24    2.06
2001    36.98     2.70    2.37
2002    30.28     3.30    2.78
2003    22.89     4.37    3.51
Today's value of P/E10 is in the neighborhood of 28. This is similar to, but slightly less than, the level in 1997. The Half-Failure Withdrawal Rates for 80% stocks in 1997 were: Safe 1.00%, Calculated 2.87% and High Risk 4.73%.

Those who withdraw 2.9% or more from a high stock (80%) portfolio have a 50-50 chance at best of seeing their portfolio stay above half of its initial purchasing power for a full 30 years.

Have fun.

John R.
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