CTVR80 versus Earnings Yield

Research on Safe Withdrawal Rates

Moderator: hocus2004

JWR1945
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Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

CTVR80 versus Earnings Yield

Post by JWR1945 »

hocus2004 has requested data of this nature.

This data could have been collected using the original Retire Early Safe Withdrawal Calculator, Version 1.61, 7 November 1972.

CTVR80 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 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.

The Retire Early Safe Withdrawal Calculator presents 10, 20, 30, 40, 50 and 60 year nominal and real terminal values in columns S through AK and rows 10 through 144. For this investigation, I made use of column S, which lists the start year, and column AB, which has the 30-year terminal amount in real dollars. By using $100000 as my initial amount, it was easy to spot when a final balance fell below the initial amount. It would have five or fewer digits or it would have parentheses to indicate a negative number.

I have tabulated the 30-year Constant Terminal Value 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 1923-1972 Constant Terminal Value Rates versus the Percentage Earnings Yield 100E10/P. The equation that it produces is y = 0.7014x + 0.2313%, where y is the Constant Terminal Value Rate and x is the Percentage Earnings Yield. R squared was 0.8499, which is outstanding. I have not calculated confidence limits yet. Using an eyeball estimate, they are likely to be about plus and minus 1%.

These graphs have slopes similar to those using Historical Surviving Withdrawal Rates (HDBR80) and Half Failure Withdrawal Rates (HFWR80). The intercepts are different.

It was necessary for me to limit the upper end of the data to 1972 because the dummy data in the calculator from 2003-2010 reduced 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.

Have fun.

John R.

[Edited to correct CVTR to CTVR in several places.]
Last edited by JWR1945 on Sun Aug 08, 2004 6:37 am, edited 1 time in total.
JWR1945
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Location: Crestview, Florida

Post by JWR1945 »

Here are the Year, P/E10, Percentage Earnings Yield 100E10/P and 30-Year Constant Terminal Value Rates with 80% stocks. All values later than 1972 have been influenced greatly (i.e., reduced sharply) by dummy data in the calculator for the years 2003-2010.
1871-1920

Code: Select all

1871   13.3     7.5    8.5
1872   14.5     6.9    8.4
1873   15.3     6.5    7.8
1874   13.9     7.2    7.8
1875   13.6     7.4    7.7
1876   13.3     7.5    8.0
1877   10.6     9.4    8.2
1878    9.7    10.3    7.8
1879   10.7     9.3    9.0
1880   15.3     6.5    6.5
1881   18.5     5.4    6.0
1882   15.7     6.4    6.3
1883   15.3     6.5    5.9
1884   14.4     6.9    5.5
1885   13.1     7.6    6.1
1886   16.7     6.0    5.2
1887   17.5     5.7    5.0
1888   15.4     6.5    4.5
1889   15.8     6.3    4.1
1890   17.2     5.8    3.8
1891   15.4     6.5    3.8
1892   19.0     5.3    3.7
1893   17.7     5.6    3.6
1894   15.7     6.4    4.1
1895   16.5     6.1    4.5
1896   16.6     6.0    4.5
1897   17.0     5.9    4.9
1898   19.2     5.2    4.6
1899   22.9     4.4    4.8
1900   18.7     5.3    4.8
1901   21.0     4.8    4.1
1902   22.3     4.5    3.5
1903   20.3     4.9    3.3
1904   15.9     6.3    4.6
1905   18.5     5.4    3.5
1906   20.1     5.0    3.4
1907   17.2     5.8    3.6
1908   11.9     8.4    4.6
1909   14.8     6.8    4.0
1910   14.5     6.9    3.4
1911   14.0     7.1    3.4
1912   13.8     7.2    3.3
1913   13.1     7.6    3.4
1914   11.6     8.6    3.9
1915   10.4     9.6    4.6
1916   12.5     8.0    4.4
1917   11.0     9.1    4.8
1918    6.6    15.2    7.3
1919    6.1    16.4    8.2
1920    6.0    16.7    7.8
1920-1980

Code: Select all

1921    5.1    19.6    8.6
1922    6.3    15.9    8.5
1923    8.2    12.2    7.6
1924    8.1    12.3    7.8
1925    9.7    10.3    7.4
1926   11.3     8.8    6.5
1927   13.2     7.6    6.2
1928   18.8     5.3    4.7
1929   27.1     3.7    3.5
1930   22.3     4.5    3.7
1931   16.7     6.0    4.2
1932    9.3    10.8    6.2
1933    8.7    11.5    7.1
1934   13.0     7.7    5.3
1935   11.5     8.7    6.3
1936   17.1     5.8    4.6
1937   21.6     4.6    3.6
1938   13.5     7.4    5.2
1939   15.6     6.4    4.8
1940   16.4     6.1    4.8
1941   13.9     7.2    6.2
1942   10.1     9.9    7.9
1943   10.2     9.8    7.7
1944   11.1     9.0    6.8
1945   12.0     8.3    5.9
1946   15.6     6.4    5.6
1947   11.5     8.7    7.8
1948   10.4     9.6    8.2
1949   10.2     9.8    8.1
1950   10.7     9.3    8.0
1951   11.9     8.4    7.0
1952   12.5     8.0    6.0
1953   13.0     7.7    5.9
1954   12.0     8.3    6.4
1955   16.0     6.3    4.5
1956   18.3     5.5    3.8
1957   16.7     6.0    4.2
1958   13.8     7.2    4.7
1959   18.0     5.6    3.5
1960   18.3     5.5    3.6
1961   18.5     5.4    3.4
1962   21.2     4.7    3.4
1963   19.3     5.2    3.5
1964   21.6     4.6    3.0
1965   23.3     4.3    2.6
1966   24.1     4.1    2.7
1967   20.4     4.9    3.3
1968   21.5     4.7    3.3
1969   21.2     4.7    3.4
1970   17.1     5.8    4.1
1971   16.5     6.1    4.0
1972   17.3     5.8    3.7
1973   18.7     5.3    3.4
1974   13.5     7.4    4.4
1975    8.9    11.2    5.9
1976   11.2     8.9    4.2
1977   11.4     8.8    3.7
1978    9.2    10.9    4.1
1979    9.3    10.8    3.2
1980    8.9    11.2    2.1
Have fun.

John R.
JWR1945
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Posts: 1697
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Location: Crestview, Florida

Post by JWR1945 »

Here are Constant Terminal Value Rates with 80% stocks in a form suitable for downloading into a spreadsheet or document.
1871-1900

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8.5
8.4
7.8
7.8
7.7
8.0
8.2
7.8
9.0
6.5
6.0
6.3
5.9
5.5
6.1
5.2
5.0
4.5
4.1
3.8
3.8
3.7
3.6
4.1
4.5
4.5
4.9
4.6
4.8
4.8
1901-1920

Code: Select all

4.1
3.5
3.3
4.6
3.5
3.4
3.6
4.6
4.0
3.4
3.4
3.3
3.4
3.9
4.6
4.4
4.8
7.3
8.2
7.8
1921-1950

Code: Select all

8.6
8.5
7.6
7.8
7.4
6.5
6.2
4.7
3.5
3.7
4.2
6.2
7.1
5.3
6.3
4.6
3.6
5.2
4.8
4.8
6.2
7.9
7.7
6.8
5.9
5.6
7.8
8.2
8.1
8.0
1951-1980

Code: Select all

7.0
6.0
5.9
6.4
4.5
3.8
4.2
4.7
3.5
3.6
3.4
3.4
3.5
3.0
2.6
2.7
3.3
3.3
3.4
4.1
4.0
3.7
3.4
4.4
5.9
4.2
3.7
4.1
3.2
2.1
Have fun.

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

Post by hocus2004 »

JWR1945:

Thanks for putting this together. I think that having this information available will prove helpful.

I think you may have calculated something a little different than what I was asking for. My sense is that what you have calculated here is the withdrawal rate that in actual fact would have permitted an investor to retain portfolio value for 30 years. That's a concept similar to the historical surviving withdrawal rate (HSWR) concept, one that involves looking back from the present in doing the calculations.

I was looking for a number more comparable to a safe withdrawal rate (SWR), one in which you are looking forward in doing the calculation rather than backward. I'm trying to get numbers comparable to the ones set forth in the "Calculated Rates of the Past Decade" thread.

We know that at today's valuation level, an investor with an 80 percent stock allocation needs to limit his annual takeout percentage to 2.5 percent to be sure that his portfolio will survive 30 years (presuming that stocks perform in the future as they have in the past). What is the take-out percentage that insures him that he will retain the full value of his starting-point portfolio at the end of 30 years?
unclemick
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Post by unclemick »

Hmmmmm - Looks like a little something for everyone to me. Look at the last number - add thirty years from 1980 to get 2010. My prejudice shows his number close to my div/interest yield,( Norwegian widow with hand grenade), albiet I'm closer to 60/40 not 80/20. The take out number is much lower than past studies giving creedance to people worried about valuations and being above the historical (1871) trend channel for stocks combined with low interest rates - the warning flags are flying. I would make the case for look back variable take -out keyed off SEC yield with some sensible upper and lower bounds based on JWR's other work - say 2- 5% ballpark(without looking at the numbers). I would also uncouple from inflation and let 'Mr. Market' tell me what I could have. Others might look and want to shift 80/20 to other mixes along a thirty year period based on numbers/valuation change. Some might look further back in the data string and deduce an RTM cycle and expect it to reoccur in a manner they can take advantage of. Hmmmm - good stuff to chew on.
JWR1945
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Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Post by JWR1945 »

Expanded CVTR80 Tables

I have collected additional CTVR80 data. I have identified the minimum balance of each sequence and the number of years after the beginning of a retirement sequence.

I took this data with my Deluxe Calculator V1.1A02 modified version of the Retire Early Safe Withdrawal Calculator, Version 1.61, 7 November 1972.

CTVR80 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 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 had already tabulated the 30-year Constant Terminal Value 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 added columns that show the portfolio's minimum amount and the number of years into the sequence at which it occurred.

I have made use of the list of Portfolio Balances in Real Dollars starting around row 3200. After entering an Initial Withdrawal Rate into cell B9, I pressed function key F5, typed a3200 and then clicked OK. That brought me to a list of all portfolio balances for all sequences from 1871-2000. The list displays all balances from N = 0 (i.e., the initial balance) to N = 60 years after the start of each sequence.

When interpreting these new tables, remember that the final balance at year 30 can be more than $100000. The final balance at year 30 falls below $100000 when the withdrawal rate is increased by 0.1%. In addition, comparisons are made based upon years 1 through 30. The initial balance is not included. It occurs in year zero.

It was necessary for me to limit the upper end of the data to 1972 because the dummy data in the calculator from 2003-2010 reduced 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 had already 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 = 0.7014x + 0.2313%, where y is the Constant Terminal Value Rate and x is the Percentage Earnings Yield. R squared was 0.8499, which is exceedingly high. I have not calculated confidence limits yet. Using an eyeball estimate, they are likely to be about plus and minus 1%.

I have made a (straight line) linear curve fit of the 1923-1972 CTVR80 Minimum Balances versus the Percentage Earnings Yield 100E10/P. The equation is y = 5518.2x + 27808 based upon an initial balance of $100000. The CTVR80 minimum balance in (real) dollars is y. The percentage earnings yield is x. R squared is 0.5185. My eyeball estimate of the confidence limits is plus and minus $25000.

I have made a (straight line) linear curve fit of the 1923-1972 CTVR80 Minimum Balances versus the value of CTVR80. The equation is y = 7977.3x + 25446 based upon an initial balance of $100000. The CTVR80 minimum balance in (real) dollars is y. The value of CTVR80 in percent is x. R squared is 0.6306. My eyeball estimate of the confidence limits is plus and minus $20000.

When you look at the number of years N into a sequence at which the minimum balance occurs, you will notice that N is usually part of a countdown from N = 30 to N = 1. This means that there is a single defining year among a collection of sequences that caused a bottom (with the smallest minimum balances).

It is reasonable to expect Minimum Balances to increase with Constant Terminal Value Rates. Stated differently, if specify a Minimum Balance and its corresponding CTVR and apply that withdrawal rate to other years, balances for those years with smaller values of CTVR would dip even deeper and they would fail to return to the initial balance. Balances for the other years (with higher values of CTVR) would dip less and end up with final balances in excess of the initial balances.

Have fun.

John R.

P.S. To convert a CTVR to something similar to a Safe Withdrawal Rate, subtract the confidence limit (of 1%, $25000 or $20000, as appropriate). To get something similar to a High Risk Withdrawal Rate, add the appropriate confidence limit.
JWR1945
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Location: Crestview, Florida

Post by JWR1945 »

Here are the Year, P/E10, Percentage Earnings Yield 100E10/P, 30-Year Constant Terminal Value Rates with 80% stocks, the Lowest Balance (after starting from $100000) and the Year N into the Sequence when the Lowest Balance occurred. All values later than 1972 have been influenced greatly (i.e., reduced sharply) by dummy data in the calculator for the years 2003-2010.
1871-1920

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1871   13.3     7.5    8.5    86124     6
1872   14.5     6.9    8.4    83649     5
1873   15.3     6.5    7.8    84782     4
1874   13.9     7.2    7.8    88378     3
1875   13.6     7.4    7.7    85060     2
1876   13.3     7.5    8.0    82683     1
1877   10.6     9.4    8.2   100280    27
1878    9.7    10.3    7.8   103444    30
1879   10.7     9.3    9.0    89241    29
1880   15.3     6.5    6.5    95006    28
1881   18.5     5.4    6.0    83957     4
1882   15.7     6.4    6.3    91391    26
1883   15.3     6.5    5.9    95344     2
1884   14.4     6.9    5.5    96557     1
1885   13.1     7.6    6.1   105780    30
1886   16.7     6.0    5.2    92576     5
1887   17.5     5.7    5.0    89359     4
1888   15.4     6.5    4.5    99421     3
1889   15.8     6.3    4.1    96755     2
1890   17.2     5.8    3.8    90605     1
1891   15.4     6.5    3.8   101492    30
1892   19.0     5.3    3.7    85982    29
1893   17.7     5.6    3.6    73802    28
1894   15.7     6.4    4.1    78098    27
1895   16.5     6.1    4.5    67959    26
1896   16.6     6.0    4.5    65190    25
1897   17.0     5.9    4.9    60042    24
1898   19.2     5.2    4.6    53522    23
1899   22.9     4.4    4.8    42224    22
1900   18.7     5.3    4.8    48630    21
1901   21.0     4.8    4.1    47808    20
1902   22.3     4.5    3.5    52017    19
1903   20.3     4.9    3.3    53787    18
1904   15.9     6.3    4.6    51932    17
1905   18.5     5.4    3.5    49158    16
1906   20.1     5.0    3.4    41277    15
1907   17.2     5.8    3.6    41232    14
1908   11.9     8.4    4.6    50899    13
1909   14.8     6.8    4.0    42958    12
1910   14.5     6.9    3.4    43766    11
1911   14.0     7.1    3.4    44231    10
1912   13.8     7.2    3.3    46135     9
1913   13.1     7.6    3.4    47063     8
1914   11.6     8.6    3.9    49705     7
1915   10.4     9.6    4.6    52812     6
1916   12.5     8.0    4.4    45553     5
1917   11.0     9.1    4.8    50805     4
1918    6.6    15.2    7.3    70641     3
1919    6.1    16.4    8.2    78341     2
1920    6.0    16.7    7.8    85270     1
More Follows.

John R.
JWR1945
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Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
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Post by JWR1945 »

Here are the Year, P/E10, Percentage Earnings Yield 100E10/P, 30-Year Constant Terminal Value Rates with 80% stocks, the Lowest Balance (after starting from $100000) and the Year N into the Sequence when the Lowest Balance occurred. All values later than 1972 have been influenced greatly (i.e., reduced sharply) by dummy data in the calculator for the years 2003-2010.
1921-1980

Code: Select all

1921    5.1    19.6    8.6    95016    28
1922    6.3    15.9    8.5    91935    27
1923    8.2    12.2    7.6    85533    26
1924    8.1    12.3    7.8    91931    25
1925    9.7    10.3    7.4    75546    24
1926   11.3     8.8    6.5    68557    23
1927   13.2     7.6    6.2    66906    22
1928   18.8     5.3    4.7    63505    21
1929   27.1     3.7    3.5    49563    20
1930   22.3     4.5    3.7    51756    19
1931   16.7     6.0    4.2    57831    18
1932    9.3    10.8    6.2    67628    17
1933    8.7    11.5    7.1    71330    16
1934   13.0     7.7    5.3    57570    15
1935   11.5     8.7    6.3    62705    14
1936   17.1     5.8    4.6    50390    13
1937   21.6     4.6    3.6    46067    12
1938   13.5     7.4    5.2    57927    11
1939   15.6     6.4    4.8    54571    10
1940   16.4     6.1    4.8    57132     9
1941   13.9     7.2    6.2    63582     8
1942   10.1     9.9    7.9    78334     7
1943   10.2     9.8    7.7    78820     6
1944   11.1     9.0    6.8    75928     5
1945   12.0     8.3    5.9    74448     4
1946   15.6     6.4    5.6    62100     3
1947   11.5     8.7    7.8    84178     2
1948   10.4     9.6    8.2    98120     1
1949   10.2     9.8    8.1   101518    30
1950   10.7     9.3    8.0   102997    30
1951   11.9     8.4    7.0    99771    29
1952   12.5     8.0    6.0    99844     2
1953   13.0     7.7    5.9    92687    29
1954   12.0     8.3    6.4    85642    28
1955   16.0     6.3    4.5    82762    27
1956   18.3     5.5    3.8    74599    26
1957   16.7     6.0    4.2    66299    25
1958   13.8     7.2    4.7    72737    24
1959   18.0     5.6    3.5    65125    23
1960   18.3     5.5    3.6    60628    22
1961   18.5     5.4    3.4    64162    21
1962   21.2     4.7    3.2    55623    20
1963   19.3     5.2    3.5    57549    19
1964   21.6     4.6    3.0    53779    18
1965   23.3     4.3    2.6    52317    17
1966   24.1     4.1    2.7    46912    16
1967   20.4     4.9    3.3    47711    15
1968   21.5     4.7    3.3    42779    14
1969   21.2     4.7    3.4    40842    13
1970   17.1     5.8    4.1    44838    12
1971   16.5     6.1    4.0    47724    11
1972   17.3     5.8    3.7    47567    10
1973   18.7     5.3    3.4    46365     9
1974   13.5     7.4    4.4    58522     8
1975    8.9    11.2    5.9    79216     7
1976   11.2     8.9    4.2    72962     6
1977   11.4     8.8    3.7    75601     5
1978    9.2    10.9    4.1    89494     4
1979    9.3    10.8    3.2    91688     3
1980    8.9    11.2    2.1    95481     2
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 »

hocus2004 wrote:I think you may have calculated something a little different than what I was asking for. My sense is that what you have calculated here is the withdrawal rate that in actual fact would have permitted an investor to retain portfolio value for 30 years. That's a concept similar to the historical surviving withdrawal rate (HSWR) concept, one that involves looking back from the present in doing the calculations.

I was looking for a number more comparable to a safe withdrawal rate (SWR), one in which you are looking forward in doing the calculation rather than backward. I'm trying to get numbers comparable to the ones set forth in the "Calculated Rates of the Past Decade" thread.
You are correct.

Here is what you are after.

With the 80% stock portfolio, the Constant Terminal Value Rate (CTVR80) equation is y = 0.7014x + 0.2313%, where y is the Constant Terminal Value Rate and x is the Percentage Earnings Yield 100E10/P. R squared is 0.8499, which is exceedingly high. My eyeball estimate of the confidence limits is that they are (close to) plus and minus 1%.

I have listed below the last decade's January values of P/E10 taken from Professor Robert Shiller's website.
http://www.econ.yale.edu/~shiller/
http://www.econ.yale.edu/~shiller/data/ie_data.htm
Here are the values of P/E10 in January.

Code: Select all

1995    20.219819
1996    24.763281
1997    28.333753
1998    32.860928
1999    40.578255
2000    43.774387
2001    36.98056
2002    30.277409
2003    22.894158
Nov 03   25.898702
The last entry in Professor Shiller's list is for November 2003. The S&P500 index was at 1054.87 and P/E10 was 25.898702. [To help with scaling: today's the S&P500 index started at 1063.97. If ten-year earnings were the same as in November 2003, today's P/E10 would be 25.898702*(1063.97/1054.87) = 26.122121.]

Here are the Constant Terminal Value Rates (CTVR80) for an 80% stock portfolio. These correspond to Calculated Rates.

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1995    3.70
1996    3.06
1997    2.71
1998    2.37
1999    1.96
2000    1.83
2001    2.13
2002    2.55
2003    3.29
Nov 03    2.94
Today     2.92
Safe, Calculated and High Risk Levels to Maintain Constant Terminal Values for 80% Stocks. The Calculated Rates correspond to CTVR80.

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Year  Safe  Calculated  High Risk
1995    2.7    3.70    4.7
1996    2.1    3.06    4.1
1997    1.7    2.71    3.7
1998    1.4    2.37    3.4
1999    1.0    1.96    3.0
2000    0.8    1.83    2.8
2001    1.1    2.13    3.1
2002    1.6    2.55    3.6
2003    2.3    3.29    4.3
Nov 03    1.9    2.94    3.9
Today     1.9    2.92    3.9
I have used plus and minus 1.0% for the confidence limits (i.e., my eyeball estimate).

Have fun.

John R.
JWR1945
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Post by JWR1945 »

unclemick wrote:I would make the case for look back variable take -out keyed off SEC yield with some sensible upper and lower bounds based on JWR's other work - say 2- 5% ballpark(without looking at the numbers). I would also uncouple from inflation and let 'Mr. Market' tell me what I could have. Others might look and want to shift 80/20 to other mixes along a thirty year period based on numbers/valuation change.
My initial response was to step aside until valuations become more favorable. That is why I have investigated switching portfolio allocations. That is why I have looked into how long someone can stay with a TIPS-only portfolio, waiting on the sidelines, until the outlook for stocks gets better.

These numbers show why I am interested in dividend and dividend growth strategies as well. Look at these numbers and compare them to dividend yields. My impression is that dividend and dividend growth strategies are safer than the conventional approach, lasting far into the future, and they allow you to withdraw more than the conventional approach (at least, at today's valuations if you demand a reasonably high level of safety).

Have fun.

John R.
hocus2004
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Post by hocus2004 »

"Today 1.9 2.92 3.9"

Thanks, JWR1945.

So you only give up six-tenths of a percentage point of withdrawal rate to increase your minimum portfolio value at the end of 30 years from $1 to the inflation-adjusted value of your portfolio at your retirement start date. That's a helpful thing to know, in my view.
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Post by JWR1945 »

Here is what happens to Minimum Balances if you withdraw at the CTVR80 rates. This is of value when monitoring progress.
I have made a (straight line) linear curve fit of the 1923-1972 CTVR80 Minimum Balances versus the Percentage Earnings Yield 100E10/P. The equation is y = 5518.2x + 27808 based upon an initial balance of $100000. The CTVR80 minimum balance in (real) dollars is y. The percentage earnings yield is x. R squared is 0.5185. My eyeball estimate of the confidence limits is plus and minus $25000.

Here are the minimum balances associated with Constant Terminal Value Rates (CTVR80) for an 80% stock portfolio assuming that the initial balance is $100000. These are the most likely minimum balances when withdrawals are at the CTVR80 rates.

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1995    $55099
1996    $50092
1997    $47284
1998    $44601
1999    $41407
2000    $40414
2001    $42730
2002    $46033
2003    $51911
Nov 03    $49115
Today     $48933
Minimum Balances to Maintain Constant Terminal Values for 80% Stocks. The Initial Balance is $100000. The Calculated Minimum Balances occur for withdrawals equal to CTVR80.

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Year  Lower-Bound   Calculated  Upper-Bound
1995    $30099    $55099    $80099
1996    $25092    $50092    $75092
1997    $22284    $47284    $72284
1998    $19601    $44601    $69601
1999    $16407    $41407    $66407
2000    $15414    $40414    $65414
2001    $17730    $42730    $67730
2002    $21033    $46033    $71033
2003    $26911    $51911    $76911
Nov 03    $24115    $49115    $74115
Today     $23933    $48933    $73933
I have assumed used plus and minus $25000 for the confidence limits.

Have fun.

John R.
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Post by JWR1945 »

Here is the other equation.
I have made a (straight line) linear curve fit of the 1923-1972 CTVR80 Minimum Balances versus the value of CTVR80. The equation is y = 7977.3x + 25446 based upon an initial balance of $100000. The CTVR80 minimum balance in (real) dollars is y. The value of CTVR80 in percent is x. R squared is 0.6306. My eyeball estimate of the confidence limits is plus and minus $20000.
Here are today's Safe, Calculated and High Risk Levels to Maintain Constant Terminal Values for 80% Stocks. The Calculated Rates correspond to CTVR80.

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For today:
Safe  1.9%
Calculated (CTVR80)  2.92%
High Risk  3.9%
Using the formula, if a rate that is calculated to be Safe is actually needed to Maintain a Constant Terminal Value with 80% stocks, these are the Minimum Balances during the 30-year period (assuming an Initial Balance of $100000).
Lower Bound: $20603.
Safe Rate: $40603.
Upper Bound: $60603.

Using the formula, if the Calculated CTVR80 rate is what is actually needed to Maintain a Constant Terminal Value with 80% stocks, these are the Minimum Balances during the 30-year period (assuming an Initial Balance of $100000).
Lower Bound: $28740.
Calculated (CTVR80) Rate: $48740.
Upper Bound: $68740.

Using the formula, if a rate that is calculated to be at High Risk actually does Maintain the Constant Terminal Value with 80% stocks, these are the Minimum Balances during the 30-year period (assuming an Initial Balance of $100000).
Lower Bound: $36557.
High Risk Rate: $56557.
Upper Bound: $76557.

I have assumed used plus and minus $20000 for the confidence limits.

These numbers help you prepare for what actually happens during the 30-year period. If you are withdrawing at the Calculated CTVR80 Rate and if it is appropriate, you should expect your portfolio balance to drop down to 48.74% of its initial value sometime during the 30 years. It could fall to 28.74%. It might only fall to 68.74%.

If you have prepared for the worst and chosen to withdraw at the Safe Rate, you have prepared for the possibility that your portfolio's balance would drop between 20.603% and 60.603% of its initial value (with 40.603% being most likely). If the balance remains above 60.603% as you monitor your progress and if it seems as if it will stay above that amount, you will know that you have been overly conservative and you can safely withdraw more.

Have fun.

John R.
Mike
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Post by Mike »

1.9% This is the dividend yield plus a little bit, the same as previous calculations. It seems to be a fairly consistent number.
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Post by JWR1945 »

unclemick wrote:I would make the case for look back variable take -out keyed off SEC yield with some sensible upper and lower bounds based on JWR's other work - say 2- 5% ballpark(without looking at the numbers). I would also uncouple from inflation and let 'Mr. Market' tell me what I could have.
We can do quite a bit along these lines. Except for the conventional type of withdrawals, everything is in terms of nominal dollars. We can withdraw a portion of the current balance and/or break it into components of dividends and/or interest. A major plus is that we can analyze data easier and better than before. In many cases what used to be extremely difficult is easy.
Mike wrote:1.9% This is the dividend yield plus a little bit, the same as previous calculations. It seems to be a fairly consistent number.
Should we be satisfied with 1.9%?

I doubt that you will be surprised that Verizon VZ is yielding 4.02% this morning. But Merck MRK has been beaten down enough that it now yields 3.49%. IIRC, these are both Dividend Achievers according to a recent tabulation by Mergent. This means that they provide consistent dividends that grow.

It seems to me that we can do better than 1.9% even now. We should be able to match the 2.5% (real) yield-to-maturity recently available from TIPS (but not this morning) through stock dividends. IMHO, we can do a lot better.

Have fun.

John R.
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Post by JWR1945 »

CTVR80 versus Earnings Yield
CTVR80 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 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 = 0.7033x + 0.2133%, where y is the Constant Terminal Value Rate and x is the Percentage Earnings Yield. R squared was 0.8501%, which is exceedingly high. I have not calculated confidence limits yet. Using an eyeball estimate, they are likely to be about plus and minus 1%.[I have corrected the equation and R-squared.]
..
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 1.10%. [This is 1.64 times the standard deviation of 0.669% using 48 degrees of freedom.]

I have reported 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 80% stocks: Year, P/E10, 100E10/P, CTVR80, Calculated Withdrawal Rate for a Constant Terminal Value

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1923    8.2    12.2    7.6   8.79
1924    8.1    12.3    7.8   8.90
1925    9.7    10.3    7.4   7.46
1926   11.3     8.8    6.5   6.44
1927   13.2     7.6    6.2   5.54
1928   18.8     5.3    4.7   3.95
1929   27.1     3.7    3.5   2.81
1930   22.3     4.5    3.7   3.37
1931   16.7     6.0    4.2   4.42
1932    9.3    10.8    6.2   7.78
1933    8.7    11.5    7.1   8.30
1934   13.0     7.7    5.3   5.62
1935   11.5     8.7    6.3   6.33
1936   17.1     5.8    4.6   4.33
1937   21.6     4.6    3.6   3.47
1938   13.5     7.4    5.2   5.42
1939   15.6     6.4    4.8   4.72
1940   16.4     6.1    4.8   4.50
1941   13.9     7.2    6.2   5.27
1942   10.1     9.9    7.9   7.18
1943   10.2     9.8    7.7   7.11
1944   11.1     9.0    6.8   6.55
1945   12.0     8.3    5.9   6.07
1946   15.6     6.4    5.6   4.72
1947   11.5     8.7    7.8   6.33
1948   10.4     9.6    8.2   6.98
1949   10.2     9.8    8.1   7.11
1950   10.7     9.3    8.0   6.79
1951   11.9     8.4    7.0   6.12
1952   12.5     8.0    6.0   5.84
1953   13.0     7.7    5.9   5.62
1954   12.0     8.3    6.4   6.07
1955   16.0     6.3    4.5   4.61
1956   18.3     5.5    3.8   4.06
1957   16.7     6.0    4.2   4.42
1958   13.8     7.2    4.7   5.31
1959   18.0     5.6    3.5   4.12
1960   18.3     5.5    3.6   4.06
1961   18.5     5.4    3.4   4.01
1962   21.2     4.7    3.2   3.53
1963   19.3     5.2    3.5   3.86
1964   21.6     4.6    3.0   3.47
1965   23.3     4.3    2.6   3.23
1966   24.1     4.1    2.7   3.13
1967   20.4     4.9    3.3   3.66
1968   21.5     4.7    3.3   3.48
1969   21.2     4.7    3.4   3.53
1970   17.1     5.8    4.1   4.33
1971   16.5     6.1    4.0   4.48
1972   17.3     5.8    3.7   4.28
1973   18.7     5.3    3.4   3.97
1974   13.5     7.4    4.4   5.42
1975    8.9    11.2    5.9   8.12
1976   11.2     8.9    4.2   6.49
1977   11.4     8.8    3.7   6.38
1978    9.2    10.9    4.1   7.86
1979    9.3    10.8    3.2   7.78
1980    8.9    11.2    2.1   8.12
1981-2003 with 80% stocks: Year, P/E10, 100E10/P, Calculated Withdrawal Rate for a Constant Terminal Value

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1981     9.3   10.71    7.75
1982     7.4   13.48    9.70
1983     8.7   11.51    8.31
1984     9.8   10.25    7.42
1985     9.9   10.07    7.30
1986    11.7    8.57    6.24
1987    14.7    6.78    4.98
1988    13.7    7.28    5.33
1989    15.2    6.60    4.85
1990    17.0    5.88    4.35
1991    15.6    6.42    4.73
1992    19.6    5.11    3.81
1993    20.4    4.90    3.66
1994    21.5    4.65    3.48
1995    20.5    4.89    3.65
1996    25.4    3.93    2.98
1997    29.2    3.43    2.62
1998    33.8    2.96    2.30
1999    40.9    2.44    1.93
2000    44.7    2.24    1.79
2001    37.0    2.70    2.12
2002    30.3    3.30    2.54
2003    22.9    4.37    3.29
1923-1980 with 80% stocks:Year, CTVR80, Safe Withdrawal Rate for a Constant Terminal Value, Calculated Withdrawal Rate for a Constant Terminal Value, High Risk Rate for a Constant Terminal Value

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1923   7.6   7.69    8.79    9.89
1924   7.8   7.80    8.90    9.99
1925   7.4   6.37    7.46    8.56
1926   6.5   5.34    6.44    7.54
1927   6.2   4.44    5.54    6.64
1928   4.7   2.86    3.95    5.05
1929   3.5   1.71    2.81    3.91
1930   3.7   2.27    3.37    4.47
1931   4.2   3.33    4.42    5.52
1932   6.2   6.68    7.78    8.87
1933   7.1   7.20    8.30    9.40
1934   5.3   4.53    5.62    6.72
1935   6.3   5.23    6.33    7.43
1936   4.6   3.23    4.33    5.42
1937   3.6   2.37    3.47    4.57
1938   5.2   4.32    5.42    6.52
1939   4.8   3.62    4.72    5.82
1940   4.8   3.40    4.50    5.60
1941   6.2   4.18    5.27    6.37
1942   7.9   6.08    7.18    8.27
1943   7.7   6.01    7.11    8.21
1944   6.8   5.45    6.55    7.65
1945   5.9   4.98    6.07    7.17
1946   5.6   3.62    4.72    5.82
1947   7.8   5.23    6.33    7.43
1948   8.2   5.88    6.98    8.07
1949   8.1   6.01    7.11    8.21
1950   8.0   5.69    6.79    7.88
1951   7.0   5.03    6.12    7.22
1952   6.0   4.74    5.84    6.94
1953   5.9   4.53    5.62    6.72
1954   6.4   4.98    6.07    7.17
1955   4.5   3.51    4.61    5.71
1956   3.8   2.96    4.06    5.15
1957   4.2   3.33    4.42    5.52
1958   4.7   4.21    5.31    6.41
1959   3.5   3.02    4.12    5.22
1960   3.6   2.96    4.06    5.15
1961   3.4   2.92    4.01    5.11
1962   3.2   2.43    3.53    4.63
1963   3.5   2.76    3.86    4.96
1964   3.0   2.37    3.47    4.57
1965   2.6   2.13    3.23    4.33
1966   2.7   2.03    3.13    4.23
1967   3.3   2.56    3.66    4.76
1968   3.3   2.39    3.48    4.58
1969   3.4   2.43    3.53    4.63
1970   4.1   3.23    4.33    5.42
1971   4.0   3.38    4.48    5.57
1972   3.7   3.18    4.28    5.38
1973   3.4   2.88    3.97    5.07
1974   4.4   4.32    5.42    6.52
1975   5.9   7.02    8.12    9.21
1976   4.2   5.39    6.49    7.59
1977   3.7   5.28    6.38    7.48
1978   4.1   6.76    7.86    8.96
1979   3.2   6.68    7.78    8.87
1980   2.1   7.02    8.12    9.21
1981-2003 with 80% 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

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1981    6.65    7.75    8.84
1982    8.60    9.70   10.79
1983    7.21    8.31    9.41
1984    6.32    7.42    8.52
1985    6.20    7.30    8.40
1986    5.14    6.24    7.34
1987    3.89    4.98    6.08
1988    4.23    5.33    6.43
1989    3.76    4.85    5.95
1990    3.25    4.35    5.45
1991    3.63    4.73    5.83
1992    2.71    3.81    4.91
1993    2.56    3.66    4.76
1994    2.38    3.48    4.58
1995    2.55    3.65    4.75
1996    1.88    2.98    4.08
1997    1.53    2.62    3.72
1998    1.20    2.30    3.39
1999    0.83    1.93    3.03
2000    0.69    1.79    2.88
2001    1.02    2.12    3.21
2002    1.44    2.54    3.63
2003    2.19    3.29    4.38
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 1.53%, 2.62% and 3.72% respectively. A person who retires today with a high stock (80%) portfolio and who withdraws 2.7% to 2.8% 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 3.8%, he is almost certain to have lost buying power at year 30. If he limits his withdrawals to 1.5%, he is almost certain to have increased his buying power at year 30.

Have fun.

John R.
hocus2004
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Post by hocus2004 »

"If he limits his withdrawals to 1.5%, he is almost certain to have increased his buying power at year 30. "

JWR1945:

I find these recent numbers most helpful. Can you say what the equivalent number is using the conventional methodology assumptions?

Under the conventional methodology, the number would be the same at all valuation levels, of course. I'm interested in knowing how far it takes you below 4 percent to be sure not of having $1 in your portfolio at the end of 30 years, but of retaining the real value of your starting-point portfolio for 30 years.
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Post by JWR1945 »

Users of the conventional methodology would select the smallest of the CTVR80 numbers and claim that it was 100% safe.

The smallest value of CTVR80 occurred in the 1966 sequence. It was 2.6%.

[The 1980 sequence is still in progress. The latest complete sequence started in 1972 (since dummy data are used in 2003-2010).]

[Before 1923, the lowest value of CTVR80 was 3.3%.]

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 2.6%. In reality, their odds would be very close to 50-50.

Have fun.

John R.
JWR1945
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Post by JWR1945 »

Here is a summary of how well the conventional methodology would have predicted safety at today's valuations. The conventional answer is taken as the minimum value between 1923 and 1980 (or 1972, when appropriate). Today's Safe, Calculated and High Risk Rates are roughly equal to those of 1997. [Today's P/E10 is close to 28, which is slightly less than that of 1997.]

HFWR50: Conventional answer: 2.8% from 1937
1997 rates: 2.37%, 3.25% and 4.13%
Confidence limits: plus and minus 0.88%
Standard deviation: 0.54%

Conventional answer (2.8%) is close to 1997 calculated rate (3.25%) minus one standard deviation. (The standard deviation is 0.54%.)

HFWR80: Conventional answer: 2.4% from 1966
1997 rates: 1.00%, 2.87% and 4.73%
Confidence limits: plus and minus 1.87%
Standard deviation: 1.10%

Conventional answer (2.4%) is close to 1997 calculated rate (2.87%) minus one-half standard deviation. (The standard deviation is 1.10%.)

CTVR50: Conventional answer: 2.4% from 1937
1997 rates: 1.83%, 2.55% and 3.27%
Confidence limits: plus and minus 0.72%
Standard deviation: 0.44%

Conventional answer (2.4%) is close to 1997 calculated rate (2.55%) minus one-third standard deviation. (The standard deviation is 0.44%.)

CTVR80: Conventional answer: 2.6% from 1965
1997 rates: 1.53%, 2.62% and 3.72%
Confidence limits: plus and minus 1.10%
Standard deviation: 0.67%

Conventional answer (2.6%) is close to 1997 calculated rate (2.62%) minus zero standard deviations. (The standard deviation is 1.10%.)

Roughly speaking, the conventional answer is close to, but less than, the calculated rate at today's valuations. If it were equal to the calculated rate, the conventional answer would have a 50% chance of predicting the correct outcome. That is, the conventional answer is claimed to provide perfect safety but it actually provides only a 50% chance of being safe. When it differs by minus one standard deviation, the conventional answer has an 84% chance of predicting the correct outcome. That is, the conventional answer is claimed to provide perfect safety but it actually provides only an 84% chance of being safe.

The conventional answer is claimed to provide perfect safety. It actually provides a chance of being safe between 50% and 84%.

It is surprising that the smallest value of HFWR80 (2.4%) is lower than the smallest value of CTVR80 (2.6%). HFWR80 is established when a portfolio's balance falls to one-half of its initial value (in real dollars), which can occur at any time within the first 30 years. CTVR80 is established when the balance at year 30 equals the initial balance (in real dollars). Portfolios typically fall at first and then rise to their balances at year 30. When one withdraws 2.6% from an 80% stock portfolio, it falls to less than one-half of its initial balance (plus inflation) before rising all the way back to its initial balance (plus inflation) at year 30.

Have fun.

John R.
Mike
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Post by Mike »

Would you think this data better fit range widening by the square root law of the bell curve, or Mandlebrot's 3/4 power (.73) (page 178)?
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