GARCH

Research on Safe Withdrawal Rates

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JWR1945
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Post by JWR1945 »

I have added easy to copy listings to my tables with HDBR50 and HDBR80. I have included the percentage earnings yield 100E10/P and P/E10 listings as well.

New HDBR Tables dated Sun Jan 11, 2004.
http://nofeeboards.com/boards/viewtopic.php?t=1962

This should make life easier for gummy if I have posted these tables soon enough. I apologize for the delay.

Have fun.

John R.
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Post by JWR1945 »

Here are the equations for the 30-year Historical Surviving Withdrawal Rates of HDBR50 when using only twenty start years.

HDBR50 Curve Fitting Results:
y=Historical Surviving Withdrawal Rate
x=percentage earnings yield 100E10/P (using Professor Shiller's P/E10).

Code: Select all

1871-1890
y = 0.4194x + 4.7548
R2 = 0.2591

1891-1910
y = 0.0241x + 5.0012
R2 = 0.0024

1911-1930
y = 0.3072x + 3.1385
R2 = 0.7875

1931-1950
y = 0.3971x + 2.3409
R2 = 0.4373

1951-1970
y = 0.658x + 1.3092
R2 = 0.9561
Look at the values of R-squared (listed as R2).

Retirement start years of 1891-1910 show very little correlation between the percentage earnings yield and the Historical Surviving Withdrawal Rates.

Since we have found that the first eleven years are the most important for predicting portfolio success, the anomalous results are associated primarily with the years of 1891-1921.

Have fun.

John R.
JWR1945
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Post by JWR1945 »

Here are the values for CPI that are actually used by the Retire Early Safe Withdrawal Calculator, version 1.61, dated November 7, 2002 (when CPI is selected). The same values are in all of my calculators, which are modified versions.

The original source is Professor Robert Shiller's database.

This is in an easy to copy form.

1871-1920

Code: Select all

12.46
12.65
12.94
12.37
11.51
10.85
10.94
9.23
8.28
9.99
9.42
10.18
9.99
9.23
8.28
7.99
7.99
8.37
7.99
7.61
7.80
7.33
7.90
6.85
6.57
6.66
6.47
6.66
6.76
7.90
7.71
7.90
8.66
8.28
8.47
8.47
8.85
8.66
8.94
9.90
9.23
9.13
9.80
10.00
10.10
10.40
11.70
14.00
16.50
19.30
1921-1980

Code: Select all

19.00
16.90
16.80
17.30
17.30
17.90
17.50
17.30
17.10
17.10
15.90
14.30
12.90
13.20
13.60
13.80
14.10
14.20
14.00
13.90
14.10
15.70
16.90
17.40
17.80
18.20
21.50
23.70
24.00
23.50
25.40
26.50
26.60
26.90
26.70
26.80
27.60
28.60
29.00
29.30
29.80
30.00
30.40
30.90
31.20
31.80
32.90
34.10
35.60
37.80
39.80
41.10
42.60
46.60
52.10
55.60
58.50
62.50
68.30
77.80
Have fun.

John R.
JWR1945
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Post by JWR1945 »

Here are the values for CPI that are actually used by the Retire Early Safe Withdrawal Calculator, version 1.61, dated November 7, 2002 (when CPI is selected). The same values are in all of my calculators, which are modified versions.

The original source is Professor Robert Shiller's database.

This is in an easy to read form.

Notice the years of declining prices in the late 1800s. They bottomed out in 1897. Even though the late 1800s were a time of great prosperity, the index fell much more than they did in the Great Depression.

Year CPI

Code: Select all

1871   12.46
1872   12.65
1873   12.94
1874   12.37
1875   11.51
1876   10.85
1877   10.94
1878    9.23
1879    8.28
1880    9.99
1881    9.42
1882   10.18
1883    9.99
1884    9.23
1885    8.28
1886    7.99
1887    7.99
1888    8.37
1889    7.99
1890    7.61
1891    7.80
1892    7.33
1893    7.90
1894    6.85
1895    6.57
1896    6.66
1897    6.47
1898    6.66
1899    6.76
1900    7.90
1901    7.71
1902    7.90
1903    8.66
1904    8.28
1905    8.47
1906    8.47
1907    8.85
1908    8.66
1909    8.94
1910    9.90
1911    9.23
1912    9.13
1913    9.80
1914   10.00
1915   10.10
1916   10.40
1917   11.70
1918   14.00
1919   16.50
1920   19.30
Year CPI

Code: Select all

1921   19.00
1922   16.90
1923   16.80
1924   17.30
1925   17.30
1926   17.90
1927   17.50
1928   17.30
1929   17.10
1930   17.10
1931   15.90
1932   14.30
1933   12.90
1934   13.20
1935   13.60
1936   13.80
1937   14.10
1938   14.20
1939   14.00
1940   13.90
1941   14.10
1942   15.70
1943   16.90
1944   17.40
1945   17.80
1946   18.20
1947   21.50
1948   23.70
1949   24.00
1950   23.50
1951   25.40
1952   26.50
1953   26.60
1954   26.90
1955   26.70
1956   26.80
1957   27.60
1958   28.60
1959   29.00
1960   29.30
1961   29.80
1962   30.00
1963   30.40
1964   30.90
1965   31.20
1966   31.80
1967   32.90
1968   34.10
1969   35.60
1970   37.80
1971   39.80
1972   41.10
1973   42.60
1974   46.60
1975   52.10
1976   55.60
1977   58.50
1978   62.50
1979   68.30
1980   77.80
Have fun.

John R.
JWR1945
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Post by JWR1945 »

Here are the equations for the 30-year Historical Surviving Withdrawal Rates of HDBR80 when using only twenty start years.

HDBR80 consists of 80% stocks and 20% commercial paper.

HDBR80 Curve Fitting Results:
y = Historical Surviving Withdrawal Rate
x = percentage earnings yield 100E10/P

Code: Select all

1871-1890
y = 0.6721x + 3.2028
R2 = 0.5259

1891-1910
y = 0.1114x + 4.9226
R2 = 0.0245

1911-1930
y = 0.4194x + 2.7638
R2 = 0.8089

1931-1950
y = 0.7189x + 1.5714
R2 = 0.5634

1951-1970
y = 1.1936x - 1.2958
R2 = 0.9495
Pay special attention to R-squared. It points to an anomaly associated with 1891-1910.

Retirement start years of 1891-1910 show very little correlation between the percentage earnings yield and the Historical Surviving Withdrawal Rates.

Variations around 1891-1910 for HDBR80
y = Historical Surviving Withdrawal Rate
x = percentage earnings yield 100E10/P

Code: Select all

1881-1900
y = 0.5113x + 3.445
R2 = 0.3858

1891-1910
y = 0.1114x + 4.9226
R2 = 0.0245

1901-1920
y = 0.4215x + 2.3582
R2 = 0.8776
Looking at these results and Professor Shiller's CPI numbers (that I extracted from my calculator), this anomaly seems to be associated with the reversal from declining prices that bottomed out in 1897. Later, prices increased.

I do not know the extent to which this reversal was a result of changing economic conditions. I do know that the late 1800s saw major advances (especially those associated with transportation) that reduced prices sharply without cutting into profitability. In addition, these were the days of the Gold standard and before the creation of the Federal Reserve Banking System.

A side effect of these generally declining prices was that commercial paper showed huge profits simply because interest rates were always above zero.

Have fun.

John R.
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gummy
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Post by gummy »

When I get a minute I'll change the HFWR charts to HSWR charts.

In the meantime, peek at this chart:


After spending a couple of weeks on GARCH (and volatility clustering) it looks so familiar!!
JWR1945
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Post by JWR1945 »

gummy wrote:When I get a minute I'll change the HFWR charts to HSWR charts....
Why not keep them both?

I think that your HFWR charts are interesting.

I know that many people, especially younger retirees, are more interested in HFWR than in HSWR. They don't want financial problems to take away from their happiness if they live longer than 30 years.

Have fun.

John R.
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Post by JWR1945 »

gummy wrote:In the meantime, peek at this chart:


After spending a couple of weeks on GARCH (and volatility clustering) it looks so familiar!!
They should if the original hypothesis that prices are closely related to withdrawal rates is true.

If so, we would expect HFWR charts and price charts to share some of their properties.

Have fun.

John R.
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Post by gummy »

Here's something to think about:

1: We'd like to predict next year's SWR.

2: We note the intimate relationship between SWR's and E10/P ... in the past.

3: We also note that GARCH (Nobel prize, 2003) is a mechanism for predicting tomorrow's daily volatility, based upon recent daily volatility data ... and that GARCH generates "clustering" (as observed in historical daily volatility).

4: We also note that historical yearly SWR exhibits similar clustering (as per the pretty chart above)

5: So we use GARCH to predict next year's SWR ... but (of course) with years instead of days.

5: Then we win the 2006 Nobel prize :D

P.S.
I have a scheme much simpler than GARCH that does a similar thing.
Mine is much like the riskmetrics model.
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Post by bpp »

Gummy wrote:I still don't understand those chart labels :twisted:
Are there two-count-em-two HDBR50 Fits ?
John R. wrote:PS#1: Yes, that is a glitch. The bottom line (magenta or reddish purple) should be labeled HDBR80. [It would have been better if the data and the lines had shared the same colors.]
Sorry about the typo in the plot labels. :oops: I ran those plots off pretty quickly, and never even noticed the mistake! Matching the colors instead of letting gnuplot pick them automatically would have been a good idea, too.

Your plots are much nicer, Gummy.

Bpp
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Post by JWR1945 »

To Bpp:

If you would like to update your plots, I am sure that ES will be glad to incorporate them. Your plots have been exceedingly helpful. Just one glance and a viewer knows that Historical Surviving Withdrawal Rates (also known as Historical Database Rates) and P/E10 are closely related.

Have fun.

John R.
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Post by ElSupremo »

Greetings John :)
I am sure that ES will be glad to incorporate them.
I'll be happy to do anything I can to help. Just let me know what you want done.
"The best things in life are FREE!"

www.nofeeboards.com
JWR1945
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Post by JWR1945 »

gummy wrote:Here's something to think about:

1: We'd like to predict next year's SWR.

2: We note the intimate relationship between SWR's and E10/P ... in the past.

3: We also note that GARCH (Nobel prize, 2003) is a mechanism for predicting tomorrow's daily volatility, based upon recent daily volatility data ... and that GARCH generates "clustering" (as observed in historical daily volatility).

4: We also note that historical yearly SWR exhibits similar clustering (as per the pretty chart above)

5: So we use GARCH to predict next year's SWR ... but (of course) with years instead of days.

5: Then we win the 2006 Nobel prize :D

P.S.
I have a scheme much simpler than GARCH that does a similar thing. Mine is much like the riskmetrics model.
While implementing your own approach, consider taking advantage of the following incomplete set of software and instructions. I think that it comes very close to describing a very useful, commercially valuable stock market price generator. My impression is that they fail this only because they are perfectionists. They do not realize the value of what they have already done.

I went to this site after following links in Benoit Mandelbrot's book.
http://classes.yale.edu/fractals/
I think that there is enough information to build reasonable surrogates for stocks and the stock market (which includes the S&P500 index).

They come very close to providing everything that we would need. They have downloadable software. (I think that it is sufficient.)

They even provide pictures. They provide comparisons of real data and generated data using various inputs to what they call Iterated Function Systems (IFS). Most of those pictures look realistic to me.

They provide sufficient detail to generate Trading Time from (the actual) Clock Time and then to drive a conventional (Brownian) probability distribution of price differences. [Making this composite function appears to be the best approach. Brownian motion corresponds to taking random steps from a standard Gaussian, normal, bell shaped distribution without any memory from previous steps.]

They do not provide a simple, standard piece of software to simulate price changes. My impression is that they are demanding too much realism. There is money to be made by packaging input software for financial planning Monte Carlo models. Few, if any, require a high degree of fidelity. All, or almost all, of them would benefit greatly from simulating price clusters.

Have fun.

John R.
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gummy
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Post by gummy »

While implementing your own approach, consider taking advantage of the following incomplete set of software and instructions.
Actually, I have no intention of doing more than providing space for your tutorial ... and maybe a few charts :D

However, when I read what's there now, I say to myself:

It's January, 2005.

I have all the historical data anyone could want, going back a hundred years and ending last month

I see all the relationships, the charts and the numbers that can be generated with this info.

Now I ask: What should my withdrawal rate be this year"
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Post by JWR1945 »

gummy wrote:However, when I read what's there now, I say to myself:

It's January, 2005.
...
Now I ask: What should my withdrawal rate be this year"
Professor Robert Shiller's database does not have today's value of P/E10. It is necessary to extrapolate from an earlier, but recent, value.

From Professor Robert Shiller's database: in January 2004, the S&P500 price (or index value) was 1132.52 and P/E10 was 27.65.

From cbs.marketwatch.com using the symbol sp500: today's index value (or price) of the S&P500 is 1185.

Assuming that E10 has not changed very much (since it is the average of a whole decade's worth of earnings), today's value of P/E10 is approximately equal to [today's S&P500 price/last year's S&P500 price]*[last year's value of P/E10] = [1185 / 1132.52]*[27.65] = 28.93.

The formulas require the percentage earnings yield 100% / [P/E10]. Today's percentage earnings yield is very close to 3.46%.

Therefore: use x = 3.46 or 3.5 in the formulas.

Have fun.

John R.
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Post by hocus2004 »

Now I ask: What should my withdrawal rate be this year"

That's always going to be a personal judgment call, isn't it?
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Post by gummy »

Look here:
http://www.gummy-stuff.org/JWR.htm#HSWR
and see if'n I got the procedure right.

In my explanation, what's N?
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Post by gummy »

That's always going to be a personal judgment call, isn't it?
I realize it's a judgment call, but if the stuff y'all have been working on for years doesn't give some guidance then I don't understand its usefullness.

Here's something which occurs to me:

Suppose that, each January (starting in Jan, 1970), you estimated (predicted?) the SWR for the coming year (using the procedure you've been working on) and actually withdrew that amount.

What would your porfolio be, 30 years later (in Jan, 2000)?
Has anybuddy looked at that?
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Post by JWR1945 »

For gummy:

Change: "Determine E10/P over the past N years. (Each value involves ten years of data.)" to something with this information: "Look up E10/P from Professor Shiller's database at the start each year of the historical sequences that you are going to use. Typically, this is 1921-1980 or 1923-1980. Sometimes, it is necessary to limit the historical sequences to completed sequences. In such cases, the final year of each sequence must be 2002 or earlier. [The Retire Early Safe Withdrawal Calculator and its modified versions available from the NoFeeBoards.com website use dummy data with heavy losses for 2003-2010.] Sometimes, you will be interested in starting from 1871, typically using start years of 1871-1980 (or 1881-1980 because of uncertainty regarding how the 1871-1880 values of P/E10 were determined)."

Professor Shiller's web address is:
http://www.econ.yale.edu/~shiller/

[P/E10 data are used by the calculators. This provides a convenient alternative source of P/E10 for those willing to look into the details of spreadsheet calculations.]

Change: "the Historical Survival Withdrawal Rates (where the final portfolio is greater than $0)... to "the Historical Survival Withdrawal Rates (where the final portfolio is an amount slightly greater than $0)...

Your procedure correctly describes how to determine the Calculated Rate. To determine the Safe Withdrawal Rate and the High Risk Rate, we must provide confidence limits. The lower confidence limit is the Safe Withdrawal Rate and the higher confidence limit is the High Risk Rate.

Eyeball estimates are sufficient in most cases. Draw lines parallel to the line given by equation that capture almost all of the individual data points. The lower line is the Safe Withdrawal Rate and the upper line is the High Risk Rate.

For more precise estimates, use standard procedures to calculate variances and standard deviations. That is, calculate the differences between the data points and the calculated rates, square them, take the sum and divide by the number of the degrees of freedom. [See the section that follows regarding the number of the degrees of freedom to use.] Take the square root to determine the standard deviation. Set the confidence limits at plus and minus 1.64 standard deviations (corresponding roughly to a 90% confidence level).

The withdrawal rates that people actually choose are called Personal Withdrawal Rates. Typically, they are a little bit higher than the Safe Withdrawal Rate but below the Calculated Rate. Some people prefer to withdraw even less than the Safe Withdrawal Rate.

Have fun.

John R.
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Post by JWR1945 »

Suppose that, each January (starting in Jan, 1970), you estimated (predicted?) the SWR for the coming year (using the procedure you've been working on) and actually withdrew that amount.

What would your portfolio be, 30 years later (in Jan, 2000)?
Has anybuddy looked at that?
No.

The procedure would require that the SWR calculation for the second year be based upon a time frame of 29 years. For the third year, it would have to be from a time frame of 28 years. And so on.

That's a lot of equations to calculate. We also have to determine the lower confidence limits for all of them.

Have fun.

John R.
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