GARCH

Research on Safe Withdrawal Rates

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Post by hocus2004 » Mon Jan 17, 2005 12:16 pm

One refers to "the most recent post," then there are a couple more in between

Don't forget, gummy, this stuff is someday going to stand the world of conventional investing advice on its head. When that happens, it may be the tutorial placed on your web site that people point to as the straw added to the camel's back that caused the "Stocks for the Long Run" Investing Paradigm to come crashing to the ground.

We are making history with this thread. And it is all being recorded in the permanent Post Archives as we speak the words that send things in Direction A or in Direction B. When you think about it from that perspective, it's kind of cool that our words are being transcribed as they are spoken in real time.

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Post by hocus2004 » Mon Jan 17, 2005 12:23 pm

And is it not more than a little bit cool that a board that is being boycotted by a large segment of the posting community can generate enough posts for a thread titled "GARCH" to extend to a second page? I sure think so.

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Post by JWR1945 » Mon Jan 17, 2005 12:59 pm

This is my first cut. The graph of Historical Database Rates (for HDBR50 and HDBR80 portfolios) from the SWR Research Section goes along with this. This presents the technical issues. The fun part is taking advantage of the pictures (i.e., using Excel to plot curves). The hard part is getting a handle on the statistics.

Safe Withdrawal Rates versus Valuations

There are many factors that affect the safety of withdrawals during retirement. Prices are one of them. Prices are special. You control the price that you pay for an investment.

Our first major advance at the SWR Research Group was to relate Safe Withdrawal Rates quantitatively with valuations. Our most successful indicator of valuations so far is Professor Robert Shiller's P/E10. [P/E10 is the price or index value of the S&P500 divided by the average of the last ten years of earnings.]

We have had to draw some precise distinctions between what has happened (which we call Historical Surviving Withdrawal Rates or Historical Database Rates), what is likely to happen (which we call Calculated Rates) and the confidence limits about the Calculated Rates. We refer to the lower confidence limit as the Safe Withdrawal Rate. We refer to the higher confidence limit as the High Risk Rate (or the High Risk Withdrawal Rate).

Early researchers estimated the Safe Withdrawal Rate to be the same as the smallest Historical Surviving Withdrawal Rate. They did not provide confidence limits.

Historical Surviving Withdrawal Rates (or Historical Database Rates) are based on using an actual historical sequence of investment returns. A hypothetical portfolio would have survived for a specified number of years at the Historical Surviving Withdrawal Rate. Its balance would have fallen to zero or become negative at a slightly higher (0.1%) withdrawal rate. Unless we identify the first year of a historical sequence, the Historical Surviving Withdrawal Rate is the lowest among those that we investigate (typically, 1921-1980). We adjust withdrawals to match inflation (and deflation).

We have learned that today's stock market is well outside of the range of the historical database. [This is true using both P/E10 and dividend yields.] We have made suitable adjustments.

We have found that earnings yield (using the average of the past decade's earnings) does an excellent job of predicting Safe Withdrawal Rates. It is better than using dividend yield (plus about 1%) as a lower bound. The earnings yield overcomes the problem of surprise dividend cuts.

When we plot Historical Surviving Withdrawal Rates (which are also known as Historical Database Rates) versus the percentage earnings yield (or 100% / [P/E10] ), it is immediately apparent that the two are related. This relationship is strongest from the 1920s on. It is not entirely clear why the relationship was not as strong in the earlier period covered by the available data (1871-2002). There are many possible reasons. One likely reason is related to falling prices at the end of the 19th century. In many of those years, commercial paper would have provided an inflation-adjusted (i.e., real) Safe Withdrawal Rate of 5% or 6% simply because interest rates always stayed positive! In any event, the data show good predictability using P/E10 from the 1920s on.

[Many of our curves start with 1923 instead of 1921. The reason is to get a better curve fit with straight lines. They have a disproportionately large effect when plotting Historical Surviving Withdrawal Rates versus the percentage earnings yield. Years 1921 and 1922 were among those with the best prices ever. In addition, they exhibit saturation. Their higher earnings yields are associated with higher Historical Surviving Withdrawal Rates, just not as much higher as a straight line would indicate.]

We use Excel for plotting Historical Surviving Withdrawal Rates (starting from 1921 or 1923) versus the percentage earnings yield (100% / [P/E10] ) and for curve fitting. It works remarkably well. We have found that even a single decade of retirement starting years provides good fits. Using more data always helps. Using curves derived from data with earnings yields similar to those of interest is always best. That is, it is a good idea to minimize the amount of extrapolation.

Statistical Approximations

Handling the statistics is a more difficult task. There are no standard formulas available for us to use.

We are content to apply the Central Limit Theorem. We restrict ourselves to very coarse levels of precision. We act as if the actual distribution were Gaussian (i.e., normal or bell shaped). We limit ourselves to 90% confidence limits. We reject outright any claims to high statistical precision (such as 98% or 99%). We hope that the actual precision is in the right ballpark (such as between 80% and 95%).

The underlying issue with statistics is that our historical sequences overlap.

One way of handling such a situation is to demand almost complete independence of all data sets. Typically, one calculates an autocorrelation function and determines the number of years that it takes to reach 70% to 90% of the total area (or energy). This kind of approach is helpful when one is most interested in eliminating false alarms.

We look at the problem differently. We want high sensitivity. We are willing to accept a reasonable amount of error.

We observe that prices swing radically from one year to the next but that E10, which is the average of a decade's earnings, varies slowly. When looking at historical sequences and overlapping data, we focus on the independent data points: the first (or last year) of a sequence. If we have two historical sequences, they will differ by two (or more) points: the first year of one sequence and the last year of the other. Next, we look at the ability of prices to shift enough in those two years to cause the observed variation in Historical Surviving Withdrawal Rates. The answer turns out to be that they easily come close to doing just that. The issue of overlapping sequences turns out to be a reduction in the effective number of data points (degrees of freedom) by something less than one half.

Keep in mind that, if Historical Surviving Withdrawal Rates were all the same number, there would be a lot of variation in a plot of them versus the percentage earnings yield (100% / [P/E10] ). This scatter would be caused by price changes.

There is the loss of a degree of freedom because we calculate the slope of the line. There is a loss of a degree of freedom because we estimate variance from the data.

In this way, we have converted our nonstandard statistical problem to something very close to a standard curve-fitting problem along with a reasonable adjustment.

Have fun.

John R.

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Post by gummy » Mon Jan 17, 2005 11:52 pm

John, I'll keep putting the stuff here

http://www.gummy-stuff.org/JWR.htm

and you can comment, modify, etc.

... all this in a thread called GARCH :?

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Post by gummy » Tue Jan 18, 2005 12:04 am

Are the labels wrong?

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Post by gummy » Tue Jan 18, 2005 12:19 am

Any objection to my redoing the charts with the data here?

http://nofeeboards.com/boards/viewtopic.php?t=2846

These old eyes ain't what they used to be :?
I find the current charts hard to read.

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Post by hocus2004 » Tue Jan 18, 2005 1:37 am

I have two suggestions:

1) I would change the title to "Valuations Affect Safe Withdrawal Rates;" and

2) I would add a new paragraph as the second paragraph in the article. The second paragraph would read: "When you take into account the effect of changes in valuation levels (not considered in conventional SWR studies, such as the famous "Trinity Study" [a link to an explanation of the Trinity study, perhaps from somewhere else on the gummy site, would be good here], you find that the 4 percent withdrawal rate identified in conventional methodology SWR studies as "safe" is in fact often not safe at all. In January 2000, the SWR for a portfolio with an 80 percent allocation to an S&P index fund was only 1.6 percent. In January 2005 (the time at which this article was prepared), the SWR for an 80 percent S&P allocation portfolio was 2.5 percent [or whatever the number really happens to be today]. The other side of the story is that, when valuations drop to levels lower than the historical mid-point, the SWR for high-stock portfolios will rise to levels higher than the 4 percent figure cited as the constant SWR in conventional SWR studies.

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Post by hocus2004 » Tue Jan 18, 2005 1:48 am

I have a third suggestion, which I have put forward separately because it is a little on the nitpicky side. The suggested change is to this sentence: "We have found that earnings yield (using the average of the past decade's earnings) does an excellent job of predicting Safe Withdrawal Rates." I would replace the word "predicting" with the word "determining" or with the phrase "helping to determine."

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Post by JWR1945 » Tue Jan 18, 2005 4:01 am

hocus2004 wrote:I have a third suggestion, which I have put forward separately because it is a little on the nitpicky side. The suggested change is to this sentence: "We have found that earnings yield (using the average of the past decade's earnings) does an excellent job of predicting Safe Withdrawal Rates." I would replace the word "predicting" with the word "determining" or with the phrase "helping to determine."
How about for calculating? Or when determining or when calculating?

Have fun.

John R.

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Post by JWR1945 » Tue Jan 18, 2005 4:21 am

gummy wrote:Any objection to my redoing the charts with the data here?
http://www.nofeeboards.com/boards/viewtopic.php?t=2846

These old eyes ain't what they used to be :?
I find the current charts hard to read.
Redoing the charts is a good idea.

Yes, there are some glitches with the charts. Yes, they are hard to read. I find that I have to use Full Screen mode. [Click Full Screen under View or press F11.]

I have posted many tables with Historical Surviving Withdrawal Rates (referred to as Historical Database Rates) versus calendar year and percentage earnings yield (100/ [P/E10] ). They can be used to generate similar charts.

As a matter of fact, you could post such tables and allow readers to make their own charts in Excel. They would be able to do such things as varying the retirement start years used for determining the equations.

The data that you selected differ from those in the charts. From the link that you provided:
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.
These tables list Half-Failure Withdrawal Rates, not Historical Surviving Withdrawal Rates (=Historical Database Rates). With Half-Failure Withdrawal Rates, the portfolio's balance is allowed to drop to 50% of its original balance at some time within the first 30 years. The balance often begins to recover by year 30.

Have fun.

John R.

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Post by gummy » Tue Jan 18, 2005 4:22 am

About the charts (which are presumably the main reason for calculating SWR based upon P/E 10), how about charts like so:

(They're smaller and one can see several on the screen at the same time.)

About the possible wordings, I'll let you guys decide :D

PS#1
I still don't understand those chart labels :evil:

Are there two-count-em-two HDBR50 Fits ?

PS#2
I see JanSz mentioned. How did he get into the picture?

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Post by JWR1945 » Tue Jan 18, 2005 4:42 am

gummy wrote:About the charts (which are presumably the main reason for calculating SWR based upon P/E 10), how about charts like so:...
(They're smaller and one can see several on the screen at the same time.)
...
PS#1
I still don't understand those chart labels :evil:

Are there two-count-em-two HDBR50 Fits ?

PS#2
I see JanSz mentioned. How did he get into the picture?
Yes. The new graph looks great. (The charts were helpful in determining and in presenting the relationship between Safe Withdrawal Rates and valuations. But the main reason is the relationship itself. Hocus's original request back in May 2002 was to know Price-Adjusted Safe Withdrawal Rates. He wanted the information in order to determine his stock allocation.

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.]

The reference to JanSz has to do with a version of the calculator. [My calculators are modified versions of the Retire Early Safe Withdrawal Calculator, version 1.61 dated November 7, 2002. The changes have become extensive.]

JanSz was interested in removing a fraction of a portfolio's gains (but none of the losses) when compared to six years earlier. I made some calculators with that algorithm. The algorithm was not used for the calculations that you see.

My most recent calculators allow you to remove a fraction of the gains (buy not losses) over the previous year's balance, a fraction of dividends from stocks and/or a fraction of interest from bonds or commercial paper. However, I cannot calculate your Sensible Withdrawal Rates.

Have fun.

John R.

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Post by gummy » Tue Jan 18, 2005 4:51 am

If (as you have said) you're using HSWR rather than HDBR, then perhaps it's better to eliminate all references to the latter.

The reason I asked about JanSz:
Once upon a time I was invited to join the Motley Fool.
After my first post several people asked for spreadsheets on this or that.
JanSz was one of 'em.

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Post by hocus2004 » Tue Jan 18, 2005 5:07 am

How about for calculating? Or when determining or when calculating?

Any of those are OK. It is the word "predicting" that I don't like. You are not predicting what is safe, you are reporting what the historical data reveals to be safe. It is a current-day reality that the take-out numbers reported as safe are indeed safe if stocks perform in the future as they have in the past (a necessary caveat to all SWR claims).

When the weatherman says that "there is an 80 percent chance of rain on Wednesday," people say that he is "predicting" rain. That is loose speaking. The precise way to report the reality is that, presuming that the tools he is using to assess the chances of rain are effective tools for making such assessments, there is a 80 percent chance that there will be rain and a 20 percent chance that there will not be rain. If there is not rain, the one-in-five shot happened to come through. There was not a failed prediction.

If I say "I think the Yankees will win the World Series next year," that's a prediction. I am looking into the future and saying what I think will happen. Presumably I am looking at some of the factors that in the past have been shown to have an effect on the question at hand (the strength of the pitching staff, etc.) but I have not done a precise scientific analysis and assigned percentage odds to various possible outcomes. When you do that, you are making a shift from "predicting" to "reporting," in my view.

The distinction is not a trivial one. When you are reporting, all of the facts that determine whether you are correct or not in what you said are available for review in the current day. Predictions cannot be determined to be true or false in the current day. Reports can be. If someone reports today's SWR as 4 percent, he is making a statement that is false and that can be demonstrated to be false by making a check of what the historical data says re this question.

If any "prediction" that anyone happens to put forward is to be viewed as an analytically valid SWR, then the SWR can be anything. One person could say that the number is 4, another could say 1.2, another could say 23, another could say 37. For SWR analysis to have significance, the claims put forward must be verifiable by making reference to data. True SWR analysis is data-based SWR analysis. The historical data does not offer any support for the 4 percent number. Therefore, the 4 percent number is wrong.

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Post by JWR1945 » Tue Jan 18, 2005 5:13 am

gummy wrote:If (as you have said) you're using HSWR rather than HDBR, then perhaps it's better to eliminate all references to the latter.

The reason I asked about JanSz:
Once upon a time I was invited to join the Motley Fool.
After my first post several people asked for spreadsheets on this or that.
JanSz was one of 'em.
For presentation at your site, it does make sense to restrict all references to HSWR. However, it is not practical to do so on this board since it would change so many posts.

JanSz asked for a spreadsheet here. I made such calculator modifications as I could to come close to meeting his request. I collected some data to see what his algorithm would do.

My impression is that JanSz really wanted a spreadsheet for tracking his investments for today and looking forward. I do not think that he is overly concerned about what has happened in the past and what it tells us about his algorithm.

Have fun.

John R.

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Post by JWR1945 » Tue Jan 18, 2005 5:52 am

gummy wrote:About the charts (which are presumably the main reason for calculating SWR based upon P/E 10), how about charts like so:

(They're smaller and one can see several on the screen at the same time.)
...
Look closely at those charts, gummy. You may have uncovered something significant.

The graph from the middle period differs significantly from those of the earlier period and the later period. This is a new finding. Now to figure out why!

Looking at the numbers on the x-axis (the percentage earnings yield 100 / [P/E10] ), my guess is that you are using HFWR80, not HDBR80. I will examine both in terms of these new time frames later this morning.

Have fun.

John R.

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Post by gummy » Tue Jan 18, 2005 6:33 am

Oops!
Yes, I was using the data here
http://nofeeboards.com/boards/viewtopic.php?t=2846
and I now see it's HFWR :?

One thing I find a wee bit bothersome ... perhaps 'cause I'm short-sighted.
Why do you say that after 1920 the "relationship is strongest".
Are you calculating the correlation and seeing that it's larger after 1920?

For the charts I generated (the HFWR stuff), the correlation is greatest for the 1871-1906 data (???)

Maybe the HSWR data (or is it HDBR ?) is different ... once I find where that data is located.

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Post by gummy » Tue Jan 18, 2005 7:14 am

Okay, I see why 1920+ is better :lol:

For the three 36-years periods plotted in the above chart, the initial period (starting in 1871) is unusual 'cause it depends greatly upon which year you start.

Here's what I get for a moving 36-year window:

Imagine a NFB thread started in 1881 ...

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Post by JWR1945 » Tue Jan 18, 2005 7:29 am

I have examined the effects of several criteria. For example, I have looked at CTVR50 and CTVR80. Those portfolios are identical to HDBR50 and HDBR80. Their special names are to associate them with a different criterion: the final portfolio balance is equal to the initial portfolio balance at year 30. CTVR stands for Constant Terminal Value Rate.

[I use inflation adjusted (real) dollar balances with these special criteria.]

This is where I first noticed strange behavior in the earlier time period. Notice that during the early years, portfolios that started at low P/E10s and high P/E10s behaved the same but middle range P/E10s were different. Back in those days, my Historical Surviving Withdrawal Rates (which I called Historical Database Rates) were calculated on dory36's FIRECalc.
The 1881 to 1920 Anomaly dated Wed Jul 23, 2003.
http://nofeeboards.com/boards/viewtopic.php?t=1166

This anomaly is one of the reasons why it took so long to discover the relationship between SWRs and valuations.

The earliest data are not as reliable as later data. Almost every source except for Professor Robert Shiller's S&P500 data starts in the middle 1920s. Failure of others to see effects similar to these may be tied in with their using a limited time frame.

These are my earliest HDBR50 and HDBR80 tables:
FIRECalc HDBR50 and 80 Tables dated Sat Mar 20, 2004.
http://nofeeboards.com/boards/viewtopic.php?t=2245

These are the tables to use. They were using my calculators, which are modified versions of the Retire Early Safe Withdrawal Calculator.
New HDBR Tables dated Sun Jan 11, 2004.
http://nofeeboards.com/boards/viewtopic.php?t=1962

Have fun.

John R.

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Post by JWR1945 » Tue Jan 18, 2005 7:34 am

gummy wrote:Okay, I see why 1920+ is better:
...
Imagine a NFB thread started in 1881 ...
Thanks for the correlation chart. I had not seen anything like it.

I was composing a post when you posted your graph.

Thanks. Have fun.

John R.

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