Definitions

Research on Safe Withdrawal Rates

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JWR1945
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Definitions

Post by JWR1945 »

Definitions

The careful use of terms is vitally important for understanding Safe Withdrawal Rates. Too many times in the past, arguments have been based upon conveniently selected alternative definitions.

There are many subtle issues involved in selecting a definition of the Safe Withdrawal Rate. This thread provides a good background and resolves several issues.
Summary Thread: SWR Definition dated Sun, Jul 13, 2003.
http://nofeeboards.com/boards/viewtopic.php?t=1107

We currently identify three rates of importance:
1) The Calculated Rate (or Zero Balance Rate), which is the best estimate of what will survive in the future.
2) The High Risk Withdrawal Rate, which is the upper confidence limit placed about the Calculated Rate.
3) The Safe Withdrawal Rate, which is the lower confidence limit placed about the Calculated Rate.

Most often, we use the 90% confidence limits. [See footnote.]

Historical Database Rates are also known as Historical Surviving Withdrawal Rates.

Refer to this post for some additional insights.
SWR as a Tool dated Mon, Jun 14, 2004.
http://nofeeboards.com/boards/viewtopic.php?t=2607

Have fun.

John R.

[Footnote (added on July 8, 2004): This is using two-sided statistics. In terms of Safe Withdrawal Rates themselves, the confidence level is 95% (using one-sided statistics).

Refer to the exchange of posts between Bpp and me (JWR1945) starting with:
http://nofeeboards.com/boards/viewtopic ... 163#p22163
and continuing to this:
http://nofeeboards.com/boards/viewtopic ... 290#p22290
for an in depth discussion related to one-sided and two-sided statistics.]
Last edited by JWR1945 on Thu Jul 08, 2004 4:24 am, edited 1 time in total.
hocus2004
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Post by hocus2004 »

"Too many times in the past, arguments have been based upon conveniently selected alternative definitions. "

That's so. But I don't think that the real problem is a failure to understand the definitions of terms or even a failure to understand the importance of coming to agreement on acceptable definitions. The real problem in my view is a lack of appreciation of what the phrase "safe withdrawal rate" signifies.

Here is a link to the Andrew Smithers thread.

http://nofeeboards.com/boards/viewtopic.php?t=2462

Smithers: "Equity investing is much less risky than it would be if returns followed a random walk."￾

That's a powerful insight, in my view. Smithers is not only rejecting the random walk hypothesis. He is saying that it is a darn good thing for stock investors that stocks do not follow a random walk scenario in the long term.

I think that Smithers is right about this. What if stocks truly did follow a random walk in the long term, what if long-term stock returns were truly unknowable? If these things were so, ALL forms of SWR analysis would be invalid.

If future stock returns are truly unknowable, then we cannot say with any confidence whatsoever that a 4 percent withdrawal is "100 percent safe." If returns are truly random, then it could be that the next 30-year sequence is going to be a sequence in which there are 30 straight years of negative returns. That return sequence is just as likely as any other return sequence if stock returns are a truly random event.

The reality is that the random walk theory simply does not apply in the long term. Long-term stock returns are "bounded" (I picked up the word "bounded" from a post by Mikey at the Early Retirement Forum) by the earnings generated by the underlying companies. Some long-term return possibilities are more likely to turn up than others. By looking at the historical data, you can gain a sense of which options are most likely and which are least likely. The future is not a random walk. Long-term returns are very much knowable.

Once people come to an appreciation of the fact that long-term returns are knowable, then it is just a question of determining what factors have always played a role in determining long-term returns. All factors that have played a critical role in the past must be included in any analytically valid SWR analysis.

The analytical mistake being made by defenders of the conventional methodology is that they are starting with their conclusions and then performing their analysis solely for the purpose of backing up their preconceptions. They "know" that stocks are always the best investment class for the long-term, so they permit analysis only of enough data to "prove" that conclusion to be so. Once they have enough data to generate a number consistent with that "finding," the analytical process comes to a close; no additional data may be considered after that point.

The idea of the Data-Based SWR Tool is to make use of the scientific method in analysis of investment options. What I am proposing is that we set up the analytical process first and then allow the data to guide us in reaching our conclusions re investment strategy. When you do it that way, you come up with very different answers than the answers you come up with when the analysis is employed to justify your investment choices rather than to inform them.

My sense is that many people are threatened by the idea that long-term stock returns are to a large extent knowable. People have come to like the idea of believing that the future is unknowable because, so long as the future is unknowable, any sort of return is possible, even a good long-term return from an extremely overvalued asset class.

I see this rejection of the reality principle as a grave error in judgment, one rooted in the emotions that often unfortunately dominate the investing decision-making process. It is a good thing that long-term stock returns are to a large extent predictable, not a bad thing. Knowing what the historical data says helps us invest more successfuly than we could hope to invest not knowing what it says.

Defenders of the conventional methodology are locked in an internal contradiction. They maintain that the future is completely unknowable and yet they also maintain that a 4 percent withdrawal is "100 percent safe." Both things cannot be true. The reality is that long-term returns are to a large extent knowable, that the valuation level in effect at the beginning of a 30-year sequence of returns "bounds" the long-term return likely to apply for that sequence, and that it is a good thing to know both the low, middle and high points of those bounds.
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Post by JWR1945 »

hocus wrote:The reality is that the random walk theory simply does not apply in the long term. Long-term stock returns are "bounded" (I picked up the word "bounded" from a post by Mikey at the Early Retirement Forum) by the earnings generated by the underlying companies. Some long-term return possibilities are more likely to turn up than others. By looking at the historical data, you can gain a sense of which options are most likely and which are least likely. The future is not a random walk. Long-term returns are very much knowable.
I refer to this as the strongest form of mean reversion. The link between prices and earnings (especially when earnings are averaged over a number of years) is demonstrated easily. Even though the relationship between prices and earnings changes slowly over time as people's enthusiasm with stock market investing changes, the link is always present.

Have fun.

John R.
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Post by JWR1945 »

hocus wrote:My sense is that many people are threatened by the idea that long-term stock returns are to a large extent knowable. People have come to like the idea of believing that the future is unknowable because, so long as the future is unknowable, any sort of return is possible, even a good long-term return from an extremely overvalued asset class.

I see this rejection of the reality principle as a grave error in judgment, one rooted in the emotions that often unfortunately dominate the investing decision-making process. It is a good thing that long-term stock returns are to a large extent predictable, not a bad thing. Knowing what the historical data says helps us invest more successfully than we could hope to invest not knowing what it says.
I have never been able to understand this. Yet, I see it every day.

Perhaps it is a strong desire that this were true.
any sort of return is possible, even a good long-term return from an extremely overvalued asset class.
Probability theory allows for such possibilities. It is just that the odds of its being true are remote. After all, there are people who win the lottery.

Have fun.

John R.
th
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Post by th »

May I interject a difference of opinion?

It appears that we're forcing opinions into black and white segments.

I, and others, have said "the future is unknowable", and considerable liberty is taken with that statement here.

Such statements, at least when I've uttered them, mean "the near term future", although I think I said as much as least a few times that apparently slipped through the cracks.

The Gordon Equation (the construct referred to above for 30 year periods) says that the long term (30+ year) return on equities is somewhat predictable. The equation has been applied to many economies in many time periods and is pretty darn close.

Falls roughly on its head in short (less than 20 year) periods. In fact, all measurement of stock market direction for periods of less than 10-20 years largely fail.

So its reasonable to say that the future of market directions of equities (or most asset classes for that matter) for periods of less than 10, possibly less than 20 and maybe less than 30, are not predictable. But equity returns over 30+ year periods are largely predictable.

The problem in trying to do shorter term (less than 30 year) predictions is that while things may become over or under valued, there is no way to know if they will become even more over or undervalued before they return to the gordon equation mean over the full 30 year period.

The bigger problem is that many of these ups and downs occur in a very small number of days in each of those thirty years.

Hence any system that tells you stocks are overvalued vs the mean and suggests not owning them will save you from a majority of those RTM drops. It will also "save" you from a majority of the up days that create the upside of the 'mean'. If for no other reason than it will always tell you too late that its time to buy or sell. You're more likely to remain in a 'dont buy' loop and miss the upsides entirely.

Which means such a persons mean will be a lower mean than the mean mean. And thats gonna make ya mean 30 years from now.

Bernsteins analogy for this, and I do love it. A man is walking from his apartment to the park, and he's walking a dog on a long extensible leash. At the end of the walk (30 years), the man WILL be at the park. In the meanwhile the dog will have run back and forth, side to side.

Measuring the man is feasible. His destination is largely known.

Measuring the dog is a fools errand. As an owner of several, I can attest that even the dog doesnt know where its going to go next, and no two walks are ever alike. Random events (someone peed over here, something moved over there), psychological events (today I'm going to bark back at those dogs behind that fence...tomorrow I wont care about them), and unexpected events like the leash breaking or getting pulled out of your hand...all effect the dogs walk. But we always end up at the same place.

Suggesting I shouldnt walk the dog today because it might bark at the neighbor dogs, or run onto the cranky guys lawn because it thought it saw something twitch there certainly creates some safety. But then you get a fat dog.

Nobody wants a fat dog.
He who fights with monsters might take care lest he thereby become a monster. And if you gaze for long into an abyss, the abyss gazes also into you. - Nietzsche
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Post by JWR1945 »

Such statements, at least when I've uttered them, mean "the near term future", although I think I said as much as least a few times that apparently slipped through the cracks.
Then say so!

And stop rejecting all evidence contrary for the middle term. At least, look at what the data show.

Have fun.

John R.
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Post by JWR1945 »

The bigger problem is that many of these ups and downs occur in a very small number of days in each of those thirty years.
This is a common mistake. Go over the Crestmont's site and read what he found out.

Almost always, up days are balanced by almost identical down days. It is entirely artificial to eliminate individual days instead of pairs.

What does happen is that in an up market, the number of up days exceeds the number of down days. In a bear market, they are about equal. [On average, up moves are smaller than down moves.]

Have fun.

John R.
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Post by th »

Oh I did say so, but that seems to have been selectively filtered out.

And I have reviewed any and all claims to determine stock market movement of periods less than 30 years. None work.

None currently proposed can be determined to be successful until the period of time expires that they were supposed to predict.

At which point they will no longer be useful.

History shows that such attempts are less than 50% successful.

So flip a coin. Bet it all on black. Buy a monkey to throw a dart.

Better still...buy a monkey to flip a coin onto black. You'll triple your chances. By my system anyhow.

As far as up and down days, you missed my point.

My point was the big movements usually happen in a day or two, not in a month or two. And if you're timing due to valuations, you're simply going to miss those days.

Not my say-so, its proven by millions of people every year. So far only two of them have beaten this and only one persistently.

I want to check and see if he owns a monkey.
He who fights with monsters might take care lest he thereby become a monster. And if you gaze for long into an abyss, the abyss gazes also into you. - Nietzsche
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Post by JWR1945 »

And I have reviewed any and all claims to determine stock market movement of periods less than 30 years. None work.
I seriously doubt this.

You have not evaluated properly the degree of risk involved.

Have fun.

John R.
th
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Post by th »

Ok, show me one that will work for the next 30 year period. I'll wait 30 years...

I think the risks of owning a monkey are very low. I hear they poop a lot, but having three dogs and cats I'm rather used to that.
He who fights with monsters might take care lest he thereby become a monster. And if you gaze for long into an abyss, the abyss gazes also into you. - Nietzsche
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Post by hocus2004 »

"Oh I did say so, but that seems to have been selectively filtered out. "

Do you believe that the conventional SWR methodology is analytically invalid for purposes of determining SWRs?
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Post by th »

Anyone remember an old piece of software (I remember this from the 70's but saw incarnations of it well into the early 90s). It was called "eliza" and it was supposed to emulate talking to a shrink.

It started out saying "So tell me how you feel" and would look for certain key words in your response and combine those with a bank of pre determined "shrinky" responses.

For example, you would say "I hate this guy intercst and want to see him naked", and it would see the word "hate" and ask "tell me more about why you hate intercst".

With a small margin of "intelligence", this rudimentary program could generate some surprisingly interesting and sometimes funny "conversations". Particularly if you sat someone down and didnt tell them the conversant wasnt human.

Eventually it'd say something dumb or ask you the same stupid question twice, and you'd figure it out though.
He who fights with monsters might take care lest he thereby become a monster. And if you gaze for long into an abyss, the abyss gazes also into you. - Nietzsche
th
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Post by th »

Ah HAH! He HAS been involved with a monkey!!!

I KNEW it.

http://money.cnn.com/2003/04/09/news/co ... lion_game/

"NEW YORK (CNN/Money) - Joe Millionaire? This fall, someone will have a chance to become Joe Billionaire, thanks to the marketers at Pepsi, Warren Buffett, and a nimble-fingered monkey."

That does it. I'm getting a monkey. Right after I make lunch...
He who fights with monsters might take care lest he thereby become a monster. And if you gaze for long into an abyss, the abyss gazes also into you. - Nietzsche
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Post by bpp »

Hi John R.,
Most often, we use the 90% confidence limits.
For your 90% confidence limits, I noticed you are using +-1.64 sigma, the double-sided 90% confidence limits, which corresponds to a 5% chance of failure. Since failure can only happen in one direction (we won't go broke from withdrawing too little money), mightn't it make sense to use 1.28 sigma instead, to give you a 10% chance of failure? Otherwise, you're really talking about a 95% confidence limit.

Bpp
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Post by JWR1945 »

Thank you, bpp. You have opened up a refreshing line of thought.

One sided confidence limits are one of my pet peeves. Unless the other side of the distribution cannot possibly happen, I reject the logic of using one sided confidence limits. Quite often, I see the correct side of a null hypothesis selected after the fact.

You are right about each side's corresponding to 5%. We do make use of the upper confidence limit. It is the High Risk Withdrawal Rate. Withdrawing more than that rate is almost certain to result in a failure.

I do not believe that the confidence levels really are as good as calculated. There are some approximations such as normality and the effective number of degrees of freedom that make me very hesitant to claim too great a precision.

There is always a possibility of a completely unexpected disaster. That is not built into our calculations.

Have fun.

John R.
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Post by hocus2004 »

"There is always a possibility of a completely unexpected disaster. That is not built into our calculations."

That's the "the future might turn out worse than the past" thing. All SWR research includes a caveat to cover that possibility.
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Post by th »

Except there has been a completely or largely unexpected event that has markedly affected stocks in an unusual manner at least once every 5 years in recorded history. Sometimes positive and sometimes negative. Sometimes more often than 5 years.

This is why, in short to intermediate time periods, the future is always worse than the past, in some way. Over 30-40 year periods, the sharp turns turn into little bumps. Over 50-100 year periods they disappear. But its why you cant 'game' the market or guess equity directions.
He who fights with monsters might take care lest he thereby become a monster. And if you gaze for long into an abyss, the abyss gazes also into you. - Nietzsche
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Post by JWR1945 »

For bpp:

Here is an example of why I dislike one-sided statistical tests.

Assume that you have three people working for you on similar, but different tasks. You get three reports. All of them are accurate.
1) Test sample A was higher than the standard at a 90% level of confidence.
2) Test sample B was lower than the [identical] standard at a 90% level of confidence.
3) We were not able to discern any differences between samples A and B and the [identical] standard at the 90% confidence level.

The first two cases use different sides of a one-sided test. The third case uses a two-sided test.

Have fun.

John R.
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Post by bpp »

Hi John R.,
Here is an example of why I dislike one-sided statistical tests.
Sure, mixing your definitions can be confusing. But I think in the case of SWR, the commonsense definition would be the one-sided one, since as I said, failure can only happen in one direction. If you tell me that you think some rate is safe at the 90% confidence level, I expect that to mean that there is a 10% chance of failure (assuming Gaussian distribution, extrapolating from historical data, etc.). It is somewhat counter-intuitive to use a two-sided test in this particular case. I know it surprised me, at least, when I noticed that that is what you were doing.

Of course, you're free to pick whatever cut-offs you think make sense. But you're likely to confuse people about what you are saying with the definitions you are using right now.

Bpp
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Post by JWR1945 »

Even though the details are highly technical, people can make helpful contributions without having a technical background. This is an example of discussing the logic behind statistics as opposed to statistical tests themselves.

Here is the essence of my position.

When I look at data, I want learn the story that they have to tell. I want that story to be the same regardless of who asks a question and what question is asked. When we introduce confidence limits, the data tell us whether to reject the null hypothesis (that there is no underlying effect, only randomness). I do not want the data to accept and reject what is essentially the same null hypothesis, just phrased a little bit differently.

There are three different answers if we include one-sided statistics. A withdrawal rate can cause a significantly different result from the Calculated rate because it is too high (the High Risk Rate). A withdrawal rate can cause a significantly different result from the calculated rate because it is too low (the Safe Withdrawal Rate). A withdrawal rate can cause a significantly different result from the Calculated rate (using two-sided statistics).

I want the logic to follow the sequence that (a) first, there is a significant difference and then (b) we identify this difference as being either (above) a High Risk Rate or (below) a Safe Withdrawal Rate.

I do not want to allow the logic to follow a sequence such as (a) there is no significant difference and (b) the difference is above the High Risk Rate or below the Safe Withdrawal Rate.

WARNING: If you are a student, follow the one-sided procedures when questions are phrased appropriately. That is what I have told my daughters. These comments should be treated as a side discussion, not used as an excuse for getting the wrong answers on a test.

Have fun.

John R.
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