No! It isn't that simple.

Financial Independence/Retire Early -- Learn How!
Post Reply
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

No! It isn't that simple.

Post by JWR1945 »

No! It isn't that simple.

Recently, ataloss cited this quote, taken from the Motley Fool's discussion boards, to suggest that we have not made progress over the last year.
I'm not aware of anyone who has been successful in timing when stock prices are high or low over the long-term. If you possess this unique ability that others lack, perhaps the easiest thing to do is to adjust the safe withdrawal rate by the amount that you consider stocks to be higher than they have ever been. If stocks are 25% higher, drop the 4% withdrawal to 3%. If you feel stocks are 50% higher than they have ever been, then drop the 4% down to a 2% withdrawal.

http://nofeeboards.com/boards/viewtopic ... 8461#p8461

Question: Didn't that answer the question about valuations?

The answer is NO! This is the kind of question that must be answered by a numbers guy.

It is only a throw away remark. It does not answer the question. It suggests no more than linear scaling. That is the most common first step one uses when he makes an extrapolation. Frequently, it is sufficient. It is not a proper answer for a serious question. In fact, you will find that it breaks down in a variety of ways when you really look into the matter. My own correction, which includes the results of my own investigations, produces a similarly looking adjustment, but only when viewed on a superficial level.

The first difference in the two answers has to do with how valuations are determined. You will find that the original answer did not address this whatsoever. Valuation was whatever the reader might suppose it to be. If someone felt that stocks were overvalued by xx%, then he should scale accordingly.

In stark contrast my answer is drawn from Yale Professor Shiller's careful research and his credible finding that stock returns correlate closely to P/E10. (His original findings were even stronger. They were based on P/E30. The shorter time period for averaging earnings, ten years instead of thirty, is a reasonable compromise that reveals changing conditions faster.) Professor Shiller credits Benjamin Graham with the original idea that led him to look at P/E10 and P/E30.

The original quote is based on one's feelings. Our current adjustments make use of quantitative calculations that are based on validated academic research.

The original quote treated valuation adjustments linearly. My own investigations showed that Safe Withdrawal Rate calculations are distinctly nonlinear. The original methodology is wrong. It is as simple as that and it is as difficult as that.

[This is a highly technical point. But it is also highly significant. If Safe Withdrawal Rates were linear, we could take advantage of a wealth of mathematical theorems and apply them directly. For those with technical training, I simply direct you to gummy's Safe Withdrawal Rate formula and its distinctly nonlinear form.]

[I first discovered this nonlinearity empirically. I was examining stock and bond allocations and the effects of volatility. If linearity were even approximately true, variances would add. (There is a covariance term as well and I included it.) This would be an extremely powerful result because it would allow you to optimize stock and bond allocations directly from theory. I proved conclusively that linearity does not hold. It is not useful even with smaller allocation shifts. (I used dory36's FIRECalc in my investigations. FIRECalc uses the historical sequence methodology.)]

[If you look at gummy's Safe Withdrawal Rate formula, you can see why a linearity assumption is especially bad for looking at allocations. The gain multiplier terms in the formula are the result of combining the separate gains for stocks and bonds. At that point we are looking at a linear combination dependent upon allocations. Then you invert this combination. That is, gMS depends on 1/(gain multipliers). Even worse, gMS combines various products of 1/(gain multipliers) for different years and sums them up. At this point the equation has become hopelessly nonlinear in terms of allocations.]

The third difference is that my calculations are based upon a well-defined theoretical hypothesis. I assume that Safe Withdrawal Rates are ultimately related to corporate earnings. The earnings (averaged over ten years) that would have supported withdrawals at a high degree of safety in the past should still provide a high degree of safety up to the point of equal levels of P/E10. I exclude the excess and calculate the safe withdrawal amount based upon that P/E10.

This result looks similar to the one quoted but it is quite different. It scales only at one point, a point corresponding to a high degree of safety. I do not use an arbitrary point for scaling. One should not apply my adjustment directly to peteyperson's new approach. His approach makes use of intrinsic value. The intrinsic value of your portfolio is quite different from the extreme value (of P/E10) that underscores my formula.

Part of the quoted approach is the misuse of the old adage that nobody can time the market successfully. That adage has been applied to short circuit any claim that there really is such a thing as valuation. If there were, it would be possible to time the market successfully and that is known to be impossible. Examined closely, that assertion means that prices are always irrelevant. Thus, people like Warren Buffett and Sir John Templeton are idiots because they have been willing to avoid buying stocks when prices are high.

What the old adage refers to are approaches such as relying solely on technical indicators and/or trading excessively, which generates lots of fees. It also refers to hyper-activity traceable to the high degree of randomness in short-term prices instead of relying on long-term effects, which are much more predictable. Successful value investors are not part of this group because they have a different rationale behind their decisions.

Much of the difficulty in applying the adage properly is that it is extremely difficult to differentiate the two groups in a totally objective manner. Quite frequently, when it comes to actual behavior, the reasons stated for making investment decisions are not accurate. This happens even when a person believes what he is saying. This introduces a subjective element, which makes things difficult.

The original remark, found in the quote, was casual, flippant and superficial. It was not suitable for providing guidance. It was a meant to humor those who might cause problems. It was based on several false assumptions. It emphasized how people feel. It did not search for the truth. It has serious technical errors. It avoided any serious discussion of valuations. As an additional means to avoid the topic, the originator misapplied an old adage.

Have fun.

John R.
User avatar
ataloss
**** Heavy Hitter
Posts: 559
Joined: Mon Nov 25, 2002 3:00 am

Post by ataloss »

JWR1945, Of course more sophisticated mathematical approaches are desirable if they help us approximate swr better. I find it interesting that Bernstein's 2% withdrawal rate corresponds to the 4/7ths rule. That is, if you get 3.5% real returns from the Gordon equation and use the ratio of hswr/historical real returns you get 2%. I don't object to trying to get a better "answer."

This idea that if we try hard enough we will get the "right" answer is absurd.
SWR analysis, when it is true to what the data says, is different.
What the data says is not a matter of opinion. Data analysis involves
numbers. Data is hard, objective. You add up all the numbers that bear on the question being examined and you get a right answer to the question posed.
:shock:
Have fun.

Ataloss
peteyperson
**** Heavy Hitter
Posts: 525
Joined: Tue Nov 26, 2002 6:46 am

Re: No! It isn't that simple.

Post by peteyperson »

Don't understand his formulas, but ya gotta love the way John writes!

Fun indeed.

Petey


JWR1945 wrote: Part of the quoted approach is the misuse of the old adage that nobody can time the market successfully. That adage has been applied to short circuit any claim that there really is such a thing as valuation. If there were, it would be possible to time the market successfully and that is known to be impossible. Examined closely, that assertion means that prices are always irrelevant. Thus, people like Warren Buffett and Sir John Templeton are idiots because they have been willing to avoid buying stocks when prices are high.

What the old adage refers to are approaches such as relying solely on technical indicators and/or trading excessively, which generates lots of fees. It also refers to hyper-activity traceable to the high degree of randomness in short-term prices instead of relying on long-term effects, which are much more predictable. Successful value investors are not part of this group because they have a different rationale behind their decisions.

Much of the difficulty in applying the adage properly is that it is extremely difficult to differentiate the two groups in a totally objective manner. Quite frequently, when it comes to actual behavior, the reasons stated for making investment decisions are not accurate. This happens even when a person believes what he is saying. This introduces a subjective element, which makes things difficult.

The original remark, found in the quote, was casual, flippant and superficial. It was not suitable for providing guidance. It was a meant to humor those who might cause problems. It was based on several false assumptions. It emphasized how people feel. It did not search for the truth. It has serious technical errors. It avoided any serious discussion of valuations. As an additional means to avoid the topic, the originator misapplied an old adage.

Have fun.

John R.
PainInTheAS
* Rookie
Posts: 14
Joined: Tue May 06, 2003 3:16 am

Re: No! It isn't that simple.

Post by PainInTheAS »

JWR1945,

I at once agree and disagree with you.

I basically agree with the technical merit of your arguments, but I can't help wondering how much practical difference it makes to someone embarking on their SWR calculation.
JWR1945 wrote: No! It isn't that simple.

The first difference in the two answers has to do with how valuations are determined. You will find that the original answer did not address this whatsoever. Valuation was whatever the reader might suppose it to be. If someone felt that stocks were overvalued by xx%, then he should scale accordingly.

In stark contrast my answer is drawn from Yale Professor Shiller's careful research and his credible finding that stock returns correlate closely to P/E10. (His original findings were even stronger. They were based on P/E30. The shorter time period for averaging earnings, ten years instead of thirty, is a reasonable compromise that reveals changing conditions faster.) Professor Shiller credits Benjamin Graham with the original idea that led him to look at P/E10 and P/E30.


Yes, but... why is a more precise calculation a more accurate representation of stock valuation? (Actually intercst didn't seem to rule out any technique for measuring comparative valuations, so your argument here is a bit of a strawman, it seems to me. Nonetheless, the question stands, is your way The One True Way of calculating valuation?)
The original quote treated valuation adjustments linearly. My own investigations showed that Safe Withdrawal Rate calculations are distinctly nonlinear. The original methodology is wrong. It is as simple as that and it is as difficult as that.

[This is a highly technical point. But it is also highly significant. If Safe Withdrawal Rates were linear, we could take advantage of a wealth of mathematical theorems and apply them directly. For those with technical training, I simply direct you to gummy's Safe Withdrawal Rate formula and its distinctly nonlinear form.]


Another yes, but... coming up with, say, 2.1036% versus 2.5% looks a little suspect considering all the unknowns facing the aspiring retiree. If the SWR algorithm of choice mandates 2.5% withdrawals, but the requirement is 2.6% (of an existing portfolio) in retirement, what would/should be a realistic course of action for a flesh-and-blood aspiring retiree (shouldn't that be "retirer")?

(Incidentally, I would agree that the arithmetic as quoted seems wrong, in any case; a 100% overvaluation would imply a halving of the withdrawal rate, I think [assuming linear extrapolation].)
The third difference is that my calculations are based upon a well-defined theoretical hypothesis.


And once again, yes, but... does well-defined automatically imply more correct (or more useful)?
I assume that Safe Withdrawal Rates are ultimately related to corporate earnings.


Fair enough, but even if you are correct, we are always subject to the caveat that markets may remain "irrational" (in our view) far longer than we can remain solvent enough to take advantage of the inefficiency (I find it easy [after the last 3 years!] to imagine a market that remains uncooperative for the better part of a retirement lifetime, enough to jeopardize portfolio survival.

In sum, it is not quite clear to me what additional guarantee the theoretical underpinning (however reasonable) gives us.
The earnings (averaged over ten years) that would have supported withdrawals at a high degree of safety in the past should still provide a high degree of safety up to the point of equal levels of P/E10.


At risk of sounding overly pedantic, I think most would acknowledge the relative paucity of the historical record in terms of the quantity of useful, independent data points. As such, we might wish to be mindful of a fat tail event rearing its head just as we become complacent. In other words, in your shoes, I would think twice about predicting what the future "should" do based on the past. Certainly, it is useful to know that things could happen that way again, since they did before, but it seems to me a bit of a stretch to claim that they should.

As you yourself noted at the beginning of your post, linear scaling frequently suffices. I am not entirely convinced by your post that in this case that's not true.

PITA
User avatar
ataloss
**** Heavy Hitter
Posts: 559
Joined: Mon Nov 25, 2002 3:00 am

Post by ataloss »

As such, we might wish to be mindful of a fat tail event rearing its head just as we become complacent. In other words, in your shoes, I would think twice about predicting what the future "should" do based on the past.


I think that the historical swr is one factor a retiree could consider. That is, I would hesitate to take withdrawals at a rate that would have failed in the past. OTOH, if monte carlo analysis based on reasonable return assumptions related to current valuations suggests a lower safe withdrawal rate rate, I would consider that.
Have fun.

Ataloss
Post Reply