GARCH

[gummy]

I'll keep putting your sentences into your tutorial (even though I have little understanding of the procedure). I hope that readers are smarter than I.

If you haven't checked to see if the Calculated Rate or the Safe Withdrawal Rate or the High Risk Rate (however calculated) actually worked well in the past, how would anybuddy have condidence in the procedure?

I've done the following (on an Excel spreadsheet):

1: Calculated the SLOPE and INTERCEPT for the regression line, using the E10/P vs HSWR data you provided (from 1920 to 1949).

2: Used that line to estimate the 1950 SWR (or whatever you want to call it) by plugging the 1949 E10/P value in for x
... as in y = SLOPE*x + INTERCEPT.

3: Looked up the actual inflation and return for a 80% / 20% portfolio of S&P500 /Govt Bonds for the year 1950.

4: Withdrew the percentage generated by the E10/P procedure (for the year 1950).

5: Repeated the above ritual each year for thirty years, each time using the data from 1920 and actual returns.

I got something like this for the portfolio, ending in the year indicated:



Of course, I probably don't know what I'm doing

[hocus2004]

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.

My guess (it's possible that I am wrong) is that what you are looking for here is a modified version of your Sensible Withdrawal Rate strategy. I presume (I am not sure) that it is possible to work up a methodology that would provide that.

My understanding (a greatly limited one) of the Sensible Withdrawal Rate strategy is that it calls for smaller take-outs following bad return years and larger take-outs following good return years. The benefit to this is that you are not stuck going with a number derived from looking at the worst-case-scenario returns sequence. By agreeing up front to limit your take-out in some circumstances, you are able to increase your take-out in other circumstances. I see a good bit of appeal in this idea since in all likelihood you are not actually going to personally experience a worst-case returns sequence.

The problem that I see with the Sensible Withdrawal Rate strategy is that it does not include an adjustment for the effect of changes in valuation levels. I have never looked at this up close, but my sense of things is that it starts with a number determined along the lines by which the conventional SWR is determined, and then makes adjustments in that number in bad years. If the starting-point number were developed using a methodology that included an adjustment for the valuation level that applied on the start date for the retirement, I believe that all of the take-out numbers that apply with this approach would be different.

Again, I am not at all familar with the Sensible Withdrawal Rate strategy. My focus has been elsewhere. I am going here by what I have picked up from posts describing this approach, and it may be that I have not picked up a proper understanding of the concept.

[gummy]

hocus
You've got "sensible withdrawals" right.

My own feeling is that you must withdraw enough to pay the bills.
If that's too large a percentage, then you gotta think about selling your house and moving to a less expensive neighbourhood

Beyond that "minimum" withdrawal, you withdraw "extras" only if you've just experienced a good year (financially speaking) ... in the sense that your portfolio (after last year's withdrawal) has increased by more than inflation. That's adhering to the motto: "Sell High"

How much of this "extra" you withdraw is (as you've said) a judgement call and may be (for example) 50% of the "extras" ... if you're planning a trip to the Bahamas.

The thing about this ritual is that it would have worked very well in the past. Without this test on historical performance, I wouldn't have dared to stick it on my website.

[hocus2004]

If you haven't checked to see if the Calculated Rate or the Safe Withdrawal Rate or the High Risk Rate (however calculated) actually worked well in the past, how would anybuddy have condidence in the procedure?

There was a post that you put to the FIRE board on a thread from a long time ago which I thought made the essential point pretty well, Gummy. You drew a picture of a Black Box and made the point that what comes out of the Black Box depends on what is put into it. The difference betwee the conventional SWR methodology and the data-based SWR methodlogy is all a question of what you put into the black box.

You can't calulate an SWR without starting with an asumption as to the long-term return you are likely to get from stocks. There is just no way to generate a number without doing this. The number used in the conventional studies is the long-term average return for stocks (about 7 percent real). The implicit assumption is that stocks provide the same sort of return from all possible valuation-level starting points.

This assumption is false. William Bernstein says in "The Four Pillars of Investing" that changes in valuation affect long-term returns as a matter of "mathematical certainty." We have checked the data, and the data shows that Bernstein is right on this point. It is not reaonable to assume that stocks will earn a long-term real return of 7 percent (the number that applies on average) for the 30-year returns sequence starting on January 2000. The expected long-term return starting from the valuation level that applied on January 2000 is about 3.5 percent real.

That's what this all comes down to. What you get out of the black box depends on what you put into it. If you assume what intercst assumes in the REHP study, you get the numbers that that study generates. But his assumptions are not reasonable ones. Changes in valuation levels have always affected long-term returns in the past, and it is not reasonable ton assume that they will begin having zero effect on the date of your retirement.

The way we checked to see whether this works or not is by checking on whether the historical data supports what Bernstein says is true as a matter of mathematical certainty. The data supports him all down the line. Bernstein is right. Intercst is wrong.

[gummy]

hocus:
Try to imagine Sally with a spreadsheet that uses the E10/P- Valuation model you're proposing.
She has all the historical data in the spreadsheet and various mathematical justifications (including HSWR data and statements about the importance of valuations and charts with regression lines and probabilities associated with 2 standard deviations etc..

Now she would like a suggested withdrawal rate for the coming year

... and gets none.

The problem I find with many suggested strategies ( not yours, of course :^) is that's it exhibits the mathmanship I've been exposed to for some thirty years, namely:

Couch all statements in mathematical jargon and "proofs" of efficacy, but never check to see if would have worked in the past.
This will guarantee that readers will be impressed, knowing that "mathematics doesn't lie".

[hocus2004]

Without this test on historical performance, I wouldn't have dared to stick it on my website.

That's a good statement, Gummy. I think that it is a fair interpretation of this statement that you are saying that, if you become convinced that this approach as currently designed lacks analytic validity, you would not promote it on your site. That is of course exactly the right attitude to take towards it.

If I understand the current design of the Sensible Withdrawal Rate strategy properly (and, again, it is possible that I do not), then the current design lacks analytic validty. I of course do not mean that this failing is a deliberate one. I don't think that for 10 seconds, anymore than I think that the REHP study was set up deliberately to lack analytic validity. The conventional approach was employed by a lot of smart and well-intentioned people for a good number of years. All the same, it lacks analytic validity.

The thing about this ritual is that it would have worked very well in the past.

That's not good enough, Gummy. I mean no disrespect with this statement. I believe that you want to know if the approach is not good enough, so I believe that I have to tell you if I know that it is not. I know that it is not.

Say that you have driven home successfully from a friend's house 130 times. Tonight he throws a party and you get rip-roaring drunk. You start out to your car and he makes a move to take your keys from you. You say "Oh, I have made this drive 130 times before, it is 100 percent safe for me to try it again." Who is right in this scenario?

Your friend is right. You were not rip-roaring drunk on those earlier occasions, so those earlier successes do not mean anything. It is not enough just to look at what worked in the past. You need to consider why it worked, and then assess the circumstances that apply in the current scenario, and then determine whether it is safe to try what worked in earlier times in the current scenario.

If you had only drank one mouthful of wine, perhaps you could argue that the past history still applies. If you are rip-roaring drunk, the past history is irrelevant to the question under examination--Is it safe to drive home? It is NOT safe, regardless of the 130 times it worked out in the past.

A 4 percent withdrawal is NOT safe for a retirement beginning at today's valuation levels. We don't know whether it will work or not. That is yet to be revealed. What we know for certain is that it is not safe. The historical data says that a 4 percent withdrawal from a high stock portfolio is a high-risk proposition for a retirement beginning at today's valuation levels.

[hocus2004]

Couch all statements in mathematical jargon and "proofs" of efficacy, but never check to see if it would have worked in the past.

We have checked whether our approach works. But our checks look at both of the two factors that affect SWRS: (1) the valaution level that applies at the start date of the retirement; and (2) the returns sequence that happens to pop up in your retirement.

You are asking us to ignore one of the two critical factors and see whether our approach still works. Obviously, it doesn't. If something is determined by two factors, and you only look at one, you always get the wrong answer.

To drive a car, you need to know how to work both the steering wheel and the accelerator. What if I said to you, "I want to know whether you really know how to drive a car. So I want you to show me that you can do it using only the accelerator, and never once touching the steering wheel." Could you do it?

You can't drive a car properly without using the steering wheel and you can't determine a SWR properly without taking valuation levels into account. What you are asking of us cannot be done. It is an absurdity to "check" the accuracy of an analysis by ignoring one of the two key factors being examined in it.

[gummy]

We have checked whether our approach works.

Could you point me to that check?
I think it would give some confidence to an individual who may use your scheme.

You are asking us to ignore one of the two critical factors and see whether our approach still works.

Which one?
I only ask you to indicate that, had Sally used your scheme, she would have fared very well ... in the past, since nobuddy knows the future, eh?

The thing about this ritual is that it would have worked very well in the past.

That's not good enough, Gummy.

The scheme I propose isn't justified simply by the fact that "it worked well in the past". It's also a question of logic.

If you lost a bundle last year, why would you withdraw a bundle this year, regardless of what SWR is suggested by some E10/P ritual?

If your portfolio has doubled in the past five years, would you still limit yourself to 2.7% if that's what some ritual suggested?

About working well in the past:
What if a scheme did not do work at all in the past?
How much confidence would you have in it?

P.S.
I've never had any faith in rituals that ignore current market machinations ... which is the reason for the "sensible withdrawals" mechanism. It doesn't.

If you like to called "current market machinations" as "current valuations", that's just playing with words.

[JWR1945]

I'll keep putting your sentences into your tutorial (even though I have little understanding of the procedure). I hope that readers are smarter than I. "?

If you haven't checked to see if the Calculated Rate or the Safe Withdrawal Rate or the High Risk Rate (however calculated) actually worked well in the past, how would anybuddy have confidence in the procedure?

I've done the following (on an Excel spreadsheet):

1: Calculated the SLOPE and INTERCEPT for the regression line, using the E10/P vs HSWR data you provided (from 1920 to 1949).

2: Beginning of an ERROR [Used that line to estimate the 1950 SWR (or whatever you want to call it) by plugging the 1949 E10/P value in for x
... as in y = SLOPE*x + INTERCEPT.]

3: ERROR [Looked up the actual inflation and return for a 80% / 20% portfolio of S&P500 /Govt Bonds for the year 1950.

4: THIS IS THE ERROR [Withdrew the percentage generated by the E10/P procedure (for the year 1950).]

5: WRONG RITUAL Repeated the above ritual each year for thirty years, each time using the data from 1920 and actual returns.
...
Of course, I probably don't know what I'm doing

All withdrawals with the data that you have used (HDBR50 and HDBR80 and HFWR50 and HFWR80) are held constant in terms of real dollars. Each rate is a percentage of the initial balance.

[I have also investigated strategies that vary withdrawals in terms of the current balance and in terms of combinations of the initial and the current balance.]

The correct procedure is to generate a single equation (or a set of equations). You look up P/E10 for the beginning of a historical sequence. [Most of the time, I have examined sequences that last 30 years.] You use the equation to predict the Historical Surviving Withdrawal Rate for that start year. The Calculated Rate is the best estimate. Withdrawing at the true Historical Surviving Withdrawal Rate ends up with a balance above zero dollars (at year 30). Withdrawing at a rate that is 0.1% higher results in a balance that is zero or negative (at year 30).

Half of the time, the true Historical Surviving Withdrawal Rate should be higher than the Calculated Rate. Half of the time, it should be lower than the Calculated Rate.

The Safe Withdrawal Rate is meant to guarantee safety. Almost all true Historical Surviving Withdrawal Rates should be higher than the Safe Withdrawal Rate. [I use a two-sided confidence level of 90% about the Calculated Rate. The Safe Withdrawal Rate has a one-sided probability of error of 5%.]

For HDBR50 and HDBR80, which have a final balance very close to zero, I generally choose 1923-1980. The distortions caused by the dummy data for years 2003-2020 are small.

For HFWR50 and HFWR80, I have used 1923-1972 because the dummy data in years 2003-2010, which assume heavy losses, greatly distort the results.

After calculating the equations, you should then compare the survivability of portfolios with the Calculated Rates (from the equations) and with the Safe Withdrawal Rates (after determining the lower confidence limit).

When I apply this procedure to recent years, I am making a prediction of the maximum withdrawal rate that will survive to year 30 with an increment of 0.1%. The Calculated Rate is that prediction. There will be scatter about such predictions. The actual rate should turn out to be between the Safe Withdrawal Rate and the High Risk Rate.

To check out this procedure, I have made comparisons in which I have restricted the years chosen to generate the equations to be distinct from the application of the equations (sometimes before, sometimes after and sometimes both). The equations do a good job in predicting the relationship between the value of P/E10 at the beginning of a retirement sequence and the largest withdrawal rates for which those sequences survive.

Have fun.

John R.

[gummy]

When I apply this procedure to recent years, I am making a prediction ...

Why wouldn't you apply the procedure starting in 1960 (for example). Then you KNOW the data for the next thirty years and can check how well that prediction fared..

If I understand you correctly, you use the data for the past umpteen years (say, from 1920 to 1960) to generate a regression equation and a withdrawal rate ... then you check to see how that withdrawal rate fared over the next thirty years (1960 to 1990, for example).

Then you repeat this, with the end-year 1961, then 1962 etc.

When you're finished you get a sequence of HSWR or HDBR or HFWR (depending upon how you picked your withdrawal rates).

Am I close?

[JWR1945]

Why wouldn't you apply the procedure starting in 1960 (for example). Then you KNOW the data for the next thirty years and can check how well that prediction fared..

I have. It does a great job. This is how I have evaluated the procedure.

All you have to do is look at your own graphs. The equations generated by those data produce great curve fits almost always.

I have made the other comparisons as well: using data from one era to predict results for a decade that was completely distinct. It does OK. The best estimates occur when the data that generate the equations have P/E10 values that cover the range of the decade that is used in comparisons. That is, it helps if you don't have to extrapolate.

Have fun.

John R.

[JWR1945]

If I understand you correctly, you use the data for the past umpteen years (say, from 1920 to 1960) to generate a regression equation and a withdrawal rate ... then you check to see how that withdrawal rate fared over the next thirty years (1960 to 1990, for example).

No. My primary comparisons have been with the data as a whole.

However, there is an issue about estimates made entirely from within a sample and estimates made outside of a sample. Both do fine.

Have fun.

John R.

[hocus2004]

If you lost a bundle last year, why would you withdraw a bundle this year, regardless of what SWR is suggested by some E10/P ritual?

Say that you went with a 74 percent S&P allocation for a retirement that began in January 2000, and you made your take-out number match the SWR (for a retirement beginning at those valuations) of 1.6 percent. Is a take-out of 1.6 a "bundle?" I don't think so. 1.6 is the SWR, that's all.

It''s perfectly OK to take less than 1.6 in bad years, if that makes you feel more comfortable. There is no need to do so to attain a plan that is 95 percent safe, according to the historical data.

If your portfolio has doubled in the past five years, would you still limit yourself to 2.7% if that's what some ritual suggested?

If you have a big increase in the size of your portfolio largely as a result of an increase in valuation levels, much of the increase is fluff rather than something of real economic substance. I would not be comfortable increasing my spending because of a temporary fluff increase in my portfolio size.

I would of course be comfortable spending the gains that are of real economic substance. SWR analysis is a good way of determining how much you can afford to spend and still retain the desired level of safety in your retirement plan.

I've never had any faith in rituals that ignore current market machinations ... which is the reason for the "sensible withdrawals" mechanism.

I think (based on my limited understanding of the Sensible Withdrawal Rate strategy) that the adjustments you make to the conventional methodology approach make sense. The problem is in how you come up with the number to which you perform the adjustments. If I am right in my understanding that you do not include an adjustment for the valuation levels that apply at the starting date of the retirement in coming up with this number, then the proper adjustments are being made to an incorrect number. That combination of steps produces an problemmatic result (again, assuming that I am right in my understanding of how the core number is generated).

[gummy]

Aha!
All this time I've completely misunderstood how you calculate those HSWR numbers ... and what they mean.
I've assumed that you use past data to predict future withdrawal rates.
I see that I was wrong. Your withdrawal rates are not "predictions" at all.

As I now understand it, it goes like this:

1: It's 1950 (for example) and you make let x1 = E10/P for 1949.
2: You follow a $100K porfolio for the next 30 years (using known market returns and inflation rates) and calculate the actual withdrawal rate that would reduce your portfolio to "slightly more than $0" (for example) and you call this y1.
3: You repeat the above for 1951, 1952, ... generating (x2, y2) and (x3,y3) ...
4: You plot these points, generate a regression line, calculate their correlation and discover that there is a close relationship between the x- and y-sequences.

If I've (finally!) got it right, then the "latest" regression line ended 30 years ago ... which explains why you kept referring to "dummy data" to 2010, starting in 1980

Now (for Sally's sake, in Jan, 2005), I'd like to take the "latest" regression line (ending 30 years ago) and last year's E10/P (which is known) and use it to suggest a withdrawal rate for the coming year.

Then the withdrawal rate would change each year depending upon the latest E10/P value ... and it would be easy enough see how this would have done in the past (where the withdrawal rate is a prediction based upon the latest E10/P value).

Presumably, as the years go by, more historical data is available and that would also affect the regression line hence the predicted withdrawal rate.

[JWR1945]

If I've (finally!) got it right, then the "latest" regression line ended 30 years ago ... which explains why you kept referring to "dummy data" to 2010, starting in 1980.

Now (for Sally's sake, in Jan, 2005), I'd like to take the "latest" regression line (ending 30 years ago) and last year's E10/P (which is known) and use it to suggest a withdrawal rate for the coming year.
...
Presumably, as the years go by, more historical data is available and that would also affect the regression line hence the predicted withdrawal rate.

I think that you understand this completely.

If I am wrong, it is because you started in 1950 and you used only 30 data points.

You could have started earlier.

Most of the time I use 1923-1980. [I originally used 1921-1980 to start with the beginning of a decade instead of selected from the data.] The late start date was because there is a problem with P/E10 and earlier years. Something is different. Your correlation chart shows that I could have gone back a little bit earlier.

My choice of 1923 instead of 1921 is simply an artifact of the curve fitting process. Years 1921 and 1922 have exceptionally high earnings yields, which causes them to have a disproportionate influence on the slope of the line. [That is, these two data points are almost by themselves and their earnings yields are almost twice as big as is typical for other data points.]

The "latest" regression line depends upon what I have available in my calculator. If your inputs are more up to date, go ahead and use the latest data.

[Dr. Shiller has provided some stock market data and the CPI later than 2002 at his website. I do not know off-hand where he might have placed data on commercial paper and bond yields.]

Have fun.

John R.

[gummy]

hocus, maybe you can tell me if I got this right:

Suppose that, sometime in the future (year 19N0), there was a E10/P of 5.3%.
You look at the data and find that E10/P was also 5.3% in 1973.
The SWR (HSWR80) for 1973 was 4.6%.

Relying on the E10/P relationship, you conclude that a withdrawal of 4.6% is appropriate.
Now an 80% S&P + 20% bond portfolio dropped 12% in 1973!
That's a bundle and, because of that, a 4.6% withdrawal is also a bundle.

In 1974 that 80% + 20% portfolio dropped over 20%!
That, too, is a bundle ... in spite of the fact that the "evaluation" in 1973 was 5.3% (which ain't that bad).

Personally, after a 12% drop I would NOT withdraw 4.6% regardless of the current E10/P value. Who knows, year 19N1 may be like 1974

[gummy]

oops]
Future is 20N0, not 19N0.
Sorry 'bout that

[JWR1945]

You are getting very close, gummy.

What you have listed are the Calculated Rates, not Safe Withdrawal Rates. The 4.6% is the data point for 1973. It is not even the calculated rate.

The Calculated Rate for HDBR80 with an earnings yield 100E10/P of 4.6% is close to 4.8%. [I read this from one of my old charts. I did not apply the equation, which is the best thing to do.]

[Notice that 1973 was a mildly unlucky year. HDBR80 had a true surviving withdrawal rate of 4.6% in 1973, which is slightly below the Calculated Rate of 4.8%.]

At the Calculated Rate of 4.8%, there is a 50-50 chance of success. The confidence limits for HDBR80 are plus and minus 1.58% (if my memory is right) or roughly 1.6%.

Your Safe Withdrawal Rate would be 4.8% minus 1.6%, which equals 3.2%. If you really wanted safety, you would limit yourself to withdrawing 3.2% plus inflation. [You would be highly likely to run out of money within 30 years if you were to withdraw 4.8% + 1.6% = 6.4% or more.]

If you selected to withdraw 4.6% of your portfolio's initial balance (plus inflation), your probability of success would be only a little bit higher than 50%. Perhaps, it would be around 60%.

Interestingly enough, the dividend yield was close to 3.2% in 1973 and in 1974. [I think that the yields were 2.9% and 3.5%, respectively.]

The notion that it is safe to withdraw the initial dividend yield plus just a little bit more (something no bigger than 1%) in terms of real dollars makes an excellent first approximation. [Even this has failed at least once among the 1960s start years.]

Have fun.

John R.

[hocus2004]

Personally, after a 12% drop I would NOT withdraw 4.6% regardless of the current E10/P value.

The numbers stuff is a mile over my head, Gummy. I rely on JWR1945 for that stuff.

Here is a link to the "Out of Sample SWR (non-US)" thread.

http://nofeeboards.com/boards/viewtopic.php?t=3125

Near the bottom, JWR1945 set forth the SWRs that applied for all the various years going a ways back. His SWR for an 80 percent S&P portfolio at the valuations that applied in 1973 is 3.6.

I would feel comfortable sticking with that number even after a price drop. I can see why someone like Peterv, who is concerned about demographic issues, might want to go with something lower. That is a matter of personal preference. My personal view is that the SWR has enough safety built into it that I would be OK with sticking with it even after a price drop.

That said, I think that an approach like your Sensible Withdrawal Rate strategy, where the take-out varies, can be better in some circumstances. I see that as an implementation question rather than a calculation question. The focus of my concern has been with what I see as the flawed calculation model used in the conventional studies.

I have a "Let a Thousand Flowers Bloom" philosophy re the implementation questions. I like to hear discussions of them, but I don't have particularly strong views re most implementation questions. My rough sense is that some implementation strategies work better for some types of circumstances and that others work better for other types of circumstances.

[gummy]

Here's something interesting (which y'all can probably check, just in case I goofed, which I do ... often)

If E10/P is a good representation of "current valuation", then you'd think there would be some good correlation between E10/P for a given year and the market return for that year.

But E10 involves the average earnings over ten years, so large market changes are smoothed by this averaging.

In fact, I find that the annual returns for one of those 80%+20% portfolios, and E10/P (for the same year), had a correlation of only 40% (for 1928-2000, since I've got the market data 1928-2000 in that "sensible" spreadsheet).

Maybe that's why I prefer "last year's market performance" rather than a valuation involving a ten year average.

Actually, although I wrote that "sensible" stuff years ago, my investigation of Nobel 2003 and volatility clustering makes me believe even more that last year's performance is a good "valuation".

I'll let you know in 30 years whether it's better than E10/P