Bernstein's 2%

Research on Safe Withdrawal Rates

Moderator: hocus2004

Post Reply
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Bernstein's 2%

Post by JWR1945 »


hocus2004
Moderator
Posts: 752
Joined: Thu Jun 10, 2004 7:33 am

Post by hocus2004 »

Thanks very much for putting up that post. It helped clear up several points of confusion for me.

Bernstein says on Page 73 of "The Four Pillars of Investing" that: "Although the discounted dividend model (DDM) informs us well about expected returns, it tells us nothing about future risk. We are dependent on the pattern of past returns to inform us of the potential risks of an asset."

He is pointing out here that there are two distinct types of factors that must be considered in determining the return (and thus the SWR) provided by a stock investment. There is: (1) the expected return factor; and (2) the various factors that affect future risk.

The overall return you obtain from your investment is the result of the particular combination of these two types of factors that applies in your particular retirement. If you do well on both the expected return factor and the various future risk factors, you make out like a bandit. If you do poorly on both types of factors, you might well go bust. If you do well re one of the factor types and not so good re the other, your overall return is OK but not outstanding.

It is my sense that the biggest source of confusion in the SWR discussions is over this point. Many people are not accustomed to thinking of their stock return as being determined by two separate types of factors. People understand that there are multiple factors affecting their return. But they think of all of these factors as being similar in kind. They lump together all of the various factors that affect their return as if they were all of the same type.

The factor that Bernstein refers to as "expected return" is different in kind; that is why he discusses it separately in the passage quoted above and why he devotes an entire chapter of his book to helping people understand how to determine their expected return. One way in which it is different is that it is an elective factor. The investor elects what expected return will apply to his stock investment by deciding whether to purchase the shares at a time of low, medium, or high valuation. The future risk factors are not elective. All stock investors are subject to the same degree of future risk, regardless of when they purchase their shares.

Another difference is that the expected return is determined at an earlier stage of the investment life cycle. The expected return is determined on the day you make the investment. The future risk factors play out over the following 30 years; the extent to which they will affect your return becomes known only at a much later stage in the investment life cycle.

A third difference, which is a consequence of the second, is that the expected return factor is a predictable factor whereas the future risk factor is not predictable. There is one sense in which you can know the effect of the future risk factor. You can look to historical returns to place limits on the scope of the future risk factor. You can say, presuming that the future is no worse than the past, the future risk factor will never pull your overall return below x amount. You can indentify a likely range of future risk possibilities. But you cannot say with precision in advance what role the future risk factor is going to play in your particular retirement.

I believe that the key to communicating what the historical data says re SWRs is helping people to understand the distinction between the two types of factors that affect one's overall long-term return. We need to find ways to make it clear that the expected returns factor is not just one of many future risk factors, but a separate and distinct type of factor.

Conventional methodology studies do a good job of informing us as to the range of future risk possibilities. They do not address the expected returns factor at all. The Data-Based SWR Tool more accurately reports what the historical data says because it takes into consideration both types of factors, the future risk factors examined in the conventional methodology studies AND the expected returns factor, which requires making reference to the valuation level that applies on the retirement start date.

You say in your post above that: "When the effect of starting valuations is removed, there is a residual variation of plus and minus 1.01% (with 50% stocks) to 1.58% (with 80% stocks) about the calculated rate. " I am wondering if the significance of this point might be better conveyed with use of a graphic. Would it be possible to set something up where, down the verticle line on a graphic you listed the various retirement starting date S&P valuation levels that might apply and along the horizontal line you reported (perhaps with a bar graphic) the range of withdrawal rates likely (at a 90 percent confidence level) to succeed?

The likely results would obviously be a lot better for retirements beginning at a moderate S&P valuation level than for those beginning at a high S&P valuation level. But the graphic would also show that the Data-Based Tool does not permit one to make precise predictions of outcomes. There would be overlap in the results. That is, the graphic would show that an investor starting from a higher valuation level would stand a chance of doing better than an investor starting from a lower valuation level because the former investor might get a better result from the future risk factor. The graphic would also show that the odds would favor the investor with a favorable expected returns factor, of course.
Mike
*** Veteran
Posts: 278
Joined: Sun Jul 06, 2003 4:00 am

Post by Mike »

I hope that you are able to figure out where William Bernstein's 1.5%-2.0% rule of thumb comes from. Supposedly, it was from these numbers.
That number seems to be an initial attempt to get a ballpark estimate of a 100% safe rate. He then goes on to say that trying to get more than 90% safety for a 40 year retirement is probably unrealistic, if only because nations have not historically had sufficient political stability to justify such a number. On page 236 he estimates that a 95% success rate implies nations with an average political stability of 800 years (40 years divided by a failure rate of 5% equals 800 years).

I think all this means that he is suggesting a practical withdrawal rate a bit higher than 2%, because the extra margin of safety provided by 1.5 to 2% is an illusion. Is this how you understand page 236?
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Post by JWR1945 »

hocus2004 wrote:You say in your post above that: "When the effect of starting valuations is removed, there is a residual variation of plus and minus 1.01% (with 50% stocks) to 1.58% (with 80% stocks) about the calculated rate. " I am wondering if the significance of this point might be better conveyed with use of a graphic. Would it be possible to set something up where, down the vertical line on a graphic you listed the various retirement starting date S&P valuation levels that might apply and along the horizontal line you reported (perhaps with a bar graphic) the range of withdrawal rates likely (at a 90 percent confidence level) to succeed?
We already have a graphic that shows this information, but somewhat differently. Go to the special SWR Research section.
http://www.nofeeboards.com/jwr/jwr.html

Scroll down to the very bottom and click on the 1923-1980 plots (at the bottom of the selections from those at the bottom of the page). I find it necessary to view the graphs in Full Screen (that is, to click on View and then to click on Full Screen). The plots show Historical Surviving Withdrawal Rates on the vertical scale and earnings yield on the horizontal scale. (This is rotated 90 degrees from what you asked for.)

The lines show 30-year survival results for 50% stocks (HDBR50) and for 80% stocks (HDBR80). There are lines for each. Those lines are Calculated Rates. Individual data points are color coded and presented as well. [There is a typo. The lines are identified correctly. The data points correspond to the lines just above them in the legend. Data points with different colors correspond to different portfolios.]

Mentally, draw lines parallel to those for the calculated rate. The lines parallel to the HDBR50 should be plus and minus 1.01% (above and below the Calculated Rate line). The lines parallel to HDBR80 should be plus and minus 1.58%. The parallel lines above the Calculated Rates are the High Risk Rates. The parallel lines below the Calculated Rates are the Safe Withdrawal Rates.

Are you having a hard time imagine parallel lines at plus and minus 1.01% or 1.58%? I do. You don't really have to go to that extreme. Just look one of the lines on the graph and its associated data (according to its color code) and imagine what at broad strip (centered around the Calculate Rate line) would look like. Notice how well the data stay within such a strip. [As a technical detail, the spread of the actual data increases slightly as the earnings yield increases. When we use a single pair of confidence limits, we overestimate the spread slightly at high valuations (and low earnings yield) and underestimate it slightly at low valuations (and high earnings yield).]

It will be a little bit confusing at first because there are two different plots on the same display. It becomes much easier after you are able to associate the correct colors together. [It would have been easier with at total of two colors instead of four.]

Please make an effort to do this and to understand what you are seeing. I think that it goes a long way towards providing what you have asked for.

Have fun.

John R.
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Post by JWR1945 »

Mike wrote:I think all this means that he is suggesting a practical withdrawal rate a bit higher than 2%, because the extra margin of safety provided by 1.5 to 2% is an illusion. Is this how you understand page 236?
No. The 1.5% to 2.0% was an adjustment to the stock market's return. He gave it as a general rule of thumb although it was in the context of 30-year survival rates.

It was different from the 2% withdrawal rate that he considered appropriate for new retirees (when he wrote his book). That number was specifically for 30-year retirement periods. It took the likely future stock market return into account. [It more or less included a 1.5% to 2.0% adjustment to something.]

His point about placing too much emphasis on the claimed level of safety is a different point. His illustration was for 40-year retirements. We take this point into account on this discussion board when we limit ourselves to 90% confidence limits about our Calculated Rates. [This is using a two-sided test. If we were to emphasis only Safe Withdrawal Rates and use a one-sided test, we would claim to have a 95% confidence level.]

One of my points is that it is extremely difficult to pin down any of William Bernstein's numbers. That makes his book hard to read. It causes different people to come up with different answers to the same question.

There is a lot of useful information in what Bernstein has to say. Just realize that you have to be exceedingly careful about his numbers.

Have fun.

John R.
Mike
*** Veteran
Posts: 278
Joined: Sun Jul 06, 2003 4:00 am

Post by Mike »

Thank you John.
hocus2004
Moderator
Posts: 752
Joined: Thu Jun 10, 2004 7:33 am

Post by hocus2004 »

"We already have a graphic that shows this information, but somewhat differently."

I understand. I am trying to come up with different ways of making the case until we come up with the approach that clicks with people.

My sense is that the question that is causing the most trouble is the question of whether the future is knowable or not. People don't really believe that future stock prices are totally unknowable. If that were the case, buying stocks would be like betting on horses; they wouldn't be an investment, they would be a gamble. But people have a hard time accepting that future stock prices can to a large extent be accurately predicted. Our job is to show clearly the extent to which future prices are predictable and the extent to which they are not.

The existing graphic does a good job of illustrating what has happened historically. My thought is that we can better make the case for the importance of taking valuation levels into account by showing how the range of long-term results obtained from a stock purchase made today varies according to the valuation level that applies today. The graphic would be based on the same data as the existing graphic, but it would illustrate the point in a somewhat different way.

Say that you had a chart along the lines that I described above for the results of the Data-Based SWR Tool and a second chart showing the results of the Conventional SWR Methodology Tool. Both charts would show a range of possible results from each valuation-level purchase point. The difference would be that the conventional methodology chart would show the exact same figures for each point on the spectrum of valuation level possibilities while the data-based chart would show that the figures contained within the range vary from valuation level to valuation level.

My thought is that no reasonable person could conclude that the conventional methodology is analytically valid when faced with that comparison. It just defies common sense to think that valuation plays no role whatsoever in the determination of future returns. We have said this with words many times, but sometimes a graphic gets things across in a way that words do not.

I'm not trying to suggest that we need to produce this chart immediately. I'm thinking ahead a little bit to things that we might want to do as we aim to take this concept public and make the case to a larger group of people. I think that a chart along these lines is something that we might want to provide along with some other visual aids illustrating other points.

My purpose in putting the idea forward was just to see if others thought that the idea had any merit. I've been thinking a lot lately about the two types of factors affecting returns (expected return and future risk) and trying to come up with ways to show clearly the distinction between them. My sense is that, if we succeed in making that distinction clear, a better understanding of a host of other issues may well follow.
hocus2004
Moderator
Posts: 752
Joined: Thu Jun 10, 2004 7:33 am

Post by hocus2004 »

"The uncertainty in the Historical Surviving Withdrawal Rates without taking valuations into account was plus and minus 3% to 4% about a mid-point rate close to 7% or 8%. Including the effects of valuation allows us to drop those ranges to 1% to 1.6%."

I'm not a Numbers Guy. But that sounds like a big deal to me.

"If we were able to predict subsequent annualized returns exactly, the residual variation would drop down to 0.64% (with 50% stocks) to 1.02% (with 80% stocks) about the calculated rate. This is the part that is caused by the sequence of returns alone. "

I appreciate the point you make above re the confusion Bernstein causes re the numbers, JWR1945. But it seems that by happenstance it turns out that the adjustment for the Future Risk factor really does turn out to be close to 2 percent for an 80 percent stock portfolio. The High-RIsk Withdrawal Rate for today is 5.62% (I am pulling this number from the "Calculated Rates of the Past Decade" thread). There are two adjustments for the Future Risk factor needed to transform that number into an SWR (one adjustment of 1.02% going up from the Calculated Rate of 4.04, and one adjustment of 1.02 going down from the Calculated Rate of 4.04). So the total adjustment for the Future Risk factor appears to me to be 2.04. Is that right?

I liked it that Bernstein went through a two-step analysis in explaining why the SWR for a high-stock-percentage portfolio was 2 percent at the top of the bubble. He first determined (using the Gordon Equation) the likely annualized return (which was 3.5%). Then he made an adjustment for the Future Risk factor. The benefit of working through the steps is that it highlights the failure of the conventional methodology analyses to include one of the key steps.

Are you able to give a figure for Expected Return that applies in your analysis showing the current-day SWR to be 2.46?

It appears to me that your Expected Return number would be some number lower than 5.62 (the High-Risk Withdrawal Rate). The fact that the High-Risk Withdrawal Rate assumes depletion of principle over 30 years pulls whatever the Expected Return number is up to 5.62. Then there are subtractions of 1.12 for residual uncertainty re medium-term returns (as explained in your post above) and of 2.04 for the Future Risk factor. After subtracting 3.16 from 5.62, you are left with 2.46, your SWR number. Does all that sound right?

One last question. Is it possible to assign an implicit Expected Return assumption for the conventional methodology analytical approach?

Thanks for your help with this. It's painful for me to struggle with the numbers, but over time it clarifies things.
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Post by JWR1945 »

hocus2004 wrote:I appreciate the point you make above re the confusion Bernstein causes re the numbers, JWR1945. But it seems that by happenstance it turns out that the adjustment for the Future Risk factor really does turn out to be close to 2 percent for an 80 percent stock portfolio. The High-RIsk Withdrawal Rate for today is 5.62% (I am pulling this number from the "Calculated Rates of the Past Decade" thread). There are two adjustments for the Future Risk factor needed to transform that number into an SWR (one adjustment of 1.02% going up from the Calculated Rate of 4.04, and one adjustment of 1.02 going down from the Calculated Rate of 4.04). So the total adjustment for the Future Risk factor appears to me to be 2.04. Is that right?
Your reasoning here is far better than what William Bernstein has presented. I believe that your logic is more accurate as well because your numbers are traceable. We don't really know how Bernstein came up with his numbers. We have lots of hand waving, but very little that is specific.

In terms of the graphics, the conventional methodology draws a line parallel with the x-axis (earnings yield axis, the Survival Rates do not vary with valuations when using the conventional methodology). The line equals the smallest Historical Surviving Withdrawal Rate in the entire plot. (Of course, the lines for HDBR50 and HDBR80 are different. It would be easier if we has two separate graphs instead of having to rely on color codes.) Everything above the line is OK. Everything below the line is not OK.

The conventional methodology does not draw the upper line (corresponding to a High Risk Rate). It would be another line parallel to the x-axis (earnings yield axis), but it would equal the value of the highest Surviving Withdrawal Rate.

The two parallel lines would be close to 4% for the lower confidence limit (which is the Safe Withdrawal Rate according to the conventional methodology) and 10% to 12% for the upper confidence limit (which would be the High Risk Rate according to the conventional methodology).

When you look at the graphs (and the lines that the data produce), you can see a distinct upward slant: Surviving Withdrawal Rates increase as Earnings Yields increase (which is also as valuations decrease). You can fit a relatively narrow strip parallel to the lines produced by the data. In contrast, the conventional methodology has produces a very wide band which is parallel with the x-axis. Its slope is zero. It does not have the upward slant that we see in the data.

I will be getting back with additional comments in the next day or two. I have been working on calculators in the last few days. One is a major upgrade to what we have now. I have checked it out. The other is almost identical to the first upgrade, but I have changed the algorithm for withdrawing a fraction of portfolio gains to year-to-year increases instead of the current six year comparisons (my implementation of the JanSz feature). I have not checked it out yet.

These new calculators should help with strategies that take a fraction of dividends (and/or interest) and/or capital gains for withdrawals instead of (or in addition to) withdrawing according to a portfolio's initial balance. I now produce tables showing the size of your withdrawals versus time using complex strategies.

Have fun.

John R.
hocus2004
Moderator
Posts: 752
Joined: Thu Jun 10, 2004 7:33 am

Post by hocus2004 »

"The conventional methodology produces a very wide band which is parallel with the x-axis. Its slope is zero. It does not have the upward slant that we see in the data. "

That's a good point, JWR1945. What the conventional methodology is really assuming is that there is no correlation between the valuation level that applies at the retirement start date and the long-term return that follows. The conventional studies are suggesting that you have just as much chance of having a 10 percent withdrawal rate work when you start from a high valuation level as you do when you start from a low valuation level, and that you have just as much chance of having a 4 percent withdrawal fail when you start from a low valuation level as you do when you start from a high valuation level. The assumption is that valuation makes no difference, that stock prices are a random walk in the long term as much as they are in the short term.

When you have a chance, could you let me know the PE10 level that generates in your methodology the withdrawal rate identified as "100 percent safe" in the REHP study? It also would be helpful to know the last year in which that PE10 level applied.
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Post by JWR1945 »

hocus2004 wrote:The conventional studies are suggesting that you have just as much chance of having a 10 percent withdrawal rate work when you start from a high valuation level as you do when you start from a low valuation level, and that you have just as much chance of having a 4 percent withdrawal fail when you start from a low valuation level as you do when you start from a high valuation level.
You are correct.

I erred a little bit because I did not identify the confidence levels associated with the 4% and 10% from the conventional studies. The conventional methodology does not attempt to determine confidence levels. It just assumes that previous historical outcomes are predictive of future outcomes while ignoring such things as valuations and dividend yields. Therefore, it guesses that the confidence level is high. That is a reasonable starting point. It becomes unreasonable as soon as you look deeper into the matter.

A more refined application of the conventional methodology would have produced confidence limits. Biggalloot had started to produce some numbers along those lines back when I still subscribed to the Motley Fool.
When you have a chance, could you let me know the PE10 level that generates in your methodology the withdrawal rate identified as "100 percent safe" in the REHP study? It also would be helpful to know the last year in which that PE10 level applied.
The smallest Surviving Withdrawal Rates correspond to P/E10 levels of 24 (such as 1965-1966) and 27 (unique to 1927). Those were the highest pre-bubble valuations. They defined the top of the historical range. The exact values of P/E10 for worst case conditions depend upon the stock allocation, but using 24 is always a good number. Including 27 as the extreme provides helpful additional information. There may be a stock allocation that would have caused the P/E10 level to be as low as 23, but I do not know what it might be.
The assumption is that valuation makes no difference, that stock prices are a random walk in the long term as much as they are in the short term.
Yes and this has been demonstrated by several recognized authorities as being untrue. I generally refer to Drs. Campbell and Shiller's papers related to P/E10. But there are many others. For example, John Bogle's book on Common Sense on Mutual Funds produces credible evidence related to the speculative factor (of expanding and contracting P/E levels). William Bernstein's presentation of the Gordon Model reveals the fallacy as well.

Have fun.

John R.
hocus2004
Moderator
Posts: 752
Joined: Thu Jun 10, 2004 7:33 am

Post by hocus2004 »

"It just assumes that previous historical outcomes are predictive of future outcomes while ignoring such things as valuations and dividend yields."

The root assumption is that stocks returns are a random walk in the long term as well as in the short term. If it were true that stock prices were a random walk in the long term, I think it would be reasonable to use the conventional methodology to determines SWRs. In that circumstance, all of the data points would be relevant to the question of "what withdrawal rate is safe at any one particular valuation level?"

Given that the historical data shows that stock returns are not a random walk in the long term, it is not reasonable to use all the data points to determine what withdrawal rate is safe at any one particular valuation level. You need to limit yourself to relevant data points, data points from similar valuation levels.

That means that you need to make adjustments for valuation so that you have enough relevant data points to perform a meaningful analysis. When you include the valuation adjustment, you of course get different results.

"The smallest Surviving Withdrawal Rates correspond to P/E10 levels of 24 (such as 1965-1966) and 27 (unique to 1927). Those were the highest pre-bubble valuations. "

I don't think that is the number that I was looking for. I understand that those are the PE10 levels that produced the 4 percent number reported in the conventional studies as "100 percent safe." My understanding is that the 4 percent number was not actually safe at those PE10 levels. The 4 percent number survived in the two times it was tried at those levels. But that does not mean that it was safe. It may have survived because of a lucky turn of events in those two cases. It may be that the returns sequences that applied in those two cases were not worst-case scenarios.

What I was looking for was the PE10 number that your methodology reveals as applying for a 4 percent SWR (or whatever the precise number is that is reported as the "100 percent safe" number in the REHP study). I presume that this number would be a bit lower than the numbers above. It would be a valuation number very much on the high side, but not the highest of all that applied in the pre-bubble era. I also was hoping you could tell me the last year in which that PE10 level applied.

Thanks again for all your help. Please understand that these questions are not at all a rush matter. I ask only because there are times when I need access to the answers to them in trying to explain this stuff to others. I am looking forward to hearing about your calculator revisions.
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Post by JWR1945 »

hocus2004 wrote: What I was looking for was the PE10 number that your methodology reveals as applying for a 4 percent SWR (or whatever the precise number is that is reported as the "100 percent safe" number in the REHP study). I presume that this number would be a bit lower than the numbers above. It would be a valuation number very much on the high side, but not the highest of all that applied in the pre-bubble era. I also was hoping you could tell me the last year in which that PE10 level applied.
This is easy to answer (unless you want greater precision, which should not be necessary). Look at the From Earnings Yield thread starting on Thu, Apr 15, 2004.
http://nofeeboards.com/boards/viewtopic.php?t=2368

Here are my answers for 1929 when the P/E10 was 27.
In 1929 the P/E10 was 27.0 and the calculated Zero Balance Rate for a 50% stock portfolio is 4.12% [or 4.1171037%] plus and minus 1.01%. The Safe Withdrawal Rate is 3.11%. The Unsafe Withdrawal Rate is 5.13%.

With the 80% stock portfolio, the 90% confidence limits are plus and minus 1.58%.

For 1929 with P/E10 equal to 27.0, the calculated Zero Balance Rate for an 80% stock portfolio is 4.12% [or 4.1183259%] plus and minus 1.58%. The Safe Withdrawal Rate is 2.54%. The Unsafe Withdrawal Rate is 5.70%.

Notice that the Safe Withdrawal Rate for 1929 was lower with the 80% stock allocation than with the 50% stock allocation. The Zero Balance Rates were almost identical. The Unsafe Withdrawal Rate was higher with 80% stocks. The actual 1929 Historical Database Rates of 4.4% (for 80% stocks) and 4.5% (for 50% stocks) fell within the confidence intervals.
The numbers are almost identical when P/E10 equals 24. Whether in 1929, 1937, 1965 or 1966, the comparisons are very close. Depending upon the stock allocation, the conventional methodology produces (30-year) Surviving Withdrawal Rates of 3.9% or 4.0%.

Have fun.

John R.
hocus2004
Moderator
Posts: 752
Joined: Thu Jun 10, 2004 7:33 am

Post by hocus2004 »

"In 1929 the P/E10 was 27.0 and the calculated Zero Balance Rate for a 50% stock portfolio is 4.12% [or 4.1171037%] plus and minus 1.01%. The Safe Withdrawal Rate is 3.11%."

This is saying that, when the PE10 was 27, the SWR was really 3.11%. I am coming at this from the other direction.

What I want to know is, when the SWR was really 4% (or whatever number is the precise number reported as "100 percent safe" in the REHP study), what was the PE10 number?

I don't want to know the PE10 at the highest pre-bubble valuation. I want to know the PE10 at the somewhat lower valuation that produces a SWR of 4% under your Data-Based SWR Tool methodology.

Sorry for the confusion.
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Post by JWR1945 »

The claims of safety by users of the conventional methodology are accurate only at typical valuations, close to P/E10 = 17 (or lower). This is only slightly higher than the median valuation in the historical record.

From Earnings Yield Thu, Apr 15, 2004.
http://nofeeboards.com/boards/viewtopic.php?t=2368
With the 50% stock portfolio, the Historical Database Rate (HDBR50) equation is HDBR50 = 0.3979x+2.6434%, where x = 100*(E10/P) or 100/[P/E10] = the earnings yield in percent and R squared equals 0.6975. When using this equation, the standard deviation of HDBR50 is 0.6178. The 90% confidence limits are plus and minus 1.01% of the calculated value.

With the 80% stock portfolio, the Historical Database Rate (HDBR80) equation is HDBR80 = 0.6685x+1.6424%, where x = 100*(E10/P) or 100/[P/E10] = the earnings yield in percent and R squared equals 0.7274. The standard deviation of HDBR80 using this formula is 0.9649. The 90% confidence limits are plus and minus 1.58%.
The conventional methodology claims 100% safety at a 3.9% withdrawal rate for HDBR50 (30 years and 50% stocks).

Using our terminology:
Safe Withdrawal Rate = Calculated Rate - Confidence Limit
For HDBR50:
3.9% = Calculated Rate - 1.01%.
Solving, Calculated Rate = 4.91%.
Calculated Rate is HDBR50 in the first equation:
HDBR50 = 0.3979x+2.6434%, where x = 100*(E10/P) or 100/[P/E10] = the earnings yield in percent.
4.91% = 0.3979x+2.6434%
x = [4.91-2.6434]/0.3979 = 5.6964061 or 5.70%.
Earnings Yield = 5.70% or P/E10 = 17.6 to assure safety when withdrawing 3.9% from HDBR50. The conventional methodology claims 100% safety at 3.9% regardless of valuation.

The conventional methodology claims 100% safety at a 4.0% withdrawal rate for HDBR80 (30 years and 80% stocks).

Using our terminology:
Safe Withdrawal Rate = Calculated Rate - Confidence Limit
For HDBR80:
4.0% = Calculated Rate - 1.58%.
Solving, Calculated Rate = 5.58%.
Calculated Rate is HDBR80 in the first equation:
HDBR80 = 0.6685x+1.6424%, where x = 100*(E10/P) or 100/[P/E10] = the earnings yield in percent.
5.58% = 0.6685x+1.6424%
x = [5.58-1.6424]/0.6685 = 5.8902019 or 5.89%.
Earnings Yield = 5.89% or P/E10 = 17.0 to assure safety when withdrawing 4.0% for HDBR80. The conventional methodology claims 100% safety at 4.0% regardless of valuation.

Claims of safety by users of the conventional methodology apply only at typical valuations. P/E10 = 17 is only slightly higher than the median valuation in the historical record.

If you look at the charts at the very bottom (the bottom of the bottom of the page) of the special SWR Research section, mentally draw a line parallel with the x-axis (x = earnings yield) with a y value of 4% (y = surviving withdrawal rates).

The hard part is imagining strips about each data set. The data for HDBR50 has a very gentle slope and (absent knowledge that the confidence limits are plus and minus 1.01 %), I wouldn't feel too safe unless the earnings yield were above 5% (and close to 6%) because of two outliers. Those outliers are at earnings yields close to 11 and 12 and with surviving withdrawal rates around 5% and 5.5%. A line parallel to the line for HDBR50 Calculated Rates (the green line) would cross y = 3.9% or 4% somewhere close to but higher than x = 5%.

Similarly for HDBR80. The outliers are around an earnings yield x of 10% to 12% and surviving withdrawal rates y close to 8%. (It looks as if there is another outlier around x = 11% and y = just under 7%.) Once again, draw a mental line parallel to the (reddish) purple (or lavender?) line consistent with the blue data points. It will cross y = 4% when x is close to (but greater than) 5%.

Have fun.

John R.
hocus2004
Moderator
Posts: 752
Joined: Thu Jun 10, 2004 7:33 am

Post by hocus2004 »

"The claims of safety by users of the conventional methodology are accurate only at typical valuations, close to P/E10 = 17 (or lower). This is only slightly higher than the median valuation in the historical record."

Thanks very much.

I have always thought that this aspect of the thing was a big deal. It's not just that the conventional methodology is "out of date" because we have in recent years experienced valuation levels never seen before. The real problem is that the conventional methodology is analytically invalid for purposes of determining SWRs.

What happened in the bubble period is that the flaws of the conventional methodology became more evident. It used to be that the conventional methodology number was off by a few tenths of a percentage point or perhaps half of a percentage point. Then all of a sudden it was off by two full percentage points. The problem became a much more serious one when we reached bubble level valuations. But the analytical flaw was always present in the methodology. You can't accurately determine SWRs without taking valuation levels into account.
Post Reply