Calculated Rates of the Last Decade

Research on Safe Withdrawal Rates

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JWR1945
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Calculated Rates of the Last Decade

Post by JWR1945 »

I have applied the following equations from the thread From Earnings Yield dated 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%.
I have listed below the last decade's January values of P/E10 taken from Professor Robert Shiller's website.
http://www.econ.yale.edu/~shiller/
http://www.econ.yale.edu/~shiller/data/ie_data.htm
Here are the values of P/E10 in January.

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1995    20.219819
1996    24.763281
1997    28.333753
1998    32.860928
1999    40.578255
2000    43.774387
2001    36.98056
2002    30.277409
2003    22.894158
The last entry in Professor Shiller's list is for November 2003. The S&P500 index was at 1054.87 and P/E10 was 25.898702. [To help with scaling: today's the S&P500 index started at 1134.41. If ten-year earnings were the same as in November 2003, today's P/E10 would be 25.898702*(1134.41/1054.87) = 27.851533.]

Safe, Calculated and High Risk Rates with 50% stocks

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Year  Safe  Calculated  High Risk
1995     3.60   4.61   5.62
1996     3.24   4.25   5.26
1997     3.04   4.05   5.06
1998     2.84   3.85   4.86
1999     2.61   3.62   4.63
2000     2.54   3.55   4.56
2001     2.71   3.72   4.73
2002     2.95   3.96   4.97
2003     3.37   4.38   5.39
Nov03    3.17   4.18   5.19
Today    3.06   4.07   5.08   
Safe, Calculated and High Risk Rates with 80% stocks

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Year  Safe  Calculated  High Risk
1995     3.37   4.95   6.53
1996     2.76   4.34   5.92
1997     2.42   4.00   5.58
1998     2.10   3.68   5.26
1999     1.71   3.29   4.87
2000     1.59   3.17   4.75
2001     1.87   3.45   5.03
2002     2.27   3.85   5.43
2003     2.98   4.56   6.14
Nov03    2.64   4.22   5.80
Today    2.46   4.04   5.62   
Remarks

For those who are invested 50% in stocks, the Safe Withdrawal Rate bottomed out near 2.54%. The odds in favor of success (i.e., having the portfolio last 30 years) are at least 50-50 in all cases with a withdrawal rate of 3.55% and lower. Except for 1998-2002, the odds in favor of success have been at least 50-50 at a withdrawal rate of 4.00%. Those who started withdrawing 5.00% in 1998-2002 are almost certain to run out of money within 30 years.

For those who are invested 80% in stocks, the Safe Withdrawal Rate bottomed out near 1.59%. It was below 2.00% from 1999-2001. It was below 3.00% from 1996 until today. The odds in favor of success are at least 50-50 in all cases with a withdrawal rate of 3.17% and lower. Except for 1998-2002, the odds in favor of success have been at least 50-50 at a withdrawal rate of 4.00%. Those who started withdrawing 5.00% in 1999-2000 are almost certain to run out of money within 30 years.

Have fun.

John R.
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Post by hocus2004 »

Thanks, JWR1945.
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Post by hocus2004 »

JWR1945:

Would you be able to put up SWR numbers for a 100 percent TIPS portfolio (for the years in which TIPS were available) that could be compared to the SWR numbers for an 80 percent stocks portfolio listed above?
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Post by Mike »

For those who are invested 80% in stocks, the Safe Withdrawal Rate bottomed out near 1.59%.
Hmm, so many people have fled to equities for inflation protection in the wake of the post high inflation 70s period that equities no longer seem to return a reasonable profit. The boomer saving period started in earnest right after people lost faith in fixed income, and the 401k plan permitted them only equities or the dreaded fixed income. The perfect storm is brewing, although it has so far greatly helped those who got in early.
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Post by JWR1945 »

hocus2004 wrote:Would you be able to put up SWR numbers for a 100 percent TIPS portfolio (for the years in which TIPS were available) that could be compared to the SWR numbers for an 80 percent stocks portfolio listed above?
Here is a comprehensive reply, which takes notice of the luck of retirees of the mid-1990s.

Refer to an earlier thread:
3% SWR for 56 Years dated Mon, Oct 13, 2003.
http://nofeeboards.com/boards/viewtopic.php?t=1541

I presented formulas and their derivations for TIPS Equivalent Safe Withdrawal Rates (TESWR) in this post on that thread.
http://nofeeboards.com/boards/viewtopic ... 536#p12536

This table is on that post.
Here is a table of TIPS Equivalent Safe Withdrawal Rates for interest rates of 2.2%, 2.5% and 2.8% and N = 10, 15, 20, 25 and 30 years.

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TIPS     N=10     N=15     N=20     N=25      N=30
2.2%   11.249%   7.899%   6.234%   5.243%   4.589%
2.5%   11.426%   8.077%   6.415%   5.428%   4.778%
2.8%   11.604%   8.256%   6.598%   5.616%   4.971%
I have extracted this as well.
This is the formula. If you own TIPS (so that we do not have to make any special adjustments to account for inflation) with an interest rate r, you can withdraw the TIPS Equivalent Safe Withdrawal Rate TESWR for exactly N years. At the end of N years, your balance is exactly zero.

This assumes that you can sell some TIPS at the same price at which you bought them. That is unlikely to be true. But very few TIPS have to be sold until you get close to their maturity. It causes very little fluctuation in your total income until then.

Let g = 1+r (for convenience in presenting the formula). Then:
TESWR = r * [ 1 / (1 - [ 1 / g^N] ) ].
Here are the TIPS Equivalent Safe Withdrawal Rates for 30-year TIPS with coupons between 0% and 4%. [When 30-year TIPS first came out during the 1990s, their coupons were around 3.5% to 4.0%. Today's 30-year TIPS on the secondary market have 3.375% coupons. They were issued in 2002. They now sell at substantial premiums.]

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coupon r       TESWR
0%       3.33%
1%       3.87%
2%       4.46%
3%       5.10%
4%       5.78%
I am not sure about what the highest TIPS coupon rate was. I recall that somebody has mentioned 4.25%, but I am not sure of its accuracy. I remember for sure that it got at least as high as 4.0% if not higher.

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3.000%      5.10%
3.125%      5.18%
3.250%      5.27%
3.375%      5.35%
3.500%      5.44%
3.625%      5.52%
3.750%      5.61%
3.875%      5.70%
4.000%      5.78%
4.125%      5.87%
4.250%      5.96%
All investors who purchase 30-year TIPS in the 1990s received a (true) 30-year Safe Withdrawal Rate in excess of 5.0%.

This is in contrast to the (initial) Safe Withdrawal Rates for those who invested heavily (80%) in stocks.
Safe, Calculated and High Risk Rates with 80% stocks

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Year  Safe  Calculated  High Risk
1995     3.37   4.95   6.53
1996     2.76   4.34   5.92
1997     2.42   4.00   5.58
1998     2.10   3.68   5.26
1999     1.71   3.29   4.87
2000     1.59   3.17   4.75
2001     1.87   3.45   5.03
2002     2.27   3.85   5.43
2003     2.98   4.56   6.14
Nov03    2.64   4.22   5.80
Today    2.46   4.04   5.62   

From our New Tool, we have found that the 30-year retirement sequences in the mid-1990s have turned out to be lucky sequences. That is to be expected because they were at the beginning of the bubble.

This is from Monitoring Pre-bubble Retirement Portfolios dated Wed, Jul 07, 2004.
http://nofeeboards.com/boards/viewtopic.php?t=2748
The 1994 return after 6 years was 16.22%. The Calculated Rate (from the formula) is 11.31%. With confidence limits of plus and minus 2.98%, the Safe Withdrawal Rate [with the 2002 estimate] is 8.33% and the High Risk Rate is 14.29%. Because subsequent years reduced the real, annualized return, we anticipate that the 10-year Calculated Rate will be lower, but it will still be very high.

The 1995 return after 6 years was 15.08%. The Calculated Rate (from the formula) is 10.81%. With confidence limits of plus and minus 2.98%, the Safe Withdrawal Rate [with the 2002 estimate] is 7.83% and the High Risk Rate is 13.79%.

The 1996 return after 6 years was 8.24%. The Calculated Rate (from the formula) is 7.80%. With confidence limits are plus and minus 2.98%, the Safe Withdrawal Rate [with the 2002 estimate] is 4.82% and the High Risk Rate is 10.78%.
[References to the 2002 estimate have to do with the formulas of the New Tool. Those formulas were applied to the years 1994-2000, 1995-2001 and 1996-2002 along with their actual rates of return.]

Unless a super bubble follows the bubble, we would expect all of the retirements begun after 1997 to have updated Safe Withdrawal Rates well below 5.0% and well below the truly safe rates of those who bought 30-year TIPS from the US Treasury Department.

Have fun.

John R.
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Post by Mike »

Unless a super bubble follows the bubble...
We might very well get that if the Republican plan to divert future Social Security taxes into the stock market takes effect. Only a small portion of the population saving significantly in 401k plans has helped lower the earnings yield substantially. If all US workers simultaneously tried to live off of the after tax earnings of corporations, the dividend yield could wind up below 1%. Again, great for the people who get in early.
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Post by unclemick »

My read of Bernstein's Birth of Plenty says that the Dutch - way way back in the early days of capitalism went abroad in search of yield, and I believe Victorian England tryed some of that in a wild and wooly place called America. Wonder if it's our turn in history's story.

Question two - we are relative rookies on inflation adjusted securities. Anyone run across info on how other countries have fared thru the decades and whether other fixed income instruments have adjusted to reflect the availiblity of inflation protected debt instruments.

Clearly JWR's numbers are showing some marked trending.
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Post by Mike »

My read of Bernstein's Birth of Plenty says that the Dutch - way way back in the early days of capitalism went abroad in search of yield, and I believe Victorian England tryed some of that in a wild and wooly place called America. Wonder if it's our turn in history's story.
Notice how many of the Dutch lost money that way. In the Dutch situation, there was actually a surplus of capital in Holland that led to lower interest rates. In our case, interest rates are set by bureaucratic fiat rather than the market. The same bureaucratic fiat method is used in many other countries, limiting profitable international options in fixed income loans. Since this is a relatively new experiment, the long term consequences of interfering with the free market in this way are unknown. Investors could have a rough time if the bureaucrats don't really know what they are doing.

The main problems with TIPS and I Bonds in this country are the taxation of the inflation adjust portion by the organization that issues the securities, and the CPI being set by the same organization that pays the inflation adjust. This leads to a conflict of interest.
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Post by JWR1945 »

unclemick wrote:Clearly JWR's numbers are showing some marked trending.
My research shows that the Calculated Rates and Safe Withdrawal Rates vary with the percentage earnings yield 100E10/P or 100% / [P/E10]. The trends that you have noticed follow the long-term trends in P/E10.

Look at Figure 1.2 from Professor Robert Shiller's database. It plots P/E10 for each year.
http://www.econ.yale.edu/~shiller/data/ie_data.htm

All of this ultimately relates back to the sustainable dividend yield, its growth rate and multiple compression or expansion. Percentage earnings yield captures all of this except for changes in the growth rate.

Have fun.

John R.
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Post by hocus2004 »

Thanks for the helpful information on TIPS, JWR1945.

All aspiring early retirees should take a look at TIPS in development of their investment strategies, in my view. To provide some balance to the discussion, here is a link to a column in Forbes by James Grant in which Grant makes the case against investing too heavily in TIPS at recent price levels.

http://www.forbes.com/columnists/busine ... 9/051.html

Grant: "Stocks, bonds, and real estate are not inherently good or bad. What decides the issue is price. At today's prices, I believe, the Treasury's Inflation-Protected Securities are bad. Constant readers will detect a U-turn. Three earlier installments of this column sang the praises of TIPS.

"No security is, or ever was, perfect, the argument here ran, but TIPS--at the price--offered more reward than risk. No more. Today ten-year TIPS offer an inflation-proof yield of 1.58%. As recently as two years ago the ten-year fetched 3.5%."
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Post by JWR1945 »

Jim Grant's column is dated 3-29-2004. Earlier this year, TIPS interest rates went down sharply. The 30-year TIPS rate fell below 2.0%. It rose above 2.5% briefly, fell again, but not as far down. It is currently 2.30% and rising.

From the Bloomberg website:
http://www.bloomberg.com/markets/rates/index.html
Here are TIPS (yield to maturity) rates in the secondary market just after 9:30 am EDT this morning:
5-year 1.11% matures on 1-15-2009 coupon 3.875%
10-year 2.02% matures on 7-15-2014 coupon 2.000%
30-year 2.30% matures on 4-15-2032 coupon 3.375%

Depending upon how important it is for an investor to purchase TIPS, I would suggest buying in gradually, similar to dollar cost averaging. In terms of 30-year TIPS, retirement portfolios and Safe Withdrawal Rates, any interest rate above 2.2% is attractive and 2.5% is very attractive.

In terms of my own investments, which I do not depend upon for my retirement income, I am willing to purchase at 2.5%, but not less.

Have fun.

John R.
Last edited by JWR1945 on Sun Jul 18, 2004 1:07 pm, edited 1 time in total.
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Post by hocus2004 »

The link to the James Grant column above has been picked up at two other boards. Some of the comments that have followed suggest a misunderstanding of the point that Grant is making, in my view.

Here is a snippet of what Grant says: "Inflation, after all, is a matter of dollars--an increase in the supply of money not offset by an increase in the demand for money. People will say, "Inflation is too much money chasing too few goods," but there's a lot besides goods that too much money can chase: stocks, bonds, houses, foreign currencies, etc. The cause of inflation is always the same, yet the symptoms are ever changing, and TIPS protect against only one set of symptoms. "

I think Grant is making a good point here. The inflation protection provided by TIPS is a big element of their appeal, but it's hard to imagine how any investment class could offer perfect protection from inflation. Say that the government never once engaged in any funny business re formulation of the basket of goods used to make its inflation adjustments. Would you be perfectly protected from the effects of inflation? You would not be. If your personal inflation rate were different than the government number, you would still potentially end up in trouble. There is no way for the government to know what items you personally spend money on, so there is no way for the government to provide you with perfect protection from the effects of inflation.

What concerns me about some of the posts I have seen re the Grant article is that they presume that the lack of perfect inflation protection applies only to TIPS. This is not so. Stocks also generally provide a good bit of protection against inflation and that feature is also a significant element of the appeal of stocks. But the inflation protection provided by stocks is also not perfect. Just as the inflation protection feature of TIPS may fail, so may the inflation protection feature of stocks.

Say that you understand why William Bernstein put the SWR for a high-percentage-stock portfolio at 2 percent at the top of the bubble, but that you are determined to stick with your high-percentage-stock portolio; so you lower your spending enough to be able to get by with a 2 percent annual take-out number. Now presume that you experience more inflation than the amount reflected in the official government numbers because your personal basket of purchases of goods and services is more heavily tilted towards health care spending, an area where there ends up being more inflation than for most other types of spending. If that happens, the 2 percent withdrawal rate may well not work for you.

The 2 percent take-out number is an inflation-adjusted number. It assumes that the investor is making appropriate adjustments for inflation each year in rejiggering his take-out number. If the investor is experiencing inflation higher than the government number, he is going to run out of money in a worst-case scenario. His expenses will be going up too fast for him to be able to stick to the 2 percent withdrawal while still maintaining the living standard he intended to provide for at the start of his retirement.

Anyone who adjusts his take-out number annually to reflect inflation's effects is taking a risk if the adjustment is made pursuant to the published government inflation adjustments. Both TIPS investors and stock investors take on this risk. The best way that I can see to protect yourself from this risk is to determine the adjustments in your plan by making reference to your personal inflation rate rather than to the government numbers.

It is your personal inflation rate that really matters. If you experience a lot of inflation personally, you need to take that into account, whether the government numbers suggest that inflation is mild or not. Conversely, if the government numbers call for larger increases in spending than your personal numbers suggest is appropriate, and you make adjustments in line with the government numbers, you are increasing your spending by more than the amount of inflation that applies to your personal basket of goods and services; you are increasing your spending by more than the amount that would be justified by an SWR analysis that took perfect account of the inflation factor.

I do not believe that TIPS offer perfect inflation protection. But I do not believe that stocks offer perfect inflation protection either. It may make sense for some aspiring early retirees to make adjustments in their personal withdrawal rates (PWRs) to cover themselves for the risk that the government number will understate the effects of inflation. Both TIPS investors and stock investors need to consider the merits of making such adjustments, in my view.
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Post by ben »

Good points Hocus. Personally I think it will be one of my "jobs" in FIRE to keep the personal inflation rate as low as possible through better shopping methods, repairs instead of replacements, staying in better health than when working (just the less stress will do a lot! :D ), planning purchases of consumables better (buy on sale/freeze Etc.), more do it yourself incl. cooking, repairs and on and on.

I would set myself a target of no inflation adjustment for the first couple of years - as a personal challenge.

Anyone blindly adjusting any W/R (be it 5%,4%,2% or whatever) simply based on government CPI no. is asking for trouble, just as it is silly to blindly draw a set % W/R without adjusting runningly for actual market returns.

Cheers! :D
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Post by Mike »

We might very well get that if the Republican plan to divert future Social Security taxes into the stock market takes effect.
An editorial in today's WSJ indicates that 7 trillion will be put into these accouts by the year 2019 if the plan passes.
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Post by hocus2004 »

"Personally I think it will be one of my "jobs" in FIRE to keep the personal inflation rate as low as possible through better shopping methods, repairs instead of replacements...."

That makes sense, Ben.

I feel a need to point out here a fallacy that my hero Joe Dominguez fell victim to when dealing with the inflation issue. Dominguez argued that it is possible by following the sorts of strategies outlined by Ben above to overcome the effects of inflation altogether. He maintained that, through cost-cutting, the early retiree could render inflation a non-issue.

Not so. I engaged in all sorts of cost-cutting in preparation for my early "retirement." That means that, after I turned in my resignation, there wasn't much more that could be cut. My plan presumed that I could maintain the same level of spending in retirement. But inflation will over time erode the buying power of that amount of annual spending. Dominguez was just flat-out wrong in maintaining that inflation can be rendered a non-factor, although he was wonderfully right in ways that no one else had ever been right before him on a whole host of other issues. Everyone makes mistakes.

For me, inflation matters more in connection with maintaining the size of my financial independence stash than it does in connection with determining the amount of my annual spending. My goal is to have the real value of my FI stash either stay the same or grow a bit with each passing year.

Keeping spending down is a help because lower spending numbers mean that it will be easier in future years to continue to grow the FI stash. But I am OK with increasing my annual spending by more than the rate of inflation for the year if that seems the right thing to do and does not cause me trouble in keeping the real value of my FI stash either maintaining value over time or growing in value over time.
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Post by ben »

I am OK with increasing my annual spending by more than the rate of inflation for the year if that seems the right thing to do and does not cause me trouble in keeping the real value of my FI stash either maintaining value over time or growing in value over time.
If understand you correctly that means that you are willing to increase with drawal (with more than inflation) as long as your actual market return has beaten inflation - I.e. you nest egg has grown in real value.

Same here; 2% W/R is my minimum and what I will start with, but 5% is my top level budget. I will not really care what the official CPI or whatever nos are - but do utmost to keep my personal inflation as low as possible. Keeping personal inflation at zero would be naive at best.

YMOYL by Joe is a classic and I am in the midst of re-reading it - gives me a burst of FIRE-motivation! :D
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Post by hocus2004 »

"2% W/R is my minimum and what I will start with, but 5% is my top level budget. "

I think that you could use the research that JWR1945 has published at this board to help you make better informed adjustments in your spending level, Ben.

Say that you retired on January 1, 2005, and that the nominal value of your stock portfolio went up by 50 percent in the following two years. This is not too far-fetched a scenario when you consider the price gains we saw in stocks in the late 1990s. Would you feel comfortable in that scenario with increasing your spending by a large percentage?

I would not. The intrinsic value of your assets did not go up by the nominal price increase in the stock index. You probably experienced some genuine gain in value. But the nominal stock prices you read in the newspaper are not reflecting the realities of what your assets are worth. It is hard to plan effectively when you do not even possess a good sense of the value of the assets you need to rely on to cover your future spending needs.

The Data-Based SWR Tool provides a means of coming to terms with these sorts of questions in a reasonably informed way. You can use this tool to make assessments of the intrinsic value of a stock investment.

There are all sorts of things that can be done with this tool that could not be done with the conventional methodology tool. I have worked with it for over eight years, and I have found it to offer an almost never-ending supply of new insights. I hope and believe that in time the community will come to see the value proposition in exploring the ins and outs of the new tool and will become more active participants in the exciting quest on which JWR1945 and I have embarked.
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Post by ben »

If my portfolio increased that much my mechanical re-balancing would have me selling quite some chunks of the winners (here stocks) and fill up the losers (or the ones increasing less) so I would naturally not be sitting on highly valued stocks only.

I would with that increase you mention (say overall portfolio increase from $1mill to $1.5mill) probably re-evaluate my W/R but when I kick of FIRE I would start at a set $ amount. In my current scenario say $24k/year - and not adjust same at all the first year. If it after a couple of years hit $1.5mill I would not be afraid of moving up to my "best" budget which is around $50-60k/year.

I.e. I do not follow any set % w/r - and I agree that just blindly doing same (+blindly adding infl.) is silly as I prefer safety/nest egg preservation to spending a max amount. Cheers, Ben
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