A 4% safe withdrawal rate with no risk of "failure"

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Is the calculation right?

By golly, it is
6
24%
By golly, it is
6
24%
No, you screwed up the calculation
13
52%
 
Total votes: 25

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nisiprius
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A 4% safe withdrawal rate with no risk of "failure"

Post by nisiprius »

I suddenly realized that in the case of TIPS or I bonds, you can, in fact, compute the safe withdrawal rate (SWR) precisely . You just perform a simple amortization calculation in real dollars.

The "safe withdrawal rate" is the number of real dollars, as a percentage of the initial amount, that will, when withdrawn every year, reduce the balance to zero at the end of the specified time period.

Unless I've screwed up on the calculation...

Using the Excel PV function, if the real interest rate (above the CPI adjustment) is I, the number of years is N, and if you assume that the withdrawal is made annually at the beginning of the year, then the safe withdrawal rate is

-1/PV($A6,B$5,1,0,1)

For various interest rates and time horizons, the safe withdrawal rates would seem to be:

----------25-------30-------35
1.00% 4.50% 3.84% 3.37%
1.30% 4.65% 3.99% 3.53%
1.50% 4.76% 4.10% 3.64%
2.00% 5.02% 4.38% 3.92%
2.50% 5.30% 4.66% 4.22%
3.00% 5.58% 4.95% 4.52%
3.50% 5.86% 5.25% 4.83%
4.00% 6.15% 5.56% 5.15%
4.50% 6.45% 5.87% 5.48%

For some reason, traditionally, SWR's are illustrated for a 30 year "time horizon." This doesn't really seem appropriate for (say) a 65-year-old woman, but never mind, that's my wife's problem, not mine.

Notice that a 1.3% real interest rate is sufficient to achieve a 3.99% withdrawal rate over 30 years.

Now, in the case of TIPS, there is a problem, because 30 year TIPS are no longer offered and even 20 year TIPS seem to be rarely offered. If you use 10 year TIPS there is no assurance of what the interest rate will be when the TIPS matures and must be rolled over, or even that TIPS will still be available.

I bonds, however, continue to earn interest for 30 years, and by a curious coincidence they happen to be earning exactly a 1.3% real interest rate right now. Of course you need to do something or other about the first five years, during which I bonds charge a three month's interest penalty for redemption.

Oh, so was I exaggerating when I claimed a "4%" rate when the table shows only 3.99%? The answer could be, no, not exactly, because the rate is actually just a tad higher if you assume that withdrawals are made monthly instead of making the entire year's withdrawal at the start of the year. With monthly withdrawals, a 1.3% real interest rate allows a 4.02% safe withdrawal rate.
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Post by FinanceGeek »

The "safe withdrawal rate" is the number of real dollars, as a percentage of the initial amount, that will, when withdrawn every year, reduce the balance to zero at the end of the specified time period.

My definition of the SWR is the maximum rate of withdrawal that does NOT result in running out of money at some predetermined level of confidence...

In other words its not an amortization rate, its a perpetuity rate.
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Post by lazyday »

nisiprius, just don't screw up and live for 50 or 60 years. :)

FinanceGeek, I haven't seen others use it that way. But with a conservative WR and a portfolio with, say, 50% or 75% equity, the portfolio might last as long as the stock market does.
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Post by nisiprius »

FinanceGeek wrote:The "safe withdrawal rate" is the number of real dollars, as a percentage of the initial amount, that will, when withdrawn every year, reduce the balance to zero at the end of the specified time period.

My definition of the SWR is the maximum rate of withdrawal that does NOT result in running out of money at some predetermined level of confidence...

In other words its not an amortization rate, its a perpetuity rate.
In other words, "don't invade the principal."

I think there's a lot of merit to that, but a lot of financial-planning literature seems to be talking about strategies drawing down a mixed portfolio during retirement, picking some magic number of years (usually 30), and estimating the probability of running out before then. E.g. Spitzer and Singh, 2007

I really need to read the original Trinity study sometime--anyone have a link to it? but I found a summary....

The problem with your goal of "perpetuity" is that it yields a lower number than people like, and that many retirees (cough, cough) probably don't have enough assets to meet their "needed" income at this rate.

So I think what's going on in the background, unstated, is a certain amount of denial and search for magic formulas that offer higher numbers. As well as some tension between providing for onesself and ones heir.

The New York Life summary says that "Today many retirement planners are advising a conservative 3.5 percent withdrawal rate" but also says (and I like the way this is put) that according to the original study "Stock-dominated portfolios using a 3 to 4 percent withdrawal rate may create rich heirs at the expense of the retiree's current standard of living."

But the common element in all of the things I've read, e.g. is that, according to the authors that write about them, any strategy that involves obtaining income by drawing down a portfolio of stocks and bonds, that starts at 4% or more and increases with cost of living, has a probability of around 5% or more of depleting the assets within 30 years or less. That probability is distinctly nonzero even with an initial 4% rate, and increases steeply as the withdrawal rate rises.

There's no mystery as to why almost everything works at a 3% rate. After all, in a world with no interest and no inflation, and given that mysteriously prevalent number of 30 years, the safe withdrawal rate would be 3.33%.

The thing that's interesting to me is that I just noticed that seemingly you can get something very close to the proverbial 4% with a very small risk of "failure" simply by using a portfolio of 100% TIPS or I Bonds. So why, exactly, do anything else?

I can think of reasons, but what puzzles me is that withdrawal strategies from a mixed stocks/bonds portfolio are often presented as if they were the obvious primary source of retirement income.

In other words, split retirement income into four categories:
a) Social Security
b) Single-premium immediate annities
c) Payouts from drawing down an all-TIPS portfolio (interest AND principle, at a rate that will make the portfolio last 25-40 years)
d) Payouts from drawing from a traditional portfolio of stock and bond mutual funds.

I'm much more interested in conceptual frameworks for deciding what percentages to allocate between b, c, and d then I am in deciding the stock/bond allocation in d.
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Post by bob90245 »

nisiprius wrote:I really need to read the original Trinity study sometime--anyone have a link to it?
The "original link" is no longer available on the AAII website. I extracted the contents from archive.org. And then placed it on my website:

http://bobsfiles.home.att.net/trinity.htm
nisiprius wrote:... what puzzles me is that withdrawal strategies from a mixed stocks/bonds portfolio are often presented as if they were the obvious primary source of retirement income.
This is a misconception. The studies on withdrawal rates have no knowledge of the retiree's external sources of income.

However, you will find other studies that examine the complete picture. Here are some examples:

Tools and Pools: Strategies for Increasing Retirement Cash Flow and Creating a Retirement Plan (pdf)

Annuity Ladder- Part II (pdf)
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Post by Chinwhisker »

Hi nisiprius,

Don’t forget taxes. If you are going to come up with a real SWR, you must use I-bond rates, as TIPS still offer the risk of inflation being so high the real return is eat up by taxes.

Chin
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Post by nisiprius »

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Post by nisiprius »

Chinwhisker wrote:Don’t forget taxes. If you are going to come up with a real SWR, you must use I-bond rates, as TIPS still offer the risk of inflation being so high the real return is eat up by taxes.

I have the impression--correct me if I'm wrong--that the various articles in the financial literature that discuss withdrawal strategies do not include taxes. For example, the Trinity article that Bob just posted a link to says "The study did not adjust for taxes or transaction costs." The Spritzer and Singh paper says "Taxes are ignored in this study."

I'm assuming that the authors of these studies assume that the amount you withdraw, the frequently-cited "4%," is 4% before taxes, and it's up to you to add taxes when determining the amount of income you "need."

So, when comparing the 4% income one can apparently safely get from an inflation-indexed bond that earns 1.3% real income, it's fair to compare that to the classical "4%"--for which, I see, in the Trinity study, the highest inflation-adjusted success rate was 98%.
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A puzzlement...

Post by nisiprius »

The Trinity paper (thanks again, Bob) notes in its conclusions:

"Retirees who demand CPI-adjusted withdrawals during their retirement years must accept a substantially reduced withdrawal rate from the initial portfolio."

This is the sort of thing that makes my brain slip a cog. What retiree in his right mind would not "demand" CPI-adjusted withdrawals? Even if the retiree does not "demand" it, the butcher, the baker, the the health-insurance-maker who send him bills probably would.

Even if you made the case that retirement spending decreases with age (does it? Where are the Monte Carlo simulations on that?) it's not very likely that the decline in requirements would just happen to match the declines in spending power caused by inflation...

What's the point in even presenting level-nominal-payout scenarios?
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Post by Chinwhisker »

nisiprius wrote:
Chinwhisker wrote:Don’t forget taxes. If you are going to come up with a real SWR, you must use I-bond rates, as TIPS still offer the risk of inflation being so high the real return is eat up by taxes.

I have the impression--correct me if I'm wrong--that the various articles in the financial literature that discuss withdrawal strategies do not include taxes. For example, the Trinity article that Bob just posted a link to says "The study did not adjust for taxes or transaction costs." The Spritzer and Singh paper says "Taxes are ignored in this study."

I'm assuming that the authors of these studies assume that the amount you withdraw, the frequently-cited "4%," is 4% before taxes, and it's up to you to add taxes when determining the amount of income you "need."

So, when comparing the 4% income one can apparently safely get from an inflation-indexed bond that earns 1.3% real income, it's fair to compare that to the classical "4%"--for which, I see, in the Trinity study, the highest inflation-adjusted success rate was 98%.
I’m not sure what you are saying by “fair to compare”, but if it means others don’t consider taxes so we shouldn’t, I think this a mistake. That is, of course, unless you do not consider inflation as a risk in retirement.

What you think?

BTW, the Trinity Study used 10 yr. T-bonds. 5 yr. T-bonds come out with a 100% 4% ‘Historical’ SWR.

Chin
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Re: A puzzlement...

Post by Rodc »

nisiprius wrote:The Trinity paper (thanks again, Bob) notes in its conclusions:

"Retirees who demand CPI-adjusted withdrawals during their retirement years must accept a substantially reduced withdrawal rate from the initial portfolio."

This is the sort of thing that makes my brain slip a cog. What retiree in his right mind would not "demand" CPI-adjusted withdrawals? Even if the retiree does not "demand" it, the butcher, the baker, the the health-insurance-maker who send him bills probably would.

Even if you made the case that retirement spending decreases with age (does it? Where are the Monte Carlo simulations on that?) it's not very likely that the decline in requirements would just happen to match the declines in spending power caused by inflation...

What's the point in even presenting level-nominal-payout scenarios?
Well, one might meet required expenses with a pension and SS and an annuity and use the remaining portfolio for life's extra and so be ok with some ups and downs: a cruise this year, a simple trip to the beach the next.

Most people are subject to a certain amount of financial ups and down during their working years as jobs change, maybe you end up with an extra kid, or your kid has some special talent you want to foster, or one of a million other things. I'm not saying this is desirable, just that it is a fact of life for many and most people deal with such things without too much trouble as long as the disruptions are not too severe. You know the old saying, life comes with no guarantees, I don't know why retirement is expected to be so different.

Nature abhors a vacuum. And empty closet space. And for many, a positive balance in the check book. :) I suspect many do happen to see their decrease in spending matches inflation. :)

I continue to be baffled by all the effort to compute SWR to the nearest tenth of a percentage point when the error bars are probably 10 times larger, and a static withdrawal strategy over decades is so far from what any person does in real life. I can sort of understand why it might be fun if one is an academic, after all you have to write papers on something. I just don't see the connection to reality.

That comment is not really directed to the OP or even this thread, just a comment in general on so many of the threads on SWR.
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Post by bob90245 »

nisiprius wrote:
That link currently seems to be broken?
Oops! I hadn't noticed that. :oops: I'll upload it to my website later. In the meantime, try this link from archive.org:

http://web.archive.org/web/200606200349 ... rticle.pdf
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Post by bob90245 »

Chinwhisker wrote:BTW, the Trinity Study used 10 yr. T-bonds.
Maybe you're reading a different Trinty study? This is what mine says:
The portfolio allocations examined were: 100% stocks; 75% stocks/25% bonds; 50% stocks/50% bonds; 25% stocks/75% bonds; 100% bonds. The Standard & Poor’s 500 index was used to represent stocks, and long-term, high-grade corporate bonds were used to represent bonds. (All stock, bond, and inflation data were from "Stocks, Bonds, Bills, and Inflation, 1996 Yearbook," Ibbotson Associates, 1996).
Source: http://bobsfiles.home.att.net/trinity.htm
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Post by Chinwhisker »

bob90245 wrote:
Chinwhisker wrote:BTW, the Trinity Study used 10 yr. T-bonds.
Maybe you're reading a different Trinty study? This is what mine says:
The portfolio allocations examined were: 100% stocks; 75% stocks/25% bonds; 50% stocks/50% bonds; 25% stocks/75% bonds; 100% bonds. The Standard & Poor’s 500 index was used to represent stocks, and long-term, high-grade corporate bonds were used to represent bonds. (All stock, bond, and inflation data were from "Stocks, Bonds, Bills, and Inflation, 1996 Yearbook," Ibbotson Associates, 1996).
Source: http://bobsfiles.home.att.net/trinity.htm
My apologies. I do make mistakes such as this. You are right it was not T-bonds, but the term was 10 year, right?

Chin
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Post by nisiprius »

bob90245 wrote:
nisiprius wrote:
That link currently seems to be broken?
Oops! I hadn't noticed that. :oops: I'll upload it to my website later. In the meantime, try this link from archive.org:

http://web.archive.org/web/200606200349 ... rticle.pdf
Archive.org wins again!

That looks like a very good article. I need to spend some quality time with that article. It seems to fit in better with my common sense than others I've read... and it does discuss "meta-strategy" and not just the details of drawing from a portfolio.
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Post by bob90245 »

Chinwhisker wrote:My apologies. I do make mistakes such as this. You are right it was not T-bonds, but the term was 10 year, right?
My Ibbotson information is found inside The Irwin Business and Investment Almanac. Here is what they say regarding Long-Term Corporate Bonds:
We measure the total returns of a corporate bond index with approximately 20 years to maturity.
Ibbotson also maintains a Long-Term Government Bond index. That index is also 20-year maturity. The Intermediate-Term Government Bond index is 5-year maturity.
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Re: A puzzlement...

Post by sport »

nisiprius wrote:The Trinity paper (thanks again, Bob) notes in its conclusions:

"Retirees who demand CPI-adjusted withdrawals during their retirement years must accept a substantially reduced withdrawal rate from the initial portfolio."

This is the sort of thing that makes my brain slip a cog. What retiree in his right mind would not "demand" CPI-adjusted withdrawals? Even if the retiree does not "demand" it, the butcher, the baker, the the health-insurance-maker who send him bills probably would.

Even if you made the case that retirement spending decreases with age (does it? Where are the Monte Carlo simulations on that?) it's not very likely that the decline in requirements would just happen to match the declines in spending power caused by inflation...

What's the point in even presenting level-nominal-payout scenarios?
There are many working people who have jobs that do not provide steady income. Self employed individuals can have good years and bad years. Commissioned sales people similarly can have wide variability in their earnings. Why then, must retirees have level inflation-adjusted income? It seems to me that the most important consideration is not to run out of money, as there is little one can do at an advanced age to remedy this problem. IMO, it is worth putting up with some variability in retirement income to assure that portfolio failure cannot occur. One simple way is to just withdraw a fixed percentage of the portfolio each year. Vanguard says that you can withdraw up to 5% using this method. As long as social security, pensions, and 50% of the portfolio can provide minimum income requirements, the variability of the remainder of the total income should not be a serious problem. It would just be similar to the variability that the commisioned and self-employed workers contend with normally.

Best wishes,
Jeff
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Post by Chinwhisker »

bob90245 wrote:
Chinwhisker wrote:My apologies. I do make mistakes such as this. You are right it was not T-bonds, but the term was 10 year, right?
My Ibbotson information is found inside The Irwin Business and Investment Almanac. Here is what they say regarding Long-Term Corporate Bonds:
We measure the total returns of a corporate bond index with approximately 20 years to maturity.
Ibbotson also maintains a Long-Term Government Bond index. That index is also 20-year maturity. The Intermediate-Term Government Bond index is 5-year maturity.
Thanks for that. Should I call you Bob?

I see the Trinity study mentioned often. It seems odd to me that the only study done on this would have been using LT-bonds while most now believe either intermediate-term or short-term serve better.

I used Ibbotson 5 yr. T-bonds in my own little study. Do you have any other studies on SWR on your website using intermediate and short-term T-bonds or corporates?

Thanks again,

Chin
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Post by bob90245 »

Chinwhisker wrote:Thanks for that.
You're welcome.
Chinwhisker wrote:Should I call you Bob?
I don't see why not. :wink:
Chinwhisker wrote:I see the Trinity study mentioned often. It seems odd to me that the only study done on this would have been using LT-bonds while most now believe either intermediate-term or short-term serve better.

I used Ibbotson 5 yr. T-bonds in my own little study. Do you have any other studies on SWR on your website using intermediate and short-term T-bonds or corporates?
William Bengen uses 5-yr. T-Bonds in his SWR studies. Our librarian, Barry Barnitz, placed them in the Reference Library here:

http://www.diehards.org/forum/viewtopic ... 3915#83915

For short-term T-bonds, would 90-day T-Bills be an acceptable substitute? I have an Excel spreadsheet that uses Ibbotson's 90-day T-Bill data:

http://bobsfiles.home.att.net/download.html#MWR

Sorry, but I am not aware of a data series that tracks intermediate-term or short-term corporate bonds.
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Post by rmark1 »

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Post by grayfox »

nisiprius wrote:
For various interest rates and time horizons, the safe withdrawal rates would seem to be:

----------25-------30-------35
1.00% 4.50% 3.84% 3.37%
1.30% 4.65% 3.99% 3.53%
1.50% 4.76% 4.10% 3.64%
2.00% 5.02% 4.38% 3.92%
2.50% 5.30% 4.66% 4.22%
3.00% 5.58% 4.95% 4.52%
3.50% 5.86% 5.25% 4.83%
4.00% 6.15% 5.56% 5.15%
4.50% 6.45% 5.87% 5.48%
Good Work!

I did not check your amortization calculation so I will take it as correct.

What you have shown is that with all TIPS, everything can be completely deterministic. There are no probabilities involved and no need to run Monte Carlo simulations. Basically with all TIPS the interest rate determines the withdrawal rate to however many decimal places you want to show. In other words it is EXACT.**

Today, the 30-year TIP is yielding 2.07%. From your table that puts the 30-year w/d at over 4.38 percent.
This changes everyday.
Back in June07 the 30-year TIPS was yielding about 2.7% so that would have put the w/d rate somewhere between 4.66 and 4.95 percent, with 0 chance of failure.
In late 1990s TIPS was yielding 4%, giving a w/d rate of 5.56 percent. (Wasn't there some guy who bought all TIPS at 4% and was ridiculed for doing so?)

Now when you add 50% stocks you get only 4 percent w/d with 5% chance of failure, but 50% chance of have more than twice as much.
So why add stocks when all TIPS has a higher w/d rate and is actually safe? Two reasons I can think of have already been presented:

1. Nobody really wants to spend down to zero, people want to keep their principle intact. I know I do. The only way to do this with all TIPS is to only w/d the real yield, 2.07 today.
2. 30-years is ridiculous. Nobody retires ar 65 anymore. Nowadays you get forced into early retirement at 50. And like the other guy said, there is a 95% chance that one spouse will live to 100. The time frame must be 50 years!!***

I would like to see your table filled out to 50 years. Also 1/4 percent increments. :D

footnotes
**actually after thinking about this, it depends on how you implement the TIPS strategy. If you have to sell TIPS before they mature or use a fund then it would depend on the prices/interest rates when you sell which introduces uncertainty. You would need to set up ladder that has TIPS maturing every year in order to be deterministic.

***and if you are 50 with a 25 year old wife, maybe your portfolio has to last 75 years!
Last edited by grayfox on Sun Oct 28, 2007 9:40 am, edited 1 time in total.
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Post by Chinwhisker »

bob90245 wrote: William Bengen uses 5-yr. T-Bonds in his SWR studies. Our librarian, Barry Barnitz, placed them in the Reference Library here:

http://www.diehards.org/forum/viewtopic ... 3915#83915

For short-term T-bonds, would 90-day T-Bills be an acceptable substitute? I have an Excel spreadsheet that uses Ibbotson's 90-day T-Bill data:

http://bobsfiles.home.att.net/download.html#MWR

Sorry, but I am not aware of a data series that tracks intermediate-term or short-term corporate bonds.
Thanks Bob,

I have looked at the 6 mo., 5 yr., and 10 yr. treasuries going back to 1927, and 5 yr. seems to work best. The ST. Louis FRED has (or had) data going back maybe to the 60s (CRS memory) on 2 yr. T-bonds, enough for Larry Swedroe to argue in favor of the 2 yr. term. William Bernstein also offers a good argument for ST corporates as well.

From what I have looked at in the terms I stated for treasuries, the 5 yr. T-bond works best with US stocks going back to 1927, though I also understand the arguments from Bernstein and Larry, but it is more subjective as opposed to objective back-testing. Corporates offer higher returns per term, and the short-term reduces the risks of corporates over T-bonds to the point it makes sense in an inflation sense to go with the shorter term corporates. We can’t know how ST corporates would have worked out in ‘29, but I would expect not all that well. This brings it down to figuring what offers the highest risk going forward.

On an SWR basis, I think the ST corporates make more sense, as they do offer higher returns with less exposure to term risks. On a volatility basis, such as with the extreme volatility of ‘29, I would personally think ST corporates would not hold up as well as the 5 yr. T-bond. This holds true with small value as well.

If you can trust the shorter term data for commodities and internationals, and a model for a TIPS ladder, and you feel the major threat we would face going forward might be inflation as opposed to a world wide economic crisis, you might go with Larry and Bernstein’s arguments.

Either way, you have to do a little thinking. The broader diversification brings the SWR up to a point you can go with shorter and higher percentages of fixed income, and at the same offers better diversification for stocks to where you can hold higher percentages in stocks than would be feasible without TIPS and commodities. Like I said, it’s a thinking process though. Commodities, TIPS and ST bonds may not have worked as well in ‘29.

I guess that’s a lot of words to say I don’t know. 8)

Welcome to the pea brain of the Know-nothing Investor.

Chin
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Post by Chinwhisker »

grayfox wrote:
nisiprius wrote:
For various interest rates and time horizons, the safe withdrawal rates would seem to be:

----------25-------30-------35
1.00% 4.50% 3.84% 3.37%
1.30% 4.65% 3.99% 3.53%
1.50% 4.76% 4.10% 3.64%
2.00% 5.02% 4.38% 3.92%
2.50% 5.30% 4.66% 4.22%
3.00% 5.58% 4.95% 4.52%
3.50% 5.86% 5.25% 4.83%
4.00% 6.15% 5.56% 5.15%
4.50% 6.45% 5.87% 5.48%
Good Work!

I did not check your amortization calculation so I will take it as correct.

What you have shown is that with all TIPS, everything can be completely deterministic. There are no probabilities involved and no need to run Monte Carlo simulations. Basically with all TIPS the interest rate determines the withdrawal rate to however many decimal places you want to show. In other words it is EXACT.**

Today, the 30-year TIP is yielding 2.07%. From your table that puts the 30-year w/d at over 4.38 percent.
This changes everyday.
Back in June07 the 30-year TIPS was yielding about 2.7% so that would have put the w/d rate somewhere between 4.66 and 4.95 percent, with 0 chance of failure.
In late 1990s TIPS was yielding 4%, giving a w/d rate of 5.56 percent. (Wasn't there some guy who bought all TIPS at 4% and was ridiculed for doing so?)

Now when you add 50% stocks you get only 4 percent w/d with 5% chance of failure, but 50% chance of have more than twice as much.
So why add stocks when all TIPS has a higher w/d rate and is actually safe? Two reasons I can think of have already been presented:

1. Nobody really wants to spend down to zero, people want to keep their principle intact. I know I do. The only way to do this with all TIPS is to only w/d the real yield, 2.07 today.
2. 30-years is ridiculous. Nobody retires ar 65 anymore. Nowadays you get forced into early retirement at 50. And like the other guy said, there is a 95% chance that one spouse will live to 100. The time frame must be 50 years!!***

I would like to see your table filled out to 50 years. Also 1/4 percent increments. :D

footnotes
**actually after thinking about this, it depends on how you implement the TIPS strategy. If you have to sell TIPS before they mature or use a fund then it would depend on the prices/interest rates when you sell which introduces uncertainty. You would need to set up ladder that has TIPS maturing every year.

***and if you are 50 with a 25 year old wife, maybe your portfolio has to last 75 years!
Hi grayfox,

I might argue 100% TIPS do not offer a safe withdrawal rate, as the 2% real return could be reduced to no or even negative return after inflation ‘And’ taxes.

With increased inflation, and increased taxes based on the nominal return, the 2% real return would no longer offer a 50 year 4% SWR.

What you think?

You can use Gummy’s data to play with this if you like;
http://www.gummy-stuff.org/returns.htm


Chin
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Re: A 4% safe withdrawal rate with no risk of "failure&

Post by Mike Brit »

nisiprius wrote:I suddenly realized that in the case of TIPS or I bonds, you can, in fact, compute the safe withdrawal rate (SWR) precisely . You just perform a simple amortization calculation in real dollars.

This has always been an issue to me. When the Trinity Study was published in early 1998, the 30-year TIPS were yielding 3.75% real. This means that you could get a 5%+ SWR with 100% certainty. This seems to have been a material flaw in their analysis.

Mike
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Post by Chinwhisker »

rmark1 wrote:Illustrates some of the trade offs

http://www.fpanet.org/journal/articles/ ... 7-art6.cfm
Hi rmark1,
Results show that withdrawal rates as high as 5.5 to 6 percent can be achieved, but only at a 25 to 30 percent chance of running out of money and with stock allocations of 75 to 100 percent. A 4.4 percent withdrawal rate with a 50/50 bond/stock allocation has a 10 percent chance of running out of money.
So if you can stand a 1:4 or 1:10 chance you will run out of money? :shock:

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Post by grayfox »

nisiprius wrote:
Notice that a 1.3% real interest rate is sufficient to achieve a 3.99% withdrawal rate over 30 years.
I think your table is significant because it essentially puts a safe floor under the SWR problem.

In other words, if worse came to worse you could always amortize your portfolio using TIPS and even at a mere 1.3% real rate still get a 4% w/d rate for 30 years with no chance of failure.

All TIPS should be the starting point for retirement withdrawal plans. Then whatever other asset classes, like stocks, are added you should be able to demonstrate that it actually makes some improvement and at what cost. For instance you getting a higher w/d rate but giving up some safety, compared to all TIPS.
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Post by grayfox »

Mike wrote:
This has always been an issue to me. When the Trinity Study was published in early 1998, the 30-year TIPS were yielding 3.75% real. This means that you could get a 5%+ SWR with 100% certainty. This seems to have been a material flaw in their analysis.
Hmm, interesting.
For some reason I am reminded of those engineers showing their detailed mathematical analysis proving bumblebees can't fly...as a bumblebee flies by.
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Re: A 4% safe withdrawal rate with no risk of "failure&

Post by bob90245 »

Mike Brit wrote:When the Trinity Study was published in early 1998, the 30-year TIPS were yielding 3.75% real. This means that you could get a 5%+ SWR with 100% certainty. This seems to have been a material flaw in their [Trinity] analysis.
Ah, 1998. Those were good old the days when TIPS earned 3.75% real. 8) Sadly, good things like that never last. :cry:
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Post by Vig Oren »

Just noticed that it does not relate to the OP :cry:
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Post by zigkelton »

Building on nisiprious's initial post and idea: assume one bought and held TIPS directly (not in a fund) in a taxable account (because they don't have enough room to make this viable in a tax-deferred account).

Then assume that one:
1) harvests the dividends every six months as income to fund part of their total needed spending
2) sells TIPS, when needed (say also every six months, and between the dividend payments) to make up the difference that they need each year to achieve their total needed withdrawal amount to cover annual spending

If so, then the questions are:

A) What tax rates would one pay on the income and the gains? Would the dividends be taxed as normal income but the TIPS sales would be taxed at the long term capital gains rate (assuming the bonds were held >1 year before their sale)?

B) Would this be a way to implement nisiprius's idea?

EDIT: As soon as submitted the question, I remembered the answer. The gain is taxable as ordinary income and is not a capital gain.
Last edited by zigkelton on Sun Oct 28, 2007 6:18 pm, edited 1 time in total.
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Post by DRiP Guy »

grayfox wrote:(Wasn't there some guy who bought all TIPS at 4% and was ridiculed for doing so?)
I've never seen that, myself. I have seen a guy who 'retired' with about 1/3rd of the total amount such a WR would have commended, and has subsequently said the world equities markets would fall below bonds in their total return for the next ten or twenty years, but no, I don't think TIPS themselves as a vehicle have ever been a point of ridiculing anyone, just the misunderstanding of them. I happen to think they are a pretty cool development, myself.

I also agree with the idea of working up a floor WR strategy that uses them as a baseline for comparison. Clearly, anyone who has sufficient funds to totally avoid market risk and still live well, would do well to grab the inflation-adjusted risk-free return and move along. But, not everyone is so fortunate in where they are starting from, including the hermit I think you make reference to.

Cheers!
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Post by daryll40 »

Don't you have the taxation problem with TIPS? Even in tax-sheltered accounts as most TIPS should be held, you pay regular income tax rates as the money is withdrawn to be spent. So even though you are keeping up with inflation in theory, you don't keep up after taxation.
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Post by bob90245 »

daryll40 wrote:Don't you have the taxation problem with TIPS? Even in tax-sheltered accounts as most TIPS should be held, you pay regular income tax rates as the money is withdrawn to be spent. So even though you are keeping up with inflation in theory, you don't keep up after taxation.
This is a good point. At least with a balanced portfolio (having both bonds AND stocks), a fair portion of the withdrawal would be coming from stock sales. And those stock sales would enjoy long-term capital gains tax treatment presumably at a rate more favorable relative to bond distributions. Of course, this assumes that our lawmakers don't radically change the rules in the future. :annoyed
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Post by SWP »

nisiprius, I wonder if your calculations might be too good to be true. Out of curiosity, I ran some of our numbers through John Greaney's safe withdrawal calculator (http://retireearlyhomepage.com/softlist.html). For an all TIPs portfolio bearing a 1.3% coupon and 3.99% withdrawal rate (with back end withdrawals like your Excel PV formula), Greaney's calculator says that there's only a 27% chance the withdrawals can be sustained for 30 years.

Why the difference? Greaney's calculator backtests actual inflation history against the TIPs coupon rate you specify in the input. So if you dig down into Greaney's spreadsheet (at rows below 198), you'll see that, for certain historical periods involving sustained deflation, the withdrawals eat through the principal. This doesn't involve anything to do with taxes -- it's a straight calculation summing the inflation adjusted principal plus interest payments less withdrawals for each year.

Look at the following to see how this might happen, based on actual historical inflation beginning in 1878:

Year...Principal...Infl Adj...Int Pmt...Withdrawal...Remaining...Inflation
1 10,000 (1,565) 110 (399) 8,145 -15.65%
2 8,145 (840) 95 (358) 7,043 -10.31%
3 7,043 1,457 110 (432) 8,179 20.69%
4 8,179 (467) 100 (407) 7,404 -5.71%
5 7,404 598 104 (440) 7,666 8.08%
6 7,666 (143) 98 (432) 7,189 -1.87%
7 7,189 (548) 86 (399) 6,329 -7.62%
8 6,329 (652) 74 (358) 5,392 -10.31%
9 5,392 (186) 68 (346) 4,928 -3.45%
10 4,928 - 64 (346) 4,647 0.00%
11 4,647 221 63 (362) 4,569 4.76%
12 4,569 (208) 57 (346) 4,073 -4.55%
13 4,073 (194) 50 (329) 3,600 -4.76%
14 3,600 90 48 (337) 3,401 2.50%
15 3,401 (207) 42 (317) 2,918 -6.10%
16 2,918 227 41 (341) 2,845 7.79%
17 2,845 (377) 32 (296) 2,204 -13.25%
18 2,204 (92) 27 (284) 1,856 -4.17%
19 1,856 27 24 (288) 1,619 1.45%
20 1,619 (46) 20 (280) 1,314 -2.86%
21 1,314 39 18 (288) 1,082 2.94%
22 1,082 15 14 (292) 820 1.43%
23 820 139 12 (341) 629 16.90%
24 629 (15) 8 (333) 289 -2.41%
25 289 7 4 (341) (41) 2.47%
26 (41) (4) (1) (374) (420) 9.64%
27 (420) 18 (5) (358) (765) -4.40%
28 (765) (18) (10) (366) (1,159) 2.30%
29 (1,159) - (15) (366) (1,540) 0.00%
30 (1,540) (69) (21) (383) (2,013) 4.49%

See how you run out of money in year 25? So who's right, your PV formula, or the table above?
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Post by grayfox »

SWP wrote:
See how you run out of money in year 25? So who's right, your PV formula, or the table above?
You can't run out of money if you have a ladder of bonds. It is impossible.

It is simplest to understand if you use zero coupon bonds. Say you want to spend 10K per year for 30 years. You buy 30 10K bonds with one bond maturing every year from 1 to 30 years. Each year another bond matures giving you 10K, which you spend. You don't run out of money until your last bond matures. That is what amortization is about.

The above scenario works for either nominal bonds or TIPS. The only difference is with nominal bonds you get 10K nominal every year, with TIPS you get 10K real, i.e. inflation adjusted.

With TIPS it doesn't matter what inflation is, plus, zero, minus you get to spend the inflation-adjusted amount of the bond. In fact, if there was deflation you might do even better because at maturity you always get back at least the original face amount of the bond.

The amortization approach is really simple and straightforward. As far what is wrong with your table, I don't know. Maybe your calculation assumes you sell TIPS below the face amount after there was deflation. Then I understand how you would go bust. Selling assets when they are down, stocks or bonds, explains most of the failing scenarios.
Last edited by grayfox on Mon Oct 29, 2007 4:13 am, edited 1 time in total.
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Post by grayfox »

daryll40 wrote:
Don't you have the taxation problem with TIPS? Even in tax-sheltered accounts as most TIPS should be held, you pay regular income tax rates as the money is withdrawn to be spent. So even though you are keeping up with inflation in theory, you don't keep up after taxation.

bob90245 responded
This is a good point. At least with a balanced portfolio (having both bonds AND stocks), a fair portion of the withdrawal would be coming from stock sales. And those stock sales would enjoy long-term capital gains tax treatment presumably at a rate more favorable relative to bond distributions.
If its all in a tax-sheltered account, it doesn't matter what the gains are from, interest, dividends, capital gains, short or long. Everything you withdraw is ordinary income. So basically daryll40's comment applies to every IRA portfolio no matter what it holds.

In other words, in an IRA you don't enjoy long-term capital gains tax treatment at a rate more favorable relative to bond distributions. You just pay the same ordinary income rate.
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Post by grayfox »

I also agree with the idea of working up a floor WR strategy that uses them as a baseline for comparison. Clearly, anyone who has sufficient funds to totally avoid market risk and still live well, would do well to grab the inflation-adjusted risk-free return and move along.
Yes, that is what I am getting at. Even if you can not or choose not to just amortize a TIPS portfolio, it should be the baseline for comparison. When someone proposes another portfolio or withdrawal method, demand that they show how it is an improvement over TIPS amortization, such as it has higher w/d rate or is safer or something.
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Post by nisiprius »

grayfox wrote:
I also agree with the idea of working up a floor WR strategy that uses them as a baseline for comparison. Clearly, anyone who has sufficient funds to totally avoid market risk and still live well, would do well to grab the inflation-adjusted risk-free return and move along.
Yes, that is what I am getting at. Even if you can not or choose not to just amortize a TIPS portfolio, it should be the baseline for comparison. When someone proposes another portfolio or withdrawal method, demand that they show how it is an improvement over TIPS amortization, such as it has higher w/d rate or is safer or something.
Thanks, Grayfox. That's exactly my point.

My secondary point is that I think all the withdrawal methods and portfolios that seem to do better than an all-TIPS portfolio do so only at the cost of a meaningfully higher failure rate. One might have hoped that one could add upside potential (for heirs or for a chance of an increased spending rate if the market does well) without increasing the failure rate, but that seems to in the category of a "free lunch."

My third point is, then, that there's some hard inner core of expenses for which most of us would say failure is not really an option. At least not one for which we want to see a 5-10-20% failure probability in our plans. I'm thinking one should estimate them--lowball them if you like--but definitely cover them, at least in plans, with things like Social Security, income annuities, or, it seems, a TIPS portfolio.
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Post by nisiprius »

SWP wrote:nisiprius, I wonder if your calculations might be too good to be true. Out of curiosity, I ran some of our numbers through John Greaney's safe withdrawal calculatorSee how you run out of money in year 25? So who's right, your PV formula, or the table above?
I'll look at it. But at first glance I'm puzzled, since I'd thought that in a calculation with TIPS inflation would simply cancel out.
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Post by Levett »

Nisiprius/Bob90245--

First, a thank you to Bob for drawing attention to "Tools and Pools." I'd never seen the piece before and, based on my seven years of retirement, Kreitley has described a strategy that's worked beautifully for me (doesn't mean it would work for thee, dear reader :D ).

Nisiprius--you were going to give the "Tools and Pools" piece careful review. Whaddya think? Cheers. Bob U.
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TIPS & I Bonds as Annuities

Post by Mel Lindauer »

Hello Everyone:

A number of years ago, when I Bonds had fixed rates in the 3%+ range and TIPS were paying considerably more than they are now, I suggested that one could use these vehicles as a sort of retirement annuity, but no one seemed to be very excited about the idea, perhaps because stocks were doing so well at the time. Good to see that idea being resurrected, since it should, IMO, at least establish a safe withdrawal rate baseline.

While I Bonds do have a 30-year time frame, the great unknown is predicting what new TIPS and I Bonds will be yielding, once the original ones mature and the proceeds (less any taxes due, of course) need to be reinvested. As we've seen, the fixed rates on both I Bonds and TIPS have been considerably less than those good old days, and if we have based our reinvestment estimates on the previous fixed rates, we'd certainly have been sadly disappointed.

And, obviously, for this to be safe, the investor would need adequate assets to start with.

Regards,

Mel
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Post by lazyday »

Black Swan: between now and when you planned to die, lifespan is dramatically increased.

To some, this isn't even a black swan:

http://en.wikipedia.org/wiki/Raymond_Kurzweil
Accordingly, in Kurzweil's predictions, we are currently (as of the end of the twentieth and the beginning of the twenty first century) exiting the era in which our human biology is closed to us, and are entering into the posthuman era, in which our extensive knowledge of biochemistry, neurology and cybernetics will allow us to rebuild our bodies and our minds from the ground up.
http://en.wikipedia.org/wiki/Aubrey_de_Grey
Aging and death are solvable problems, and we can live for centuries, if we approach the aging process as an engineering problem.
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Post by nisiprius »

lazyday wrote:Black Swan: between now and when you planned to die, lifespan is dramatically increased.
Well, sure. The issue isn't whether I've found some magic answer. The issue is how and in what ways, exactly, are "withdrawal strategies" from a traditional portfolio better than a TIPS portfolio if TIPS can sustain an initial-4%-then-COLAed rate, and if, for a comparable failure rate, a traditional portfolio requires a lower withdrawal rate.

I tend to discount Aubrey de Grey--I don't think he should be taken any more seriously on that topic than George Bernard Shaw (Back to Methuselah)--but don't want to go off on that tangent.

So far, and contrary to casual press statements, I see very little evidence of much true "life extension." The shape of the mortality curve just gets more and more squared off, as if there really were a natural limit to the lifespan and what medical science has done is to increase the chances of getting close to that limit, not to push back the limit.

Living to age 70 has never been unusual; Psalm 90 says
The days of our years are threescore years and ten; and if by reason of strength they be fourscore years, yet is their strength labour and sorrow; for it is soon cut off, and we fly away
. (An aunt of mine, who died recently in her early nineties remarked that she "had never had a good year since she turned 75.")

Living beyond age 90 has always been noteworthy but never extremely remarkable. Democritus supposedly lived to 100. John Adams lived past 90. Glancing over the story of the Boston Post canes, you'll see people living to 91, 89, 95, back in the early decades of the 20th century.

In a book called On comparative longevity in man and the lower animals (Google Books!), Edwin Ray Lankester cites Count Buffon as saying
the man who does not die of accidental causes reaches everywhere the age of ninety or a hundred years.
Conversely, living beyond 100 has always been rare. It is still rare today, even for women, although almost everyone knows at least one woman in her 100s, often enjoying pretty good health.

Living beyond 110 is, even today, so rare, that there is great skepticism about the truth and accuracy of anyone reported to have lived much longer.

I've read popular accounts about scientists being close to finding the aging gene, etc. and there could be a "black swan." By definition, we don't see it until it's there...
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Post by SWP »

grayfox wrote: You can't run out of money if you have a ladder of bonds. It is impossible. ... Maybe your calculation assumes you sell TIPS below the face amount after there was deflation. Then I understand how you would go bust. ....


Of course you can run out of money with a ladder of bonds, if your withdrawal rate is high enough. At its simplest, you can't buy ten $10,000 bonds and then withdraw $20,000 per year for ten years. As you note yourself, if your withdrawal rate is high enough you have to sell off your ladder before maturity. The only other alternative, not too savory, is to reduce the amount of the withdrawals.
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Post by lazyday »

The issue is how and in what ways, exactly, are "withdrawal strategies" from a traditional portfolio better than a TIPS portfolio if TIPS can sustain an initial-4%-then-COLAed rate, and if, for a comparable failure rate, a traditional portfolio requires a lower withdrawal rate.
-Great chance of ability to increase spending over time, for unexpected expenses, or for luxuries
-Great chance to leave more money to heirs
-Great chance of portfolio survival if have underestimated lifespan
-Less dire consequences of divergence between your personal inflation rate, and CPI-U (health care vs televisions)


If 4% WR from a diversified portfolio fails, IMO there is a significant chance that payments of TIPS will also be at risk. Depends on why the 4% failed--depression, war, environmental disaster, etc. (See W. Bernstein's Retirement Calculator from Hell http://www.efficientfrontier.com/ef/901/hell3.htm second half of page, starting with "The hard part, of course,")

In SWR threads, I've seen many references to the above link. Haven't seen many posts about people living much longer than we do today, but IMO that's another (perhaps remote) possibility. There's probably other unexpected futures to prepare for, that we haven't thought of.

Who knows what tomorrow might bring? To me a diversified portfolio makes much more sense than an all TIPS portfolio, but of course it depends on one's situation, and beliefs.
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Post by SWP »

nisiprius wrote:I'll look at it. But at first glance I'm puzzled, since I'd thought that in a calculation with TIPS inflation would simply cancel out.
I'm puzzled too. For some time I have been using a relative of your PV calculation, net present value (NPV), to get a fix on my TIPs allocation [=NPV(real return,array of all expenses)]. Just as you mentioned in another post, it's useful for the purposes of looking at how much TIPs you'd have to buy to cover your minimum expected expenses. But I can't see what's wrong with the John Greaney-based table, and if it's correct, the PV (or NPV) calculation method could be really wrong. I've always thought that Greaney's spreadsheet is a useful little utility, but I'd never looked before in detail at how it handles TIPs. Now I’m concerned that it is highlighting a problem with the PV (NPV) approach.

One thing that occurs to me is that this may have something to do with the different ways in which TIPs and i-bonds work. I-bonds’ earnings rate can't go below zero and the redemption value of I Bonds can't decline. That’s not true for TIPs – if you hold them to maturity, you’re guaranteed to get your par value back, but if you have to sell them before maturity you can end up recognizing a loss if there’s deflation. So, if you change Greaney’s calculator to model i-bonds instead of TIPs (AND change the withdrawals from the back-end to the front-end), you can get 99% (I think that’s his way of saying 100%) survivability at a withdrawal rate equal to your PV formula.

So, do you think the following might be an accurate statement of the problem?: (1) the timing of withdrawals matters tremendously, (2) we always knew that Mel was right about i-bonds but now we know more reasons why?!
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Post by nisiprius »

lazyday wrote:
Who knows what tomorrow might bring? To me a diversified portfolio makes much more sense than an all TIPS portfolio, but of course it depends on one's situation, and beliefs.
Nobody know what tomorrow will bring, but you have to make assumptions for planning purposes... either that or consider the lilies of the field.

Just to be clear, I don't intend to have and am not suggesting an all-TIPS portfolio. What I'm saying is that I don't think it makes sense to cover truly important expenses with a mechanism that even on paper has a 5%-10% chance of failing to meet them, however much upside potential it has. Cover those expenses with things that at least on paper can meet them: Social Security, annuities, and TIPS.

Then use a portfolio with some suitable balance of upside potential and downside risk for withdrawals that are not truly essential.

The thing that I find odd is that to the extent that my analysis is correct... and comparable to the way traditional portfolios are analyzed...

a) If you really intend to draw 4%-initial-then-COLAed from a traditional portfolio, you should not consider this to be a "safe" rate... by my personal standards of "safety," anyway. It's a good gamble, with a good chance of leaving the most for your heirs and a reasonable hope of extra spending money if the market does well--but with a need to cut back if it does not. So this should only be used to cover expenses that you can at least imagine cutting back on.

b) You actually should be able to draw 4%-initial-then-COLAed from a TIPS portfolio for 30 years, with the mortality table telling you your probability of outliving it, and leaving something for your heirs if you live less than 30 years.

c) And, obviously, you can draw more than that from an SPIA, with no risk of outliving it, but leaving nothing for your heirs. (You can elect a 10-15 year term certain at very little cost so your heirs will get something if you get hit by a bus the next day...)
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Post by Norbert Schlenker »

SWP wrote:Out of curiosity, I ran some of our numbers through John Greaney's safe withdrawal calculator (http://retireearlyhomepage.com/softlist.html). For an all TIPs portfolio bearing a 1.3% coupon and 3.99% withdrawal rate (with back end withdrawals like your Excel PV formula), Greaney's calculator says that there's only a 27% chance the withdrawals can be sustained for 30 years.

Why the difference? Greaney's calculator backtests actual inflation history against the TIPs coupon rate you specify in the input. So if you dig down into Greaney's spreadsheet (at rows below 198), you'll see that, for certain historical periods involving sustained deflation, the withdrawals eat through the principal. This doesn't involve anything to do with taxes -- it's a straight calculation summing the inflation adjusted principal plus interest payments less withdrawals for each year.

Look at the following to see how this might happen, based on actual historical inflation beginning in 1878:

Year...Principal...Infl Adj...Int Pmt...Withdrawal...Remaining...Inflation
1 10,000 (1,565) 110 (399) 8,145 -15.65%
2 8,145 (840) 95 (358) 7,043 -10.31%
[rest of table removed]
I see a wee problem here, probably in the calculator, because I assume that the data is a cut and paste of the output.

In year 1, you start with $10k and you take 3.99% of it, i.e. $399. Inflation that year is -15.65%. So what should your withdrawal be in year 2, adjusted for inflation? Most people - me included - would say it should be $399 x (1 - 15.65%), which is $337. The calculator withdraws $358 instead.

I haven't worked through the rest of the numbers but I assume that error is propagated throughout, which could easily result in the reported early crash of the portfolio.
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Post by lazyday »

(on truly important expenses)
Cover those expenses with things that at least on paper can meet them: Social Security, annuities, and TIPS.
I'm coming more from the perspective of early retirement planning, but that could make sense for someone retiring on the late side, with plenty of resources, and/or averse to market risk. Especially if they have confidence in guessing their lifespan, and important future expenses. Of course you can guess high to be more safe, if you can afford it.
If you really intend to draw 4%-initial-then-COLAed from a traditional portfolio, you should not consider this to be a "safe" rate... by my personal standards of "safety," anyway.
I don't consider it very safe either.
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Joined: Thu Sep 06, 2007 5:49 pm

Post by SWP »

Norbert Schlenker wrote:I see a wee problem here ... In year 1, you start with $10k and you take 3.99% of it, i.e. $399. Inflation that year is -15.65%. So what should your withdrawal be in year 2, adjusted for inflation? Most people - me included - would say it should be $399 x (1 - 15.65%), which is $337. The calculator withdraws $358 instead. ...
Aha! I think you may have put your finger on it. You would increase withdrawals by the prior year's rate of inflation. I think nisiprius' PV formula also makes this implicit assumption. By comparison, Greany's calculator assumes that withdrawals are increased by the rate of inflation in the year the withdrawals are made. However, so does the Trinity Study! The Trinity Study says "To counteract the effect of inflation, the dollar withdrawal in a given year must be increased by the inflation rate FOR THAT YEAR" (emphasis added).
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