Trinity Study Authors update their results

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bobcat2
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Post by bobcat2 » Mon Apr 04, 2011 1:18 pm

Dick Purcell writes.
(The) two-goals approach is most wise for folks with enough money, but most folks don’t have that much or even enough for your lower goal of “minimum acceptable." Not meaning to disagree with you, just note the common plight.
To keep their pre-retirement living standard in retirement most people will need somewhere between 55% to 70% of their pre-retirement income. Let's assume that that is the living standard goal and 16% below that is the minimum acceptable living standard goal. Let's also assume that in a particular case 63% of the pre-retirement income is what is needed in retirement to meet the primary retirement living standard goal. For a two earner household earning $40,000 per year SS will replace about 40% of pre-retirement income in retirement, if taken at the full retirement age or later.

So such a family earning $40,000 pre-retirement will need $25,000 per year in retirement income to reach their primary retirement living standard goal. Roughly $16,000 will come from SS. Coming up with $4,800 per year to reach their minimum acceptable retirement income target of $20,800 should be doable. It would probably cost about $90,000-$100,000 total for his and her inflation-indexed life annuities of $2,400 each. Coming up with the extra $4,200 of retirement income targeted out of personal savings to reach the primary income target will not be easy, but should also be doable.

They definitely won't be living on easy street, but they won't be any worse off then they were before they retired. The fact that SS replaces a higher percentage of pre-retirement income in retirement for lower paid workers is definitely helpful to those workers in retirement.

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Post by wade » Mon Apr 04, 2011 2:24 pm

I've tried to put together something Wiki-appropriate about what these studies imply for asset allocation. I've also incorporated some Monte Carlo simulation results that Dick Purcell sent me using the same data parameters as the updated Trinity study.

I've tried to do this in "encyclopedia form" with no editorializing and no mention of my "beloved" valuations. But please feel free to tear it apart.

Trinity Study and Asset Allocation

Asset allocation for retirees is a very important issue. Choosing one’s asset allocation depends on a number of important factors, including the monetary amounts you need to withdraw, the additional monetary amounts you may desire to withdraw if possible, the percentage of your wealth these needs and desires imply, the degree of flexibility you have to allow your withdrawals to fluctuate over time, taxes, your life expectancy, whether you are supporting others (such as a spouse) with retirement income, whether you wish to leave an inheritance or charitable donation, the flexibility you have to return to work should such a need arise, whether you have decided to annuitize part of your wealth, and the percentage of your needed/desired expenses available from Social Security and any other employer-based defined benefit pensions. Entire books can and have been written on this topic.

The question addressed here is not “What should my asset allocation be in retirement?,” but rather “What do the Trinity study and other related studies imply about asset allocation?”

Early studies which helped develop the 4% rule did recommend asset allocations for retirees that were on the aggressive side. In the conclusion of William Bengen’s original 1994 article that started research in this area, he wrote, “Despite advice you may have heard to the contrary, the historical record supports an allocation of between 50-percent and 75-percent stocks as the best starting allocation for a client. For most clients, it can be maintained throughout retirement, or until their investing goals change. Stock allocations below 50 percent and above 75 percent are counterproductive.”

Meanwhile, the Trinity authors in their 2011 update conclude, “The sample data suggest that clients who plan to make annual inflation adjustments to withdrawals should also plan lower initial withdrawal rates in the 4 percent to 5 percent range, again, from portfolios of 50 percent or more large-company common stocks, in order to accommodate future increases in withdrawals.”

Boglehead’s Forum user traumamoma noticed in the updated Trinity study’s Table 2 for inflation-adjusted withdrawals that the probability of success was maximized with a 75% stock allocation, writing, “I guess the only question left to be asked is how many of us approaching retirement ( I am 6-7 years away ) are prepared to head into the great unknown of retirement with 75 percent in equities? It scares the hell out of me, to be honest. It is gonna take some real intestinal fortitude. I would have a tough time with that allocation now with 2 paychecks coming in every few weeks. Once the paychecks stop, it will be exponentially tougher. I would love to know if people are prepared to jettison "age in bonds" and actually act on the data presented above…”

Fortunately for those who feel the same way as traumamoma, more recent work in this area has shown a reduced need for such an aggressive asset allocations for retirees.

First, regarding the Trinity study itself, the fact that 75% stocks increased the probability of success for 4% inflation-adjusted withdrawals is not a strong reason to choose this allocation. The difference between 100% success for 75/25 and 96% for 50/50 is just that in two years (1965 and 1966) the maximum withdrawal rate fell slightly below 4% with 50/50, but stayed slightly above 4% with 75/25. It is not that big of deal when considering your overall return requirements and tolerance for risk.

As well, already by 1996, William Bengen produced a figure showing that the safe withdrawal rate from a historical perspective varied very little for stock allocations between 35% and 90%. Using data for the S&P 500 and intermediate-term government bonds, he found that the historically-safe withdrawal rate was always above 4% for rolling 30-year periods since 1926 for stock allocations between 35% and 90%.

The difference in data choice for the fixed income component between William Bengen's work and the Trinity study deserves mention. William Bengen used intermediate-term government bonds, which allows for a 100% success rate for the inflation-adjusted 4% withdrawal rate rule. Meanwhile, the Trinity study uses corporate bonds, which caused the maximum inflation-adjusted withdrawal rate for new retirees in 1965 and 1966 to dip below 4%.

In 2010, Wade Pfau produced a similar figure using data between 1900 and 2008 for 17 developed market countries. In the U.S. case, with this dataset, the choice of stock allocations between 30% and 80% had very little impact on the safe withdrawal rate. This 2010 article also speaks to the issue that the United States experienced very favorable asset returns during the 20th century relative to most other developed market countries. Hoping for a repeat performance of this in the 21th century may be overly optimistic. Specifically on the issue of whether future U.S. asset returns will be as high as past returns, Jack Bogle wrote in 2009, "Please, please please: Don't count on it" (page 60). This viewpoint suggests caution about expecting an overly aggressive stock allocation to work out as well as it has in the past.

The above discussions were based on rolling 30-year periods from the historical data. Bogleheads Forum member Dick Purcell used the “Portfolio Pathfinder” software to investigate this issue using Monte Carlo simulations, which are simulated data based on the same underlying characteristics (means, standard deviations, and correlations) as the updated Trinity study. He reported the following results through private correspondence:

“Applying Monte Carlo with the Trinity return-rate-probability data you provided, I get success probabilities well below what I’ve seen reported from historical-sequence simulation, and remarkable insensitivity to allocations. Here is a summary of what I get:

30 years, withdrawal 4% inflation-adjusted (no fees):

1. Considering all allocations, the best success probability is 87%.

2. That 87% success probability is achieved at any allocation that is at least 60% stocks.

3. An 86% success probability is achieved with stocks allocation 40% or 50%.

Reduce withdrawal to 3.5% inflation-adjusted (no fees):

1. Considering all allocations, the best success probability is 92%.

2. That 92% success probability is achieved at any allocation from 20% stocks to 80% stocks.

Reduce withdrawal to 3% inflation-adjusted (no fees):

1. Considering all allocations, the best success probability is 98%.

2. That 98% success probability is achieved only with 0% stocks.

3. A 97% success probability is achieved with any allocation from 20% stocks to 80% stocks.”

Also relevant to this issue, in 2011, Wade Pfau produced a figure which looked at the issue of optimal asset allocation over the working phase of one’s career and measured the expected satisfaction received from the distribution of wealth accumulation possibilities at retirement for different asset allocation strategies that varied over time as one approaches retirement. Though the most aggressive of investors may wish to keep 100% stocks at their time of their retirement, the range of investors from somewhat aggressive to quite conservative would find their optimal asset allocations at retirement as ranging between 30% and 70% stocks.

Before concluding, a few key assumptions for these studies must be understood. First, they are based on historical data from the U.S., and so the applicability of these success probabilities depends on future stock and bond returns behaving with the same patterns as we have seen historically. Second, because these studies rely on long periods of historical data, they tend to only include stocks and traditional bonds. Retirees may wish to consider including TIPS in their retirement portfolios, as well as international assets, real estate, and other alternative assets. Third, though it is beyond the scope of this discussion to be considered further, retirees may wish to investigate whether they can benefit from purchasing nominal and/or inflation-adjusted annuities with a part of their retirement wealth.

These points aside, generally speaking, the studies mentioned above together tend to suggest that stock allocations anywhere between 20% and 80% will keep retirees within their area where maximum sustainable withdrawal rates will be at their highest. Beyond this, retirees should consider their own return needs and risk tolerances to decide on which asset allocation is most appropriate. One final point is that these studies do almost uniformly discourage a 0% stock allocation [though the results may or may not be different if TIPS could be incorporated into the analysis].

References

Bengen, William P. 1994. “Determining Withdrawal Rates Using Historical Data.” Journal of Financial Planning 7, 4 (October): 171-180.

Bengen, William P. 1996. “Asset Allocation for a Lifetime.” Journal of Financial Planning 9, 8 (August): 58-67.

Bogle, John C. 2009. Enough: True Measures of Money, Business, and Life. Hoboken, New Jersey: John Wiley and Sons.

Cooley, Philip L., Carl M. Hubbard, and Daniel T. Walz. 1998. “Retirement Savings: Choosing a Withdrawal Rate That Is Sustainable.” American Association of Individual Investors Journal 20, 2 (February): 16-21.

Cooley, Philip L., Carl M. Hubbard, and Daniel T. Walz. 2011. “Portfolio Success Rates: Where to Draw the Line.” Journal of Financial Planning 24, 4 (April).

Pfau, Wade D. 2010. “An International Perspective on Safe Withdrawal Rates from Retirement Savings: The Demise of the 4 Percent Rule?" Journal of Financial Planning 23, 12 (December): 52-61.

Pfau, W. D., “An Optimizing Framework for the Glide Paths of Lifecyle Asset Allocation Funds.” Applied Economic Letters. Vol. 18, No. 1 (2011), 55-58.
Last edited by wade on Mon Apr 04, 2011 4:06 pm, edited 4 times in total.

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Post by bob90245 » Mon Apr 04, 2011 2:53 pm

wade wrote:I've tried to put together something Wiki-appropriate about what these studies imply for asset allocation...
Looks good. I have one addition.

You mention here the specific bond data set for Bengen:
wade wrote:As well, already by 1996, William Bengen produced a figure showing that the safe withdrawal rate from a historical perspective varied very little for stock allocations between 35% and 90%. Using data for the S&P 500 and intermediate-term government bonds, he found that the historically-safe withdrawal rate was always above 4% for rolling 30-year periods since 1926 for stock allocations between 35% and 90%.
Maybe I missed it. But I didn't see the specific bond data set (20-year corporate bonds) for Trinity. I think it is important to include that since that accounts for the differences between 100% success (Bengen) and 95% success (Trinity) at 4% SWR for 30 years.
Ignore the market noise. Keep to your rebalancing schedule whether that is semi-annual, annual or trigger bands.

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Post by wade » Mon Apr 04, 2011 3:00 pm

bob90245 wrote:
wade wrote:I've tried to put together something Wiki-appropriate about what these studies imply for asset allocation...
Looks good. I have one addition.

You mention here the specific bond data set for Bengen:
wade wrote:As well, already by 1996, William Bengen produced a figure showing that the safe withdrawal rate from a historical perspective varied very little for stock allocations between 35% and 90%. Using data for the S&P 500 and intermediate-term government bonds, he found that the historically-safe withdrawal rate was always above 4% for rolling 30-year periods since 1926 for stock allocations between 35% and 90%.
Maybe I missed it. But I didn't see the specific bond data set (20-year corporate bonds) for Trinity. I think it is important to include that since that accounts for the differences between 100% success (Bengen) and 95% success (Trinity) at 4% SWR for 30 years.
Thanks Bob. I added this in:

The difference in data choice for the fixed income component between William Bengen's work and the Trinity study deserves mention. William Bengen used intermediate-term government bonds, which allows for a 100% success rate for the inflation-adjusted 4% withdrawal rate rule. Meanwhile, the Trinity study uses corporate bonds, which caused the maximum inflation-adjusted withdrawal rate for new retirees in 1965 and 1966 to dip below 4%.

By the way, you have done so much work in this area yourself. Do you have any articles about asset allocation that you think are relevant for my last post?

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Post by bob90245 » Mon Apr 04, 2011 3:19 pm

wade wrote:Thanks Bob. I added this in:

The difference in data choice for the fixed income component between William Bengen's work and the Trinity study deserves mention. William Bengen used intermediate-term government bonds, which allows for a 100% success rate for the inflation-adjusted 4% withdrawal rate rule. Meanwhile, the Trinity study uses corporate bonds, which caused the maximum inflation-adjusted withdrawal rate for new retirees in 1965 and 1966 to dip below 4%.
Also mention that it is long-term corporate bonds. In my mind, long-term bonds make the data that Trinity uses much more unique (long-term bonds are more volatile and sensitive to changes in interest rates). Had a corporate bond data of intermediate term been available, maybe there wouldn't be much difference between Bengen and Trinity. Just sayin'...
wade wrote:By the way, you have done so much work in this area yourself. Do you have any articles about asset allocation that you think are relevant for my last post?
Not really. Although I do mention it as part of big picture planning in this article:

Preparing for Retirement

And there is one by the SUNY professors Spitzer and Singh on harvesting strategies which studies bonds-first, stocks-first, etc, and affects the asset allocation.

http://www.bobsfinancialwebsite.com/Har ... awals.html
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Post by dbr » Mon Apr 04, 2011 3:21 pm

Wade, I like what you wrote. I think it is important to continue to underline the broad point that a person cannot allocate themselves to success in retirement. I think the two points that jump out in Jim Otar's book are that retirement ruin is driven by withdrawal rate and luck of the draw with asset allocation a distant third. That is why many posters on this forum who ask about how to invest end up being asked "How much do you plan to spend?"

What can go in the WIKI regarding how allocating fixed income mainly to TIPS affects this? Also what can go in the WIKI regarding insurance of retirement income through annuitization, including whatever pensions and annuities the investor already has?

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Post by LadyGeek » Mon Apr 04, 2011 4:43 pm

I created a new wiki page for Wade's (collaborative!) post, as it was a bit lengthy and deserved its own page.

Wiki article link: Safe Withdrawal Rates. I removed the prior comments (which quoted wade and wbern) as they seemed out of context with this update. A link to the new page is in its place.

New --> Wiki article link: Trinity study update. This page is marked "Under Contruction" as a way to indicate that it's a work in process.

Comments / questions / concerns are welcome. Wade - feel free to continue updating your collaborative post.
Last edited by LadyGeek on Mon Apr 04, 2011 4:45 pm, edited 1 time in total.
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Post by wjo » Mon Apr 04, 2011 4:45 pm

Wade - good summary. However, I would italicize this sentence to make sure it is not overlooked:

First, they are based on historical data from the U.S., and so the applicability of these success probabilities depends on future stock and bond returns behaving with the same patterns as we have seen historically.

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Post by wjo » Mon Apr 04, 2011 4:48 pm

dbr wrote:Wade, I like what you wrote. I think it is important to continue to underline the broad point that a person cannot allocate themselves to success in retirement. I think the two points that jump out in Jim Otar's book are that retirement ruin is driven by withdrawal rate and luck of the draw with asset allocation a distant third. That is why many posters on this forum who ask about how to invest end up being asked "How much do you plan to spend?"

What can go in the WIKI regarding how allocating fixed income mainly to TIPS affects this? Also what can go in the WIKI regarding insurance of retirement income through annuitization, including whatever pensions and annuities the investor already has?
Good points. I suspect both paragraphs would be good starting points for separate topics for the wiki. It is too bad Otar doesn't post on this board. Maybe we could get permission to post one of his shorter articles? Last time I looked at his website there were several shorter distillations of his longer book available.

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Post by bob90245 » Mon Apr 04, 2011 5:35 pm

wjo wrote:It is too bad Otar doesn't post on this board. Maybe we could get permission to post one of his shorter articles? Last time I looked at his website there were several shorter distillations of his longer book available.
Fair Use should be just fine. Don't need to post the whole article. Quote the relevent excerpt (one or two paragraphs) along with a link to the original article. Go for it! :)
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Post by wade » Mon Apr 04, 2011 6:07 pm

I'll follow everyone's comments and then make some more changes in one batch. Thanks for keeping them coming.

Just a quicky, Jim Otar is indeed a Boglehead's Forum member. His ID is:

cotar@rogers.com

I have two of his books, but I haven't found the time to read them yet. If someone wishes to prepare some material, I can include it too.

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Post by mickeyd » Mon Apr 04, 2011 6:24 pm

DRiP Guy wrote: It seems to me the bigger odds of a 'failure' aren't the economic or financial risks... it's the sociological one of the 'havenots' coming in to grab what the 'haves' took time to stash away, with or without the cover of government to sanction the grab.

See:
http://teresaghilarducci.org/
http://money.usnews.com/money/blogs/cap ... in-america
http://en.wikipedia.org/wiki/Teresa_Ghilarducci
Wonderful point DG. Fear of the unknown... :shock:
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Post by rai » Mon Apr 04, 2011 6:36 pm

I've a simple question regarding the 4% rule.

4% (of starting portfolio) plus inflation adjustment each year.

What if you had a good year and instead of taking the inflation adjustment you re-set the new value as the starting value?

in other words if you start retirement at $1M and take $40K and the next year you have $1.1M. What if you took that as your starting point and take $44K (plus inflation) going forward?

I understand that's cherry picking the better year to re-set (I presume it's not the desired method since you are in a worse PE environment).
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Post by LadyGeek » Mon Apr 04, 2011 6:53 pm

wjo wrote:Wade - good summary. However, I would italicize this sentence to make sure it is not overlooked: First, they are based on historical data from the U.S., and so the applicability of these success probabilities depends on future stock and bond returns behaving with the same patterns as we have seen historically.
I updated the wiki.

Wade - If you start a different topic (annuities, etc.) put it in a separate post so we won't mix content. Depending on length, I'll create a separate article. If you have any tables or figures, PM me and I'll give you my email address.

Wiki article link: Trinity study update (currently focused on asset allocation)

Primary article: Safe Withdrawal Rates
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Post by mickeyd » Mon Apr 04, 2011 6:53 pm

in other words if you start retirement at $1M and take $40K and the next year you have $1.1M. What if you took that as your starting point and take $44K (plus inflation) going forward?
Hmmm, sure you could do it, but would you have to rejigger it every year? Spend away... :shock:
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Post by earlyout » Mon Apr 04, 2011 7:09 pm

rai wrote:I've a simple question regarding the 4% rule.

4% (of starting portfolio) plus inflation adjustment each year.

What if you had a good year and instead of taking the inflation adjustment you re-set the new value as the starting value?

in other words if you start retirement at $1M and take $40K and the next year you have $1.1M. What if you took that as your starting point and take $44K (plus inflation) going forward?

I understand that's cherry picking the better year to re-set (I presume it's not the desired method since you are in a worse PE environment).
Here is an earlier thread that addressed this question.

EO

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Post by unclemick » Mon Apr 04, 2011 7:16 pm

mickeyd wrote:
in other words if you start retirement at $1M and take $40K and the next year you have $1.1M. What if you took that as your starting point and take $44K (plus inflation) going forward?
Hmmm, sure you could do it, but would you have to rejigger it every year? Spend away... :shock:
Yep - retired since 1993 in my case. Also difficult for me to offer any precise look back - some temp work, non-cola pension cut in at 55 and then later SS plus selling and consuming some real estate $. Also some portfolio shifting.

Toss in varying withdrawal rate based on a 'sense' of expenses as well as Mr Market.

heh heh heh - hindsight says my 'emotions' overreduced withdrawal rate during perceived 'hard times'. :roll: :wink: .

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Post by Leesbro63 » Mon Apr 04, 2011 7:29 pm

I think THIS is the missing piece: Valuation at retirement:

http://www.kitces.com/assets/pdfs/Kitce ... y_2008.pdf

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Post by bob90245 » Mon Apr 04, 2011 8:29 pm

rai wrote:I've a simple question regarding the 4% rule.

4% (of starting portfolio) plus inflation adjustment each year.

What if you had a good year and instead of taking the inflation adjustment you re-set the new value as the starting value?

in other words if you start retirement at $1M and take $40K and the next year you have $1.1M. What if you took that as your starting point and take $44K (plus inflation) going forward?
We had a similar discussions here which led to two approaches to maximize withdrawals. This link will take you to my web page which summarizes the methods and also links back to the original threads here on Bogleheads:

http://bobsfinancialwebsite.com/Variabl ... html#LBill

Edit to add:

Here is chart showing how it might have worked:

Image
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Post by Dick Purcell » Tue Apr 05, 2011 4:35 am

TWEEEEET! (That’s a whistle, not a Twitter.)

I think that as a whole this discussion is way too optimistic, too overloaded with conclusions derived from historical sequences, which have way too few samples, especially too few non-duplicative samples. And as a result, this discussion is way too overloaded with 4%.

One of the first things Monte shows is that, with the StDevs of asset classes being as big as they are, we need lots of samples. For applying Monte to portfolios, the general rule is thousands of runs.

How many runs do we have from historical sequences? Just for discussion, I’ll propose the rule that to count as a separate sample, a run can’t be more than half duplication of another run. And on that basis, I'll guess that historical sequences give us ten runs.

WellSir – I used Wade’s original example – data from Shiller, 30 years, 50-50 portfolio, 4% WD, all inflation adjusted. For simple illustration, I started with $100k. Then, using Monte, I did ten runs. The ten runs are shown below. Final balances are in the little table at lower right.

[img]<table><tr><td><a%20href="https://picasaweb.google.com/lh/photo/Y ... tr></table>[/img]

100% success rate! And note that the lowest final balance is $84.5 (inflation adjusted), which is 84.5% of starting value.

Then I erased the first ten runs and did a second set of ten runs. They look like this:

[img]<table><tr><td><a%20href="https://picasaweb.google.com/lh/photo/g ... tr></table>[/img]

Sorta different, eh? 40% failure rate, with a fifth within a hair of failing. Average ending balance is lower than the lowest of the first ten.

(So help me, I didn't "choose" these two sets of runs. They are the first and only sets I ran.)

Here is what this shows: With the variations in asset classes' return rates being as big as they are, a handful of runs is nowhere remotely close to sufficient. Historical sequences aren't remotely close to sufficent.

I think this discussion needs a big dose of analyses with way more samples, which means Monte. And some of those should have StDevs higher than calculated from history, to reflect uncertainty about the return-rate probabilities calculated from history. This is, I am already pretty sure, going to make 4% appear not very safe, and make 3% WD look no safer than the discussion now makes 4% appear.

And I think it’s gonna make that inflation-adjusted lifetime SPIA awfully attractive – relatively speaking.

Dick Purcell

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Post by Leesbro63 » Tue Apr 05, 2011 6:08 am

SPIAs have 4 problems:

1. VERY expensive in this zero interest rate environment.

2. Risk of early death...can be offset w a period certain guarantee, but that is even more expensive.

3. If the very thing you want to hedge...inflation...gets virulent you will have a tax problem as the taxable portion of the payout escalates.

4. Nothing for heirs, guaranteed.

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Post by wade » Tue Apr 05, 2011 7:21 am

LadyGeek and bob90245:

The characteristics Bob is describing about long-term corporate bonds is important. I'm not exactly sure how much to include about it, but for now I added "more volatile long-term" in front corporate bonds for this paragraph:
The difference in data choice for the fixed income component between William Bengen's work and the Trinity study deserves mention. William Bengen used intermediate-term government bonds, which allows for a 100% success rate for the inflation-adjusted 4% withdrawal rate rule. Meanwhile, the Trinity study uses more volatile long-term corporate bonds, which caused the maximum inflation-adjusted withdrawal rate for new retirees in 1965 and 1966 to dip below 4%.
I'd say Dick's most recent post is also very important and deserves a spot in the Wiki, though probably in the main article rather than the asset allocation article.

Perhaps over the next month or so, we could develop some sort of point/counterpoint article about why "Trinity is too optimistic" and "Trinity is too pessimistic".

Dick's analysis definitely shows the pessimistic side. But even this may be optimistic, because it is still based on the rather optimistic historical data parameters. I kind of view the world as one big Monte Carlo simulation, and the parameters we've gotten from our historical run may not be the correct parameters. Dick, I wonder if you can see how much difference there is among each of the 10 or however many simulations in regard to their means, standard deviations, and correlations, despite the fact that each simulation was based on the same underlying parameters?

I think Dick already made a very useful point about this by increasing historical standard deviations by 30% in order to account more for the uncertainty. But perhaps the assumption about means is actually more important than the assumption about standard deviations. I'm not sure though.

More generally about why Trinity may be pessimistic:

From reading Enough, I think it is fair to say that Jack Bogle would reject the Trinity study because he believes it is foolish to define future parameters as the historical averages, which is implicitly what Trinity is doing by presenting these probabilities as representative of future events. This would apply both for historical simulations and Monte Carlo. Instead, he, as has Rob Arnott and many others, prefers to look at the building blocks of returns: their income component, underlying earnings growth, and changes in valuation levels. So, just as a hypothetical example that I think is not too far off base, if the historical real stock return is 7% but the results from combining the building blocks of returns is 5%, I think he would say that he would prefer basing Monte Carlo on the 5% instead of 7%. Dividends yields are at historic lows, bond yields are leaning to the low side, earnings growth may not be able to reach the high bar set in the past, and though I think Jack Bogle would always choose a best forecast for valuation levels as no further change from their present levels, valuations are currently on the high side as well.

I posted my figure earlier in this thread showing safe withdrawal rates for 17 countries, and I used that to point out that for the US the results were about the same for stock allocations between 30% and 80%, but now I refer to it again to ask: what if the 21st century U.S. experiences patterns closer to 20th century Denmark or Switzerland, or any of the other countries except Canada?

Also, I already showed tables about what happens in the Trinity study when one has to pay a 1% or 2% account administrative fee. This is something very real that people need to account for.

Also, the whole analysis of every withdrawal rate study I am aware of makes the implicit assumption that people can match the precise returns of the historical index. People make behavioral mistakes. But even if they don't make any mistakes, it may still just generally be difficult to match the historical returns precisely.

On the optimistic side: maybe people just need to go out and enjoy life and be prepared to cut expenses dramatically later should the need arise. Also, TIPS, international diversification, and annuities may help.

Leesbro63 and others about annuities: I mostly understand the theoretical aspect of annuities, and I've written a program to calcuate nominal/real and fixed/variable annuities that I hope to use some more one of these days. I don't know about the real world practical issues like taxes and fees. But I think the way you just wrote about it is as an "all or nothing" proposition. Annuities could be treated as a type of asset class with particular risk and return properties, and then as you develop your strategic asset allocation for retirement, you can decide what percentage of your portfolio should be allocated to annuities. It could be 0, 20, 40, 100,... It doesn't have to be all or nothing. But this is really about all I can say on the topic of annuities.

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Post by Leesbro63 » Tue Apr 05, 2011 7:41 am

wade wrote:But I think the way you just wrote about it is as an "all or nothing" proposition. Annuities could be treated as a type of asset class with particular risk and return properties, and then as you develop your strategic asset allocation for retirement, you can decide what percentage of your portfolio should be allocated to annuities. It could be 0, 20, 40, 100,... It doesn't have to be all or nothing. But this is really about all I can say on the topic of annuities.
Point well taken! Thank you!

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Post by plannerman » Tue Apr 05, 2011 7:51 am

I have a question for the Monte Carlo experts here, particularly, Dick.

We all know that stock returns, bond returns and inflation are not independent. For example, short-term Treasuries are generally negatively correlated with stocks, so when stocks go up, bonds go down. Interest rates generally go up when inflation goes up causing bond returns to go down in the short-term but up in the longer tern, etc.

Intuitively, these dependencies are “built into” the historical sequence of returns.

My question is are they accounted for in when doing a Monte Carlo analysis? Or are the stock, bond and inflation numbers assumed to be independent?

plannerman

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Post by ResNullius » Tue Apr 05, 2011 9:00 am

I wonder what the chart would look like if you didn't adjust for inflation, but reinvested the balance in any year where the portfolio gain was greater than the 4% plus inflation, but where you withdrew less in the down years?

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Post by Barry Barnitz » Tue Apr 05, 2011 9:32 am

Hi Wade:

I took a stab at wordsmithing the opening paragraph. Here is the edit (with wiki it can be easily reversed or re-edited)
Asset allocation for retirees is a very important issue. Choosing one’s asset allocation will depend on a number of important factors involving the desired retirement income level and the sources of retirement income. Desired income levels will be affected by whether or not you are supporting others (such as a spouse) with your retirement income and whether you might desire to leave an inheritance or bequeath a charitable donation. Primary sources of retirement income will include the percentage of your needed/desired expenses available from Social Security and any other employer-based defined benefit pensions you may be entitled to receive, as well as any income coming from a decision to annuitize part of your wealth. A contingent source of income can result from having the flexibility to return to work should such a need arise.

The income to be derived from an investment portfolio will reflect any monetary amounts you need to regularly withdraw over your life expectancy; any additional monetary amounts you may desire to withdraw if possible; and the taxes you will pay on the withdrawn income. The costs of administering the portfolio are also a critical factor. [1]These withdrawals will provide you with the percentage of your wealth these needs and desires imply and can indicate the degree of flexibility you may have to allow your withdrawals to fluctuate over time. The Trinity and other studies examine the question of what percentage portfolio withdrawal rate (over a number of portfolio asset allocations) is sustainable without being prematurely depleted (the early studies' suggested a sustainable withdrawal rate of 4%). Entire books can and have been written on this topic.

The question addressed here is not “What should my asset allocation be in retirement?,” but rather “What do the Trinity study and other related studies imply about asset allocation?”
Wiki article link: Trinity study update

Thanks!

edited to add a reference concerning investment costs
Last edited by Barry Barnitz on Tue Apr 05, 2011 10:35 am, edited 2 times in total.
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Barry's "wordsmithing"

Post by Taylor Larimore » Tue Apr 05, 2011 10:07 am

Hi Barry:
I took a stab at wordsmithing the opening paragraph. Here is the edit (with wiki it can be easily reversed or re-edited)
Hi Barry:

Your "wordsmithing" will be hard to beat.

Nice job!
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Post by BlueEars » Tue Apr 05, 2011 10:16 am

plannerman wrote:...(snip)...
Intuitively, these dependencies are “built into” the historical sequence of returns.

My question is are they accounted for in when doing a Monte Carlo analysis? Or are the stock, bond and inflation numbers assumed to be independent?...
Good question and I'll look forward to the answer.

A few more thoughts along those lines: If we are simulating with international equities as an asset class alternative, we should also add currency related dependencies to that mix. Value stocks tend to decline more then the market in severe bear markets, is that in the simulations?

Many investors do not own just Treasury bonds and the SP500 (or Total Stock Market).

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Post by magellan » Tue Apr 05, 2011 10:18 am

plannerman wrote:Intuitively, these dependencies are “built into” the historical sequence of returns.

My question is are they accounted for in when doing a Monte Carlo analysis? Or are the stock, bond and inflation numbers assumed to be independent
Not Dick, but I can answer based on my experience.

In the FlexibleRetirementPlanner, I don't take sequence of returns dependencies into account. It's theoretically possible to build a model that considers these dependencies, but I don't know of many instances where this has been done. Also, I'm not sure if trying to capture these dependencies in a model would actually improve the model's accuracy in the end. Similar to the known use of the inaccurate fixed normal distribution model for returns, this is yet another source of model error in most MCS approaches. My take is to embrace the model uncertainty and just live with it. It keeps us all honest and humble.

As an aside, my planner models the overall portfolio sequence of returns, rather than separate sequences for stocks and bonds that are aggregated to produce a portfolio return sequence. This is probably another source of model error, or at least loss of resolution in the model. Buy hey, that's what models are all about.

Still, despite these glaring errors and omissions, I don't agree with those who believe that historical returns based approaches are necessarily better. Personally, I like to test retirement scenarios with both approaches and compare the results.

IMO, the best feature of MCS is how easy it is to margin the inputs and test various assumptions (such as Dick's 130% std dev test). These types of what-if tests are a great way to see possible outcomes from different retirement planning assumptions and decisions.

Jim

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Post by magellan » Tue Apr 05, 2011 10:29 am

Les wrote:A few more thoughts along those lines: If we are simulating with international equities as an asset class alternative, we should also add currency related dependencies to that mix. Value stocks tend to decline more then the market in severe bear markets, is that in the simulations?
Personally, I think this is a risky way of thinking about these models.

The model error is MCS retirement tools is certainly quite large and although I'm open to ideas that can really reduce the error, IMO most of these tweaks wouldn't appreciably do that.

If you've ever worked in Photoshop or a similar tool and tried to sharpen a blurry image, you might be able to get an idea of where I'm coming from with an analogy. If the image is blurry in the first place, sometimes a little bit of sharpening can improve things. But after that, additional sharpening only increases the level of pixelation and noise in the image. The result is that the image looks worse and worse the more you over-sharpen it. The problem is not with your sharpening technique, it's that there isn't enough data in the original image to get it looking crisp. The best thing to do in this case is to reduce the crop and stay zoomed out. Find a crop that embraces the lack of detail on the subject and still makes a nice photo.

I think this "over sharpening" risk is also present in our MC models as we try to capture details in the inputs beyond what the data and our level of understanding supports.

Jim

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Post by BlueEars » Tue Apr 05, 2011 10:41 am

magellan wrote:
plannerman wrote:Intuitively, these dependencies are “built into” the historical sequence of returns.

My question is are they accounted for in when doing a Monte Carlo analysis? Or are the stock, bond and inflation numbers assumed to be independent
...
Still, despite these glaring errors and omissions, I don't agree with those who believe that historical returns based approaches are necessarily better. Personally, I like to test retirement scenarios with both approaches and compare the results.

IMO, the best feature of MCS is how easy it is to margin the inputs and test various assumptions (such as Dick's 130% std dev test). These types of what-if tests are a great way to see possible outcomes from different retirement planning assumptions and decisions.

Jim
Hi Jim, I'm not sure I understand what you mean by "margin the inputs". I would think that modeling the inputs is absolutely critical to your outputs.

I've used FIREcalc quite a bit and it's a great tool. But it is so limited in it's historic data set (the inputs). The current version does not have provision for TIPS, does not include international equities, etc. Still it points out the most difficult periods to plan for (like 1968 and 1929 retirement starts).

If another simulator constructed inputs that led to higher drawdowns, I would not know how to plan for that. Do I really want to shortchange myself in my 60's because some dubiously modeled inputs told me that things could get even worse then historically seen?

I'm retired right now. I've done lots of thinking and modeling. I'm convinced that individual situations are all over the map and so extremely difficult to model. For me the best model is the one I made up with my particular resources, investment methodolgy, and tradeoffs. On the other hand, most people don't want to even run a generic model.

Living through this stuff is a lot different then writing about it. :)

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Post by BlueEars » Tue Apr 05, 2011 10:47 am

magellan wrote:...(snip)..
I think this "over sharpening" risk is also present in our MC models as we try to capture details in the inputs beyond what the data and our level of understanding supports.

Jim
I think we're in agreement here. These models are all going to give somewhat fuzzy answers. One observation, I think that things like adding some international equities and (maybe) small value tilting can increase your returns somewhat over the long run. So that should get some modeling or at least be considered.

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Post by wade » Tue Apr 05, 2011 10:51 am

plannerman wrote:I have a question for the Monte Carlo experts here, particularly, Dick.

We all know that stock returns, bond returns and inflation are not independent. For example, short-term Treasuries are generally negatively correlated with stocks, so when stocks go up, bonds go down. Interest rates generally go up when inflation goes up causing bond returns to go down in the short-term but up in the longer tern, etc.

Intuitively, these dependencies are “built into” the historical sequence of returns.

My question is are they accounted for in when doing a Monte Carlo analysis? Or are the stock, bond and inflation numbers assumed to be independent?

plannerman
Barry: Thank you. It looks great. Thanks as well to the person who added in my note about the impact of fees on the Trinity results.

Plannerman: Let me take a stab at your question. Yes, the precise dependencies you are describing are accounted for in the Monte Carlo simulations, at least in the ones Dick used and the ones I personally use.

Some very basic Monte Carlo simulators will assume each asset behaves independently, but most do assume "contemporaneous correlation" which is what you describe here.

However, I think that most simulators available for household retirement planning do not move too far beyond that. In particular, basic Monte Carlo simulations assume "no serial correlation", which means that asset returns over time are independent from their past returns. There are exceptions to this, such as in the research done by Mark Warshawsky and his colleagues at Watson Wyatt.

The updated Trinity study discusses these limitations and explains why they prefer to use historical simulations.

This issue is relevant for the paper I recently wrote about "Safe Savings Rates" in which I am looking at 60 year periods. I use historical simulations for it, and I haven't tried it with Monte Carlo simulations yet. But I think that because, at least in the historical data, market valuations tended to revert to their historical averages, the safe savings rates are lower with historical data than they will be with Monte Carlo simulations based on the average returns, standard deviations, and contemporaneous correlations of the historical data. Actually, Dick informed me that this is indeed the case.

So which is better? Well, as Dick and magellan are both saying, it is probably best to try both approaches and compare the results. Then you can decide which you feel more comfortable for basing your decisions.

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Post by magellan » Tue Apr 05, 2011 10:57 am

Les wrote:Hi Jim, I'm not sure I understand what you mean by "margin the inputs". I would think that modeling the inputs is absolutely critical to your outputs.
At the end of the day my belief is that these tools are better suited as decision support tools than as prediction tools.

So when I say "margin the inputs" I'm thinking about doing a test like Dick did where you run the MCS with one return and std dev, then bump up the std dev by 30% and run it again. The goal is to see what happens when you have more volatility than you expected.

You can keep playing around with std dev and see what happens under a whole range of values, keeping all the other inputs constant. This is what I mean by margining the inputs. Once you've played around with one input, try another, then another.

Another term for this is sensitivity analysis. The idea is to try to gauge how sensitive the outputs are to changes in the various inputs. Understanding which inputs have the most impact, and which don't, can be very helpful in decision-making.
Living through this stuff is a lot different then writing about it. :)
I hear you. DW and I mostly retired 5 years ago in our 40s and I can only imagine how much the error in our planning will compound if we live into our 80s or 90s.

Jim

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Post by bob90245 » Tue Apr 05, 2011 11:06 am

OK, just come quick thoughts.

Wade, you incorporated my input regarding long-term corporate bonds just fine.

Second, I'll state this up front because I didn't read the Trinity update yet. And might have missed the commentary. But it looks like there is a lot of side discussions going on in this thread for what the wiki Trinity article should be. I thought the main emphasis of Trinity was to get a fix on SWRs based on historical data.

Now there appears to be lots of discussion speculating what the future might be using, among other variables, lower expected returns, additional asset classes, monte carlo, etc. This would be fine in and of itself. But should be clearly labeled in a separate section of the wiki article under the heading of "Other Commentary" (or similar paragraph heading).

That's it! Carry on... 8)
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The Trinity Study

Post by Taylor Larimore » Tue Apr 05, 2011 12:22 pm

Bogleheads:

The Trinity Study simply shows WHAT ACTUALLY DID HAPPEN to various stock/bond portfolios if we had withdrawn different percentage amounts since 1926. This period includes the Great Depression and 13% annual inflation.

I feel the Trinity Study, Table 2, is easy to understand and reasonably conservative for current and future planning. Nobody knows the future.

http://www.fpanet.org/journal/CurrentIs ... cessRates/
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Post by Dick Purcell » Tue Apr 05, 2011 1:35 pm

Wade –

1. Yes yes on where my last post goes – it belongs in discussion of SWR.

I’m not familiar with plans for subdividing this discussion in the Wiki, and have though of this whole discussion as basically about SWR.

(However, if there is a separate thing about asset allocation – or anything else – that is based mainly on historical-sequence runs, I think the same basic message illustrated in my last post is important there too.)

2. On the debate about Trinity that you suggested, my view is that the debate should be between “Trinity is too optimistic” and “Trinity is too-too optimistic.” (Same for Firecalc and Otar.) It's like throwing a pair of dice twice, and betting your financial future on the conclusion those two throws have revealed the probabilities.

Monte with more runs is “less optimistic” – for example, My Montes show inflation-adjusted 4% WR below 90% success at any allocation -- and yet I think my Monte is too optimistic for the reason you point out – it assumes future return-rate probabilities will be exactly what we calculate for them from history.

3. I like your suggestion of testing with return-rate mean and/or SD adjusted to be more conservative than calculated from history -- the discussion where you referenced Mr. Bogle’s thinking being consistent with this approach – e.g. reduce mean of 7% to 5%. I can do a little Monte testing with such adjustments if you’d like.

(Side note to Magellan – Huge roar of applause for your message saying Monte is for decision support more than prediction, and your discussion of how to use it to test alternatives and see sensitivities.)

Wade, if you’d like me to do a test with conservative adjustment of one or more of the dimensions of the return-rate probabilities calculated from history, choose one combination of settings in these three boxes –

[img]<table><tr><td><a%20href="https://picasaweb.google.com/lh/photo/b ... tr></table>[/img]

As I hope is evident, these boxes enable one-click conservative adjustment of means, SDs, and/or Correls.

(Just a day or two ago, this forum had a discussion started on reports that correlations are rising, so maybe our adjustments should include that, along with adjustment of means and SDs.)

Note that Mr. Bogle’s illustrative suggestion of reducing mean from 7% to 5% amounts to reducing it about 28%, and for a test I can approximate that by clicking “HistAve x 70%” in our “Conservatizer.”

4. Wade, I think your “Figure 2” showing historical-sequence SWRs for various countries is extremely valuable, not only for asset allocation but even more for raising doubts about relying on US historical sequences, and their resulting “safe 4%.”

Plannerman –

Yes correlations among asset classes are incorporated in our Monte. In the Montes I’m using, inflation is not included in the probabilistic return rates because it is nominal returns that are taxed, so we need nominal returns to calculate taxes in in our sims. We could simulate real (inflation-adjusted) returns, but that would not give us “correct” (chuckle) numbers for calculating taxes. Instead we make a separate inflation adjustments using a constant rate. That’s a simplification, but I’m made comfortable about it knowing it is dwarfed by the point Wade makes about it all being based on the assumption that future return rates will be the same as we calculate for the past. And then, as Wade mentions, there are those fees, and taxes….

I think we can rest assured that for future net dollar value results, uncertainty and risk are greater than what my un-conservatized Montes are showing, way-way greater uncertainties and risks than the historical sequences are showing.

Where is that SPIA order form??

Dick Purcell

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Post by plannerman » Tue Apr 05, 2011 2:27 pm

Dick,

If understand your response correctly, you are assuming in your Monte Carlo simulations that both stock and bond returns are independent of inflation. That seems to me to be a huge assumption. Is there some justification for this other than it complicates calculating taxes?

plannerman

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Post by wjo » Tue Apr 05, 2011 2:59 pm

bob90245 wrote:
wjo wrote:It is too bad Otar doesn't post on this board. Maybe we could get permission to post one of his shorter articles? Last time I looked at his website there were several shorter distillations of his longer book available.
Fair Use should be just fine. Don't need to post the whole article. Quote the relevent excerpt (one or two paragraphs) along with a link to the original article. Go for it! :)
Otar's website - www.retirementoptimizer.com is a trove of info and articles.

This one: http://www.retirementoptimizer.com/arti ... cle105.pdf
does a good job summarizing his approach. In particular, it reviews his zone approach to looking at retirement income

Note that Otar is increasingly a believer in a historical approach to looking at returns (he calls it aftcasting), which as discussed in this thread has its difficulties. Nonetheless, I like his zone approach that adjusts with age. He also has some good thinking about percent of SPIA needed if you are in the grey zone.

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Post by bob90245 » Tue Apr 05, 2011 3:44 pm

wjo wrote:
bob90245 wrote:
wjo wrote:It is too bad Otar doesn't post on this board. Maybe we could get permission to post one of his shorter articles? Last time I looked at his website there were several shorter distillations of his longer book available.
Fair Use should be just fine. Don't need to post the whole article. Quote the relevent excerpt (one or two paragraphs) along with a link to the original article. Go for it! :)
Otar's website - www.retirementoptimizer.com is a trove of info and articles.

This one: http://www.retirementoptimizer.com/arti ... cle105.pdf
does a good job summarizing his approach. In particular, it reviews his zone approach to looking at retirement income

Note that Otar is increasingly a believer in a historical approach to looking at returns (he calls it aftcasting), which as discussed in this thread has its difficulties. Nonetheless, I like his zone approach that adjusts with age. He also has some good thinking about percent of SPIA needed if you are in the grey zone.
Ah, yes... I read that one a few years ago. It's a good article. I added it to the other good articles on my recommended list on my website:

http://www.bobsfinancialwebsite.com/Rev ... story.html
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Post by wade » Tue Apr 05, 2011 8:03 pm

Dick Purcell wrote: Wade, if you’d like me to do a test with conservative adjustment of one or more of the dimensions of the return-rate probabilities calculated from history, choose one combination of settings in these three boxes –

[img]<table><tr><td><a%20href="https://picasaweb.google.com/lh/photo/b ... tr></table>[/img]

As I hope is evident, these boxes enable one-click conservative adjustment of means, SDs, and/or Correls.
Dick, that is a great feature of the software! It makes things easy.

I should really try it out for myself soon.

It could be nice to have a sensitivity analysis for the 3 parameters, but I am thinking that the average returns is by far the most important parameter. I realized why I thought this. I cannot find a copy of this article online, but once I can get back to my office I will be able to access an electronic version of it. My memory is that this article has some really nice tables providing the type of sensitivity analysis we are talking about here:

Blanchett, David M., and Brian C. Blanchett. 2008. "Data Dependence and Sustainable Real Withdrawal Rates." Journal of Financial Planning 21, 9 (September): 70-85.

An old Bogleheads thread with no further discussion provides the executive summary:
Executive Summary:

* Past research on sustainable real withdrawal rates has been overwhelmingly based on past market returns. Such research ignores the possibility, and consequently the implications, that future market conditions will vary from those in the past.
* This paper will explore the impact of varying returns and standard deviations on a distribution portfolio in order to provide the reader with information on appropriate sustainable real withdrawal rates for various market conditions.
* Experts predict that the future market return for a balanced 60/40 portfolio is likely to be 1–2 percent less than historical averages.
* Over longer distribution periods the return of a portfolio becomes increasingly important in maintaining the likelihood of success of a distribution portfolio. A 1 percent decrease in portfolio return is likely to result in an increase in the probability of failure that is approximately 4 times greater than a 1 percent increase in portfolio standard deviation.
I added some emphasis.

Also, here is a paragraph I wrote about this study before:

One study in this literature acknowledging that past market conditions may not suitably represent what will happen in the future is Blanchett and Blanchett (2008). Basing an average forecast for future stock returns on a variety of sources, they find that the future real return for a 60/40 portfolio of stocks and bonds could be between 1 and 2 percentage points less than historical averages. They use Monte Carlo simulations to consider how varying the returns and standard deviations of an investment portfolio will impact the sustainable real withdrawal rate for 30-year periods, which essentially allows the reader to choose their assumptions for these two portfolio parameters and see how the probability of success changes for various withdrawal rates.


I think this study may have already done some of our new collective research work here.

But I do think this is important and we can still provide our own twist. This type of analysis does seem to have a place in the Wiki about SWRs as an extension for the Trinity study.

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Post by Dick Purcell » Wed Apr 06, 2011 1:29 am

Plannerman -- You zero in on an issue that deserves a response.

Our answer follows the path of reasoning so well stated by Magellan – the purpose here is to help people see, focus on, and explore what counts.

From a combination of readings and our own testing, we concluded that for our purpose, correlating the inflation would be doubly counter-productive. It would take us away from helping users see and explore much more important things, and it would slow the software down enough to inhibit user exploration of more important things.

I’ll grant you that for extended, ongoing runaway inflation, we don’t have the ideal software, but other tools discussed here are not suited for that either, and statistically meaningful data for what that would do to the US is lacking. Within the ranges and patterns of US historical inflation, our approach delivers almost exactly the same result as correlation of inflation – just a hair more conservative. For this specific point I don’t want to clutter up this discussion with more graphs, but if you’d like I’ll email you illustrations.

Here’s an example of higher priorities: in this discussion we’ve been fixed on 30 years – but you might live fewer years – or more years. Especially if you’re plannerWOMAN. And, we’ve been discussing just the retirement years – but Wade’s research covers investment and retirement years together, and shows if you’re young enough, the thing to focus on is pre-retirement savings (investment) rate. WellSir, we offer an interactive graph in which the user can see a curve showing what happens to success probabilities if she lives 2 or 5 or 8 years beyond end of plan – and then add curves on the graph to see how that would be changed if she kicked up her annual pre-retirement savings by say $4000 or $8000. Or add curves on that graph to see how the curve of success probability v. lifespan changes if she cuts her annual retirement withdrawals by say $2000 or $5,000.

I describe this graph as part of my response to your inflation question. Our explorations show us that it’s far more important to enable users to see these variations than for us to put in inflation correlations. And – putting in inflation correlations would slow down the software's preparation of this graph so much it would reduce use of it. Right now, prep of this graph takes hundreds of millions of return-rate simulations. Correlating inflation would multiply that.

On our list of priorities for helping users to see and explore what counts, compared to correlating inflation there are other things our own Monte explorations show to be way more important for us to help users see and explore – lifespan, pre-retirement savings rate, return-rate means, return-rate standard deviations, when to retire. . .

But – inflation sure is important, a killer. It’s just the correlating of it that we’re discussing. And the question you raised should be addressed. It’s the use of Monte to explore these things, see what counts most, that’s most valuable, just as Magellan says.

Dick Purcell

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Post by Dick Purcell » Wed Apr 06, 2011 2:23 am

Wade, here it is -- Your original example, data from Shiller, 30 years, 50-50 portfolio, WD 4%, all inflation-adjusted -- with return-rate means adjusted down from those calculated from history, as you suggested.

If I understood your message correctly, Mr. Bogle suggested a 7% historical return-rate mean should maybe be cut down to 5%, which is a 28% reduction. So I clicked to reduce the return-rate means by 30%.

Got your SPIA order form handy??

[img]<table><tr><td><a%20href="https://picasaweb.google.com/lh/photo/T ... tr></table>[/img]

In this graph, the vertical bars are portfolios from 0% stocks at left to 100% stocks at right. Each bar is 100% tall, with the failure being the part underwater and the success being the part above water. The one shown red is your 50-50 portfolio. I selected that one to display its axis reading, and I'm sure you will note its success probability: 50%.

Somebody who is good at graphic communication once suggested that, to sharpen visual communication of what underwater means in this graph, we should add a shark in that water.

Dick Purcell

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Post by Dick Purcell » Wed Apr 06, 2011 3:29 am

Sorry -- User error. That graph has StDevs 30% above history too. I intended StDevs as calculated from history, but still return-rate means at 70% of what's calculated from history. That shows the 50-50 portfolio to have 57% success probability.

Dick Purcell

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Post by wade » Wed Apr 06, 2011 6:27 am

Dick, Thanks a lot for your work!

To summarize, and please correct any mistakes I made, you are looking at 30 year retirements, a 50-50 portfolio, WD 4%, all inflation-adjusted, using Robert Shiller's dataset for 1871 to 2009, for large-capitalization stocks and 10-year government bonds.

This is not the same dataset as the Trinity study, but it is comparable, and it is the one I like to use because it provides a longer perspective and also picks up some bad market conditions in the early 1900s which are missing from Trinity's SBBI data that begins in 1926..

Using Monte Carlo simulations with the historical parameters, the success rate was 89%

If standard deviations increase by 30%, the success rate falls to (??)

If average returns on both stocks and bonds decrease by 30%, the success rate falls to 57%

If the average returns decrease and the standard deviations increase simultaneously, the success rate falls to 50%

My 7% and 5% cases were just an approximation. I can't remember the specific details that Jack Bogle wrote about, and I can't check it until I'm in my office. Rob Arnott and John West provide a similar type of analysis.

And here are two more tables showing that from an international perspective, the U.S. enjoyed pretty favorable asset returns in the 20th century with combinations of high real returns and low volatilities. Can the U.S. get a repeat performance in the 21st century ???

Image

Image

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Post by Dick Purcell » Wed Apr 06, 2011 8:59 am

Wade, I started with '26. If for the data beginning in 1871, you send me the ArithMeans and StDevs for the two asset classes, their Correl, and an inflation mean, I can quicklychurn out those four numbers success-probability numbers for the 1871-forward period.

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Post by wade » Wed Apr 06, 2011 9:29 am

Dick Purcell wrote:Wade, I started with '26. If for the data beginning in 1871, you send me the ArithMeans and StDevs for the two asset classes, their Correl, and an inflation mean, I can quicklychurn out those four numbers success-probability numbers for the 1871-forward period.

Dick Purcell
Hi Dick, I'm sorry, I might have been confusing. The numbers I posted before were the same data used by the Trinity Study's update. This is SBBI data, 1926-2009. The asset order is:


1. S&P 500 2. Long-term Corporate Bonds 3. Inflation

Code: Select all

Arithmetic Means 
11.8425   6.1537    3.0955 

Standard Deviations 
20.5065   8.3281   4.1988 

Correlation Coefficient Matrix 
1           0.1715        -0.0014 
0.1715      1             -0.1549 
-0.0014     -0.1549       1 
I provided those numbers so that the Monte Carlo simulations would be precisely calibrated to the numbers used in the updated Trinity study.

The next numbers I provide are what I personally would use if I did such a study. These numbers are for Robert Shiller's dataset, 1871-2009. The asset order is:


1. Stock Market Composite Index (which becomes S&P 500 when available) 2. 10-Year Government Bonds 3. Inflation

Code: Select all

Arithmetic Means 
10.1344    4.8510    2.2558

Standard Deviations 
18.0246   6.1419   6.1007 

Correlation Coefficient Matrix 
1           0.0722        0.1253 
0.0722      1             -0.0937 
0.1253     -0.0937       1 
About plannerman's questions, the correlations between inflation and the other assets are close to zero anyway in both data sources, so the fact that Dick assumes that the correlation is zero will make very very little difference for the results.

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Wiki update:

Post by Barry Barnitz » Wed Apr 06, 2011 11:02 am

Hi all:

Update:

I have made some minor tweaks to the wiki page.

1. Added links to papers;
2. Footnoted references;
3. Added a navigation box for the research papers;
4. Added header for monte carlo;
5. Uploaded chart image (not sure if this will pass copyright, I have attributed it to original source).

Wiki article link: Trinity study update.

regards,
Last edited by Barry Barnitz on Wed Apr 06, 2011 1:34 pm, edited 1 time in total.
Additional administrative tasks: Financial Page affiliate blog; finiki the Canadian wiki; The Bogle Center for Financial Literacy site; Wiki Bogleheads® España.

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Post by Dick Purcell » Wed Apr 06, 2011 11:42 am

Wade --

Good thing you were specific about the years and source.

Our "Conservatizer" etc. aren't set up for going back that far and entering the data that way, so I had to enter them by hand. And note that I am using inputs carried out only to hundredths of 1%.

The numbers I get for success % are, respectively: 94, 85, 69, and 60.

First is just Hist, second is with SDs * 1.3, third is means * 0.7, fourth is SDs * 1.3 and means * 0.7.

These are definitely "less dismal" than what I've reported in prior messages in this discussion, but they support the same conclusions.

I think it would be good for you to re-state your preference for going back that far. It's definitely more data, but a cynic could argue that back that far is "more different" from more recent numbers in terms of the economy itself, what pieces are being measured, measurement and recordkeeping methods, etc . . . I'm not disagreeing with going back that far, just suggesting it be defended wherever it might be questioned.

Dick Purcell

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Re: Wiki update:

Post by LadyGeek » Wed Apr 06, 2011 4:50 pm

Barry Barnitz wrote:5. Uploaded chart image (not sure if this will pass copyright, I have attributed it to original source).
Just in case, I replaced that image (and publisher info) with the publicly available version from The RePEc Project, a volunteer-driven initiative to create a public-access database that promotes scholarly communication in economics and related disciplines.

Wiki article link: Trinity study update

I enhanced the image using GIMP. Click on the image for a larger view.
Wiki To some, the glass is half full. To others, the glass is half empty. To an engineer, it's twice the size it needs to be.

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