Representing a Safe Withdrawal Rate
Representing a Safe Withdrawal Rate
The usual SWR discussion focuses on the initial withdrawal rate, and then is sort of hazy about the length of the plan and the probability of success.
I think a useful chart would look something like this:
If I withdraw 1%, my nest egg should last for 100 years or perhaps forever. If I withdraw 4%, my nest egg should last 30 years with 90% probability, or 25 years with 100% probability (or something like that).
I think the usual SWR studies are answering the wrong question. My question is, if I wish to make a plan for 27 years, what withdrawal rate has a 90% probability of success?
I agree with everything Nisiprius said in another thread. We don't know the future. But, I would use a chart like this to evaluate my withdrawal anew each year.
Keith
I think a useful chart would look something like this:
If I withdraw 1%, my nest egg should last for 100 years or perhaps forever. If I withdraw 4%, my nest egg should last 30 years with 90% probability, or 25 years with 100% probability (or something like that).
I think the usual SWR studies are answering the wrong question. My question is, if I wish to make a plan for 27 years, what withdrawal rate has a 90% probability of success?
I agree with everything Nisiprius said in another thread. We don't know the future. But, I would use a chart like this to evaluate my withdrawal anew each year.
Keith
Déjà Vu is not a prediction
 ObliviousInvestor
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Re: Representing a Safe Withdrawal Rate
Figure 4 from this article of Wade's looks relevant.
http://wpfau.blogspot.com/2011/08/safe ... life.html
Of course, there's always the question of how closely the assumptions he uses (e.g., 40% stock allocation, MC simulations using historical return data from 19262010) match the assumptions you'd prefer to use.
http://wpfau.blogspot.com/2011/08/safe ... life.html
Of course, there's always the question of how closely the assumptions he uses (e.g., 40% stock allocation, MC simulations using historical return data from 19262010) match the assumptions you'd prefer to use.
Mike Piper, author/blogger
Re: Representing a Safe Withdrawal Rate
ObliviousInvestor wrote:Figure 4 from this article of Wade's looks relevant.
http://wpfau.blogspot.com/2011/08/safe ... life.html
Of course, there's always the question of how closely the assumptions he uses (e.g., 40% stock allocation, MC simulations using historical return data from 19262010) match the assumptions you'd prefer to use.
Mike,
Thank you. I'll try to replot Wade Pfau's data to see what comes up.
I think the shape of the curves in my chart is about right  I have convinced myself they should be hyperbolas (hyperbolae?). If so, note that lower withdrawal rates are more robust  the horizontal distance (in years) from 100% to 90% decreases as the withdrawal rate increases.
I am not so interested in the numbers as in the trends. My current withdrawal rate is higher than it might be, since I am delaying SS. I can think of three good reasons to take higher distributions when you are younger:
1. You may not live to age 95.
2. You are delaying SS.
3. You can do things now (like travel) that may not be quite so easy later on.
So, I am trying to understand the long term effects of taking larger distributions now.
Thank you again for the link.
Keith
Déjà Vu is not a prediction
Re: Representing a Safe Withdrawal Rate
A 2013 analysis by Prof. Pfau et al titled "Asset Valuations and Safe Portfolio Withdrawal Rates" discusses SWR levels given the impact of the current , low ratesofreturn for equities and bonds and it is downloadable from:
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2286146
Not exactly the charting you have outlined, but Figure 7 on page 12 plots the probability of success versus the number of horizon years for various SWR rates (from 1% to 6%) at a 40% equity level Then their Table 3 on page 13 they provide numeric data that might be plotted as points along a curve for a few different Equity levels: at 20%, 40%, 60% and 80%.
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2286146
Not exactly the charting you have outlined, but Figure 7 on page 12 plots the probability of success versus the number of horizon years for various SWR rates (from 1% to 6%) at a 40% equity level Then their Table 3 on page 13 they provide numeric data that might be plotted as points along a curve for a few different Equity levels: at 20%, 40%, 60% and 80%.
Re: Representing a Safe Withdrawal Rate
Bob wrote:A 2013 analysis by Prof. Pfau et al titled "Asset Valuations and Safe Portfolio Withdrawal Rates" discusses SWR levels given the impact of the current , low ratesofreturn for equities and bonds and it is downloadable from:
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2286146
Not exactly the charting you have outlined, but Figure 7 on page 12 plots the probability of success versus the number of horizon years for various SWR rates (from 1% to 6%) at a 40% equity level Then their Table 3 on page 13 they provide numeric data that might be plotted as points along a curve for a few different Equity levels: at 20%, 40%, 60% and 80%.
Bob,
Thank you!
I suspect I will have an opportunity to meet Dr. Pfau later this year. I hope.
Keith
Déjà Vu is not a prediction

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Re: Representing a Safe Withdrawal Rate
Thank you all for the links. But it's frustrating. Just when you think you've got the SWR answer you need to live like you want to live as long as you can.
They update the numbers and you start over.
I guess it's a nice piece of information to know before you go off on that world cruise in first class.
ObliviousInvestor wrote:Figure 4 from this article of Wade's looks relevant.
http://wpfau.blogspot.com/2011/08/safe ... life.html
Of course, there's always the question of how closely the assumptions he uses (e.g., 40% stock allocation, MC simulations using historical return data from 19262010) match the assumptions you'd prefer to use.
They update the numbers and you start over.
Bob wrote:A 2013 analysis by Prof. Pfau et al titled "Asset Valuations and Safe Portfolio Withdrawal Rates" discusses SWR levels given the impact of the current , low ratesofreturn for equities and bonds and it is downloadable from:
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2286146
Not exactly the charting you have outlined, but Figure 7 on page 12 plots the probability of success versus the number of horizon years for various SWR rates (from 1% to 6%) at a 40% equity level Then their Table 3 on page 13 they provide numeric data that might be plotted as points along a curve for a few different Equity levels: at 20%, 40%, 60% and 80%.
I guess it's a nice piece of information to know before you go off on that world cruise in first class.
"Everything will be all right in the end. If everything is not all right, then it is not the end."  The Best Exotic Marigold Hotel
Re: Representing a Safe Withdrawal Rate
Bob wrote:A 2013 analysis by Prof. Pfau et al titled "Asset Valuations and Safe Portfolio Withdrawal Rates" discusses SWR levels given the impact of the current , low ratesofreturn for equities and bonds and it is downloadable from:
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2286146
Not exactly the charting you have outlined, but Figure 7 on page 12 plots the probability of success versus the number of horizon years for various SWR rates (from 1% to 6%) at a 40% equity level Then their Table 3 on page 13 they provide numeric data that might be plotted as points along a curve for a few different Equity levels: at 20%, 40%, 60% and 80%.
Bob,
I replotted Figure 7 and the result is what I suggested in the OP. The curves are hyperbolas.
If nothing else, Figure 7 allows you to contemplate the effect of high expense ratios or an AUM fee of, say, 1%. If you add that to a "safe" withdrawal rate, your goose may well be cooked.
I intend to reevaluate my withdrawal rate every year, as though it were the first year.
Keith
Déjà Vu is not a prediction
Re: Representing a Safe Withdrawal Rate
umfundi,
That's a good idea for a figure!
I've written up a blog post to answer your question about what such a figure might look like:
http://wpfau.blogspot.com/2013/07/theb ... ource.html
If someone would like to resize the images so they can be posted in the thread, it's alright with me. I'm just not patient enough to doit.
Wade
That's a good idea for a figure!
I've written up a blog post to answer your question about what such a figure might look like:
http://wpfau.blogspot.com/2013/07/theb ... ource.html
If someone would like to resize the images so they can be posted in the thread, it's alright with me. I'm just not patient enough to doit.
Wade
Re: Representing a Safe Withdrawal Rate
wade wrote:umfundi,
That's a good idea for a figure!
I've written up a blog post to answer your question about what such a figure might look like:
http://wpfau.blogspot.com/2013/07/theb ... ource.html
If someone would like to resize the images so they can be posted in the thread, it's alright with me. I'm just not patient enough to doit.
Wade
Wade, I thank you for all your helpful information. It's a super valuable resource to me and no doubt many others on the list!
Personally I find your longevitybased portfolio survival figures to be particularly useful. It seems that there's a dearth of information like that and only looking at years of retirement in isolation from life expectancy I think focuses people on an incorrect and overlyconservative probability of portfolio failure, as most of us don't like to think about our mortality. But at the same time we don't want to defer consumption or work longer than necessary during the years that we do have to live so I think the message is important that it does make sense to factor longevity into the decumulation equation.
For folks who have a SS benefits baseline then it is even more feasible to be a bit more aggressive on withdrawals. Your 2011 paper shows a 65yearold male can take 5% with a 90% chance of not running out. If that 10% contingency would leave someone destitute that's one thing but if it would leave them with a reduced but still viable income from SS benefits then that's quite another. I for one might prefer to take that 10% chance in order to have a bit more fun in the good years that are left vs. selling the boat now and living on 3%.
Re: Representing a Safe Withdrawal Rate
wade wrote:umfundi,
That's a good idea for a figure!
I've written up a blog post to answer your question about what such a figure might look like:
http://wpfau.blogspot.com/2013/07/theb ... ource.html
If someone would like to resize the images so they can be posted in the thread, it's alright with me. I'm just not patient enough to doit.
Wade
Wade,
Thank you so much, both for the figures and your discussion.
Best wishes,
Keith
Déjà Vu is not a prediction
Re: Representing a Safe Withdrawal Rate
Wade's site has some of the clearest thinking on retirement that I have encountered by a variety of thinkers.
The article on longevity risk aversion discusses an issue that has puzzled me, why not factor in SS and definedbenefit plans and consider higher withdrawals earlier in retirement for nonrecurring expenses such as travel while keeping your base budget modest? The sacrificing and saving to retirement followed by delayed collection of SS and people now talking about withdraw rates below 3% seems like an addiction to sacrifice rather than sound life planning.
At any rate, the site has many worthwhile points to consider, thank you for the links.
The article on longevity risk aversion discusses an issue that has puzzled me, why not factor in SS and definedbenefit plans and consider higher withdrawals earlier in retirement for nonrecurring expenses such as travel while keeping your base budget modest? The sacrificing and saving to retirement followed by delayed collection of SS and people now talking about withdraw rates below 3% seems like an addiction to sacrifice rather than sound life planning.
At any rate, the site has many worthwhile points to consider, thank you for the links.
I own the next hot stock VTSAX
Re: Representing a Safe Withdrawal Rate
wade wrote:If someone would like to resize the images so they can be posted in the thread, it's alright with me. I'm just not patient enough to doit.
Wade
Wade,
I am not sure what you mean by "resize", but posting a link to display a figure already on the web is very easy:
Rightclick on the image. Choose"Copy image location".
Start to post a new message. Click on the "Img" button. Paste the image location between the IMG tags in your message.
If you "Quote" my message (the one with the image") you will see the BBCode that does this.
Keith
Déjà Vu is not a prediction
Re: Representing a Safe Withdrawal Rate
Wade, your studies are super and thank you for sharing them with us.
Two questions for clarification, if possible.
1) In Table 3 of your 2013 study "Asset Valuations and Safe Portfolio Withdrawal Rates" a 30 year horizon at a 90% Probability of Success a 20% Equity Allocation has a higher level of SWR than a 40% Equity Allocation (3.0% vs. 2.8%). This is the opposite trend compared to most prior SWR studies where success rises for greater Equity Allocations in this range. Is this correct? Is this due the lower future Equity returns that a CAPE ratio of 22 would imply? (I remember your analysis of SWR for multiple different countries  although I can not find it now and imagine this is same issue where SWR levels and success results are sensitive to the Equity returns of different markets; yes?)
2) In Figure 1 (in this thread above and in your blog) is the chart data supposed to be essentially equal to Table 3 in your study: " Asset Valuations and Safe Portfolio Withdrawal Rates"? In the Figure a 40% Equity Allocation, 30 year horizon and 90% prob of success has an SWR of 3.2%, but in Table 3 of the study it is 2.8%. Am I associating the chart with the wrong source data?
Two questions for clarification, if possible.
1) In Table 3 of your 2013 study "Asset Valuations and Safe Portfolio Withdrawal Rates" a 30 year horizon at a 90% Probability of Success a 20% Equity Allocation has a higher level of SWR than a 40% Equity Allocation (3.0% vs. 2.8%). This is the opposite trend compared to most prior SWR studies where success rises for greater Equity Allocations in this range. Is this correct? Is this due the lower future Equity returns that a CAPE ratio of 22 would imply? (I remember your analysis of SWR for multiple different countries  although I can not find it now and imagine this is same issue where SWR levels and success results are sensitive to the Equity returns of different markets; yes?)
2) In Figure 1 (in this thread above and in your blog) is the chart data supposed to be essentially equal to Table 3 in your study: " Asset Valuations and Safe Portfolio Withdrawal Rates"? In the Figure a 40% Equity Allocation, 30 year horizon and 90% prob of success has an SWR of 3.2%, but in Table 3 of the study it is 2.8%. Am I associating the chart with the wrong source data?
Last edited by Bob on Sat Jul 20, 2013 7:12 am, edited 1 time in total.
Re: Representing a Safe Withdrawal Rate
Thanks all for the nice comments.
Keith, I'm glad to see it is easy to include images again. There was a time when it was necessary to create smaller images, as the software here wouldn't do that automatic resizing.
Bob: The data is different for those two articles. For the figures here, the same assumptions are kept throughout retirement. For that newer article, the average market returns fluctuate over time as they center around what is implied by the evolving bond yields and market valuation levels. That other one is more complicated in this regard. I would like to work through the math behind that other article again to make sure it all works out okay, as I think the main benefit of those assumptions would be to allow for the testing of bucket type strategies where some fixed income assets are held to maturity. We need a good way to simulate bond yields for that. That other article also included a 0.5% fee, and it is important to note that I made these figures without any fee. A 0.5% fee should knock about 0.20.3% from the withdrawal rates seen above.
This is the article about the international comparisons:
http://www.fpanet.org/journal/CurrentIs ... awalRates/
Wade
Keith, I'm glad to see it is easy to include images again. There was a time when it was necessary to create smaller images, as the software here wouldn't do that automatic resizing.
Bob: The data is different for those two articles. For the figures here, the same assumptions are kept throughout retirement. For that newer article, the average market returns fluctuate over time as they center around what is implied by the evolving bond yields and market valuation levels. That other one is more complicated in this regard. I would like to work through the math behind that other article again to make sure it all works out okay, as I think the main benefit of those assumptions would be to allow for the testing of bucket type strategies where some fixed income assets are held to maturity. We need a good way to simulate bond yields for that. That other article also included a 0.5% fee, and it is important to note that I made these figures without any fee. A 0.5% fee should knock about 0.20.3% from the withdrawal rates seen above.
This is the article about the international comparisons:
http://www.fpanet.org/journal/CurrentIs ... awalRates/
Wade
Re: Representing a Safe Withdrawal Rate
Wade, thank you very much for the clarifications. Look forward to reading more of your work. It is really excellent.
Re: Representing a Safe Withdrawal Rate
Wade, thank you for the link to your 2010 paper on SWRs in various country markets. I always felt the implications of Figure 2 were huge, under appreciated and definitely merit deeper study  especially in terms of both retirement investor expectations and investors' portfolio construction across global markets.
Source: "An International Perspective on Safe Withdrawal Rates: The Demise of the 4 Percent Rule?", Wade D. Pfau, Ph.D., 2010.
Source: "An International Perspective on Safe Withdrawal Rates: The Demise of the 4 Percent Rule?", Wade D. Pfau, Ph.D., 2010.
Re: Representing a Safe Withdrawal Rate
Bob wrote:A 2013 analysis by Prof. Pfau et al titled "Asset Valuations and Safe Portfolio Withdrawal Rates" discusses SWR levels given the impact of the current , low ratesofreturn for equities and bonds and it is downloadable from:
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2286146
Not exactly the charting you have outlined, but Figure 7 on page 12 plots the probability of success versus the number of horizon years for various SWR rates (from 1% to 6%) at a 40% equity level Then their Table 3 on page 13 they provide numeric data that might be plotted as points along a curve for a few different Equity levels: at 20%, 40%, 60% and 80%.
Excellent study for today's markets. I am puzzled by Table 13 results or I am not interpreting correctly. Does Initial Withdrawal Rates decreases with the increases in the equity allocations? This seems to be counter intuitive to me. Is this because higher CAPE is more penalizing than lower bond yields? Thx
Re: Representing a Safe Withdrawal Rate
[/quote]Ranger wrote:
Excellent study for today's markets. I am puzzled by Table 13 results or I am not interpreting correctly. Does Initial Withdrawal Rates decreases with the increases in the equity allocations? This seems to be counter intuitive to me. Is this because higher CAPE is more penalizing than lower bond yields? Thx
I wonder if it's because of the higher volatility of the larger equity allocation....thus greater "sequence of return" effect.
1210
 CutThroat
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Re: Representing a Safe Withdrawal Rate
1210sda wrote:Ranger wrote:
Excellent study for today's markets. I am puzzled by Table 13 results or I am not interpreting correctly. Does Initial Withdrawal Rates decreases with the increases in the equity allocations? This seems to be counter intuitive to me. Is this because higher CAPE is more penalizing than lower bond yields? Thx
I wonder if it's because of the higher volatility of the larger equity allocation....thus greater "sequence of return" effect.
1210
Exactly the opposite of what the 'prostock, anti bond' folks will tell you.
Re: Representing a Safe Withdrawal Rate
A review of multiple other SWR analyses, including ones by Prof. Pfau, suggest the numbers 1210sda highlighted may be due to the unique bond and equity return levels assumed in the 2013 study. For instance, looking at the many markets (countries) which Prof Pfau assessed in another of his studies in 2010 (see Figure 2, above) all the different countries exhibited higher SWRs as Equity levels rose from 0% levels  with some country max SWR levels peaking at 2030% Equity and some country max SWRs peaking at higher Equity levels. So it will be interesting when Prof. Pfau rechecks he 2013 study equations to see if the result is due to some error or it is due to the expected return assumptions they used.
Also, it seem all these results imply that for people in the decumulation phase that Equity levels above 50% have not been shown to be economically justified. Perhaps they add risk but do not deliver any apparent, historic increase in SWR.
Also, it seem all these results imply that for people in the decumulation phase that Equity levels above 50% have not been shown to be economically justified. Perhaps they add risk but do not deliver any apparent, historic increase in SWR.
Re: Representing a Safe Withdrawal Rate
1210sda:
As you are noting, the table does show a rapid plummeting in the withdrawal rate as the stock allocation increases.
This is happening because the high market valuation level triggers lower future stock returns.
Nonetheless, this new article shouldn't be taken as the last word on the subject. It will be nice to have better Monte Carlo simulations which dynamically adjust the average stock and bond returns over time in response to evolving market valuation levels and bond yields. It remains to be seen whether someone else might come up with a better way to do this, and whether these results will still hold up.
As you are noting, the table does show a rapid plummeting in the withdrawal rate as the stock allocation increases.
This is happening because the high market valuation level triggers lower future stock returns.
Nonetheless, this new article shouldn't be taken as the last word on the subject. It will be nice to have better Monte Carlo simulations which dynamically adjust the average stock and bond returns over time in response to evolving market valuation levels and bond yields. It remains to be seen whether someone else might come up with a better way to do this, and whether these results will still hold up.
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