### Author Topic: Historical odds of getting "bumped" into a lower WR?  (Read 11603 times)

#### brooklynguy

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##### Historical odds of getting "bumped" into a lower WR?
« on: April 14, 2015, 10:20:11 AM »
Last week, arebelspy posed an interesting question:  if you follow the traditional 4% WR spending plan (i.e., constant inflation-adjusted withdrawals in an amount equal to 4% of your portfolio at the beginning of the retirement period), what are the odds that you will end up at some point using a specified lower withdrawal rate (3%, in Rebs' formulation of the question)?

The question was posed here, but did not gain much traction.  I'm curious if anyone has any good ideas for a method of determining the answer.  (The question is somewhat related to the question of determining the historical likelihood of breaching the "Oh Shit Percentage," discussed in this thread.)

I'm breaking this out in into a new thread since it's not really relevant to the topic of the original thread and hopefully will generate more discussion as a stand-alone topic.  Here is the (relatively brief) full text of each of the relevant posts from the other thread:

This AI article is also blowing my mind, and has me evaluating just how linearly my thinking is. To link this back to early retirement, for planning purposes I generally guess that I'll live to be between 85-95 because that's what I see in my family tree plus 5-10% extra due to medical science magic.

But if something truly disruptive happens that allows us to regularly live to 100-150, all of my planning and Trinity study reading goes out the window. What's the safe withdrawal rate for a 100 year retirement?

3% should last fairly indefinitely.  And if you start with a 4%, you'll very likely be under 3% at some point.  (Actually, I wonder if someone could calculate the odds on that).

But then you run into Berstein's "any success rate > 80% is basically meaningless" point.

With that much upheaval, does money even matter?  Who knows.  You may still be thinking too linearly.

And if you start with a 4%, you'll very likely be under 3% at some point.  (Actually, I wonder if someone could calculate the odds on that).

I was thinking we could figure this out by using cFIREsim's "Retire Again & Again" spending plan as a crude tool, by setting the "Threshold for Spending Increase" to 33.33% (which is how much your portfolio would have to rise in order to bump you from a 4% WR to a 3% WR, all calculated in inflation-adjusted terms), and then counting how many lines in the graph get a spending bump at some point in their trajectory out of the total number of lines.

But I just did this (using cFIREsim's default settings for everything else), and it looks like only 1 out of 115 cycles got a spending bump.  The answer can't be that the historical odds of going from a 4% WR to a 3% WR are only 1/115.  I'm not sure if this is due to a flaw in my methodology, or a defect in cFIREsim (we already know that cFIREsim's "Retire Again & Again" calculation doesn't seem to be working properly, because it only ever generates one spending bump instead of ratcheting up every time the threshold is crossed, as discussed in this thread).

my knowledge of cFIRESim is not great as I've only used it a few times. But doesn't it do simulations based on real world data from the past? If that's the case, there are not going to be many test cases that can be run realistically with a 100 year timeframe.

The cFIREsim run above was testing for the number of historical cases that went from 4% to 3% in a 30-year period, and it gives the same answer for longer periods (which makes sense, since it's reporting only a single historical case where this happened).  But I believe that answer must be wrong, so there must be a flaw either in the approach I'm using to answer the question or in cFIREsim itself.

#### BarkyardBQ

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #1 on: April 14, 2015, 10:45:50 AM »
Can I request that however we figure out this calculation we also figure out the likelihood of a 3% going to a 2%, and at what rate these bumps happen. Are they more likely, or happen sooner if you start with a <4% WR; will you get to 3% in X time and 2% in half that time? I may not understand this correctly or the math behind it, but it seems like if you experience this bump, the ROR over a given retirement would speed up to reducing your WR. It also seems likely that if inflation is <3% over that term and growth is >7% that this would affect your WR rate as well. Now I may be shooting blind here with lack of knowledge, but, if we know historical returns cannot determine future returns, and we figure this out, it seems like we could determine a starting WR rate, and use an estimated growth rate to improve the success of a retirement beyond 7-4=OK.

ie. If growth over the next 30 years is only 6% and we start with a 3.2% WR and inflation X, and the bump happens at Y; how likely is the WR to drop at what periods?
« Last Edit: April 14, 2015, 10:50:18 AM by zdravé »

#### forummm

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #2 on: April 14, 2015, 11:07:36 AM »
I don't know that this question can really be answered. All the cFIREsim style analysis is based on historical market performance. You know, when people can't live forever, and robots don't rule the world. It's really not possible to come up with any reasonably precise answer given a completely different society we might live in. The economy could be completely different.

#### brooklynguy

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #3 on: April 14, 2015, 11:21:14 AM »
I don't know that this question can really be answered. All the cFIREsim style analysis is based on historical market performance. You know, when people can't live forever, and robots don't rule the world. It's really not possible to come up with any reasonably precise answer given a completely different society we might live in. The economy could be completely different.

The question is what the odds would have been historically, which is informative but not necessarily predictive of the future (just like the historical odds of portfolio success or failure examined by SWR research).

#### velocistar237

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #4 on: April 14, 2015, 11:24:35 AM »
Run a scenario and download the graph data. Look at it and figure out how many traces reach whatever new withdrawal rate you're interested in. Divide by the number of traces.

#### brooklynguy

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #5 on: April 14, 2015, 12:03:54 PM »
Run a scenario and download the graph data. Look at it and figure out how many traces reach whatever new withdrawal rate you're interested in. Divide by the number of traces.

Yeah, I thought of that too -- basically a more labor-intensive manual version of what I tried to do with the Retire Again & Again method -- but cFIREsim won't let me download the graph and I can't make heads or tails out of the mess of lines when viewing on-screen (even after using the click-zoom feature).

#### skyrefuge

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #6 on: April 14, 2015, 12:59:55 PM »
So yeah, another way of phrasing what you're looking for is "what percentage of cycles contain a year in which your balance is 33% greater than your initial balance?", right?

I'll never pooh-pooh pursuit of knowledge-for-knowledge's-sake, but is there any particular insight you hope to gain from this knowledge? Would it tell you anything more insightful than looking at the average ending value or median ending value does? In my mind, all of those answers would simply be an attempt to quantify "how many cycles are wildly successful?" by distilling a graph into a single number. If that's the goal, then I think this is a case where simply eyeballing the graph is a lot more informative than any single number would be (since a cycle getting "bumped" to 3%, while less-likely to result in failure, isn't any special guarantee against failure).

cFIREsim already has the opposite of this task built-in to its results page in its "Dip Analysis". It shows how many cycles dropped 20% or 40% below the initial value ("bumping" you to a 5% or 6.67% WR, respectively), and while it's nice to have that information, I haven't found tons of use for it, and when I have, it's only because it shows a whole range of dip-thresholds, so you can get a feel for how often a "dip to X, but stops before it reaches Y" occurs.

#### iamlindoro

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #7 on: April 14, 2015, 01:12:20 PM »
A somewhat tangential point to the original discussion, but for those worried about either increases or decreases in SWR, the Roth ladder is actually an interesting tool to effectively "see the future."  Since you're always rolling over the expenditure of five years from now, you are cushioned from the effects of drastic changes up or down by five years, and can essentially increase or decrease your spending in the years leading up to the seasoning being complete to compensate.

Let's say the market completely crashes and you decide that you can only safely pull out 20K when you expected to pull out 30K.  You may now have:

T-1: 30K
T-2: 30K
T-3: 30K
T-4: 30K
T-5: 20K

Now you could easily plan to spend \$28K per year for the next four years and never experience more than a slight bump.  The inverse applies as well, I suppose, reserves permitting.

#### brooklynguy

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #8 on: April 14, 2015, 01:27:20 PM »
I'll never pooh-pooh pursuit of knowledge-for-knowledge's-sake, but is there any particular insight you hope to gain from this knowledge? Would it tell you anything more insightful than looking at the average ending value or median ending value does? In my mind, all of those answers would simply be an attempt to quantify "how many cycles are wildly successful?" by distilling a graph into a single number. If that's the goal, then I think this is a case where simply eyeballing the graph is a lot more informative than any single number would be (since a cycle getting "bumped" to 3%, while less-likely to result in failure, isn't any special guarantee against failure).

Why you gotta be so reasonable?

I suppose you're right; there probably isn't really any additional insight to be gained beyond what the existing cFIREsim results already tell you.  I guess the only use for this information would be something like the opposite of the Oh Shit Percentage breach rate that we were looking for in one of the threads linked to above -- if you wanted use a bump to an X% WR as a proxy for the then-applicable historical success rate that will serve as your trigger for allowing you to going hog-wild with your spending (the "Hell Yeah Percentage"?), it would be interesting to know the historical likelihood of having crossed the Hell Yeah Percentage.  But your point is well taken -- this entire exercise is really just indulging our (my) desire for assurances of certainty in an uncertain world and is piling false precision on top of false precision.

#### forummm

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #9 on: April 14, 2015, 01:27:54 PM »
I don't know that this question can really be answered. All the cFIREsim style analysis is based on historical market performance. You know, when people can't live forever, and robots don't rule the world. It's really not possible to come up with any reasonably precise answer given a completely different society we might live in. The economy could be completely different.

The question is what the odds would have been historically, which is informative but not necessarily predictive of the future (just like the historical odds of portfolio success or failure examined by SWR research).

Again, I think using historical data is inherently flawed for this. If you come up with a number, you don't really have any great security in your 100 year retirement because the economy will change with all the old people hanging around and not dying. It could be great for stocks or terrible. Who knows. But if you really want to use historical data you can just do a monte carlo simulation for whatever time period you want. 1000 years even. Use any historical period's total return and volatility for your desired asset classes.

A somewhat tangential point to the original discussion, but for those worried about either increases or decreases in SWR, the Roth ladder is actually an interesting tool to effectively "see the future."  Since you're always rolling over the expenditure of five years from now, you are cushioned from the effects of drastic changes up or down by five years, and can essentially increase or decrease your spending in the years leading up to the seasoning being complete to compensate.

Let's say the market completely crashes and you decide that you can only safely pull out 20K when you expected to pull out 30K.  You may now have:

T-1: 30K
T-2: 30K
T-3: 30K
T-4: 30K
T-5: 20K

Now you could easily plan to spend \$28K per year for the next four years and never experience more than a slight bump.  The inverse applies as well, I suppose, reserves permitting.

Actually, you'd want to do the opposite. When the market crashes, you'd want to pull out at least the same amount you were pulling out before (if not more), because then you're paying taxes on a much smaller amount of money. Since you're just immediately buying the same assets you are selling, you benefit from the increases in your after-tax account. You can leave them in your Roth for as long as you want after the conversion.

#### brooklynguy

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #10 on: April 14, 2015, 01:34:29 PM »
Since you're always rolling over the expenditure of five years from now, you are cushioned from the effects of drastic changes up or down by five years, and can essentially increase or decrease your spending in the years leading up to the seasoning being complete to compensate.

Why are you cushioned from market changes?  It sounds like what you are describing is moving your tIRA funds into cash (rather than staying invested in the market) at the time of the rollover, in which case what you are describing really has nothing to do with the Roth conversion ladder but is just a cash buffer strategy (which does provide the cushioning effect you describe but also acts as a drag on your overall portfolio performance).

#### brooklynguy

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #11 on: April 14, 2015, 01:41:02 PM »
Again, I think using historical data is inherently flawed for this. If you come up with a number, you don't really have any great security in your 100 year retirement because the economy will change with all the old people hanging around and not dying. It could be great for stocks or terrible. Who knows. But if you really want to use historical data you can just do a monte carlo simulation for whatever time period you want. 1000 years even. Use any historical period's total return and volatility for your desired asset classes.

Yes, but this is all equally true of history-based SWR research and analysis in general.  I wasn't interested in the question specifically for purposes of predicting success rates for ultra-long retirements, that just happens to be the context in which arebelspy originally posed the question.  But then again, per my response to skyrefuge, I don't really know why I was so interested in answering the question :)

#### velocistar237

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #12 on: April 14, 2015, 01:44:28 PM »
I was thinking we could figure this out by using cFIREsim's "Retire Again & Again" spending plan as a crude tool, by setting the "Threshold for Spending Increase" to 33.33% (which is how much your portfolio would have to rise in order to bump you from a 4% WR to a 3% WR, all calculated in inflation-adjusted terms), and then counting how many lines in the graph get a spending bump at some point in their trajectory out of the total number of lines.

That's the right approach, but it looks like cFIREsim only tests the threshold in the first year of any time sequence. I messaged bo_knows about the bug.

I couldn't figure out any other way of doing the analysis with cFIREsim.

FIREcalc lets you download some data, but only for 30 year cycles. Go to the Investigate tab and check the box. For an initial 4% withdrawal rate, only 6 cases out of 114 failed in 30 years, and all but 13 cases reached a 3% withdrawal rate at some point, though many of those cases rose back above the 3% withdrawal rate.

I'll never pooh-pooh pursuit of knowledge-for-knowledge's-sake, but is there any particular insight you hope to gain from this knowledge?

Lots of people get OMY syndrome and hold out for a lower withdrawal rate. If a high percentage of cases get you there anyway, then it's more encouragement to be less conservative and avoid a couple extra years of working.

#### iamlindoro

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #13 on: April 14, 2015, 01:45:18 PM »
Since you're always rolling over the expenditure of five years from now, you are cushioned from the effects of drastic changes up or down by five years, and can essentially increase or decrease your spending in the years leading up to the seasoning being complete to compensate.

Why are you cushioned from market changes?  It sounds like what you are describing is moving your tIRA funds into cash (rather than staying invested in the market) at the time of the rollover, in which case what you are describing really has nothing to do with the Roth conversion ladder but is just a cash buffer strategy (which does provide the cushioning effect you describe but also acts as a drag on your overall portfolio performance).

You're right, in my head I was treating the rolled over money as a static asset.  Oh well, move along. ;)

#### Indexer

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #14 on: April 14, 2015, 04:02:27 PM »
I don't have time to play with it right now, but I had an idea that someone else might want to try.

In cFiresim each test run is assumed to 'fail' if the dollar amount left is under 0 at the end(I'll call it age 100 for simplicity) and then it tells you what % of the tests passed VS failed.  Take a 4% WR add inflation till age 100 and see what \$ amount you would withdraw at age 100, and now do the same thing for 3%.   Subtract the yr 100 3% number from the yr 100 4% number.  This gives the difference you would still have in year 100 if you only w/d 3% instead of 4% in that year.  Now run a full simulation at 4% WR and plug in that number as the fail number instead of using 0.  That should give you what % of the simulations run at 4% are under 3% by age 100.  If you want to know the number at age 90... I think you get the idea.  ;)

EDIT:  Refined my tought some.  For a year prior to the final year you would need to figure out what total \$ amount would represent a 3% SWR instead of a 4% at those different points in time(year 10, year 15, etc.) and test just those numbers in those years.
« Last Edit: April 14, 2015, 04:19:43 PM by Indexer »

#### brooklynguy

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #15 on: April 14, 2015, 07:47:04 PM »
I don't have time to play with it right now, but I had an idea that someone else might want to try.

In cFiresim each test run is assumed to 'fail' if the dollar amount left is under 0 at the end(I'll call it age 100 for simplicity) and then it tells you what % of the tests passed VS failed.  Take a 4% WR add inflation till age 100 and see what \$ amount you would withdraw at age 100, and now do the same thing for 3%.   Subtract the yr 100 3% number from the yr 100 4% number.  This gives the difference you would still have in year 100 if you only w/d 3% instead of 4% in that year.  Now run a full simulation at 4% WR and plug in that number as the fail number instead of using 0.  That should give you what % of the simulations run at 4% are under 3% by age 100.  If you want to know the number at age 90... I think you get the idea.  ;)

EDIT:  Refined my tought some.  For a year prior to the final year you would need to figure out what total \$ amount would represent a 3% SWR instead of a 4% at those different points in time(year 10, year 15, etc.) and test just those numbers in those years.

I'm not sure I followed what you said.  I can see at least two different ways of reading your proposal, but neither of them make sense.

One is to use the difference in the average portfolio ending values of a 4% spending plan and a 3% spending plan as your "failure" trigger.  But since that difference is itself over a million dollars (using all of cFIREsim's default parameters), that will result in a 100% failure rate.

The other is to use the difference in the actual withdrawal amounts between a 4% spending plan and a 3% spending plan.  But the difference between those amounts will remain constant (on an inflation-adjusted basis, which is how cFIREsim reports everything) -- it's always going to be \$10k (the difference between \$40k and \$30k).

In any event, neither of these approaches would be relevant for answering the question of how historically likely it was for someone using a 4% withdrawal plan to see their portfolio grow to 133.33% of its original value at some point during their retirement (which is the question we were trying to answer).

Did I misunderstand what you proposed?

#### Indexer

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #16 on: April 14, 2015, 08:50:09 PM »
Yes I was referring to the difference in the withdrawal amounts, but take inflation into account.  I remember now that cFiresim uses real returns and doesn't adjust expenses for inflation.  The tools I normally use to do this sort of thing report income, expenses, and returns with inflation included.  It really doesn't matter now.  I misunderstood what you were getting at.

Anyway if the goal is to see if the portfolio grows to 133% that is pretty easy to figure as well.  If you start with 1 million just add in an extraordinary expense for 1.33 million at different times and then set the end year right after(if you do it in the same year nothing happens).  This will tell you how many portfolios had over 1.33 million at that time because all other portfolios will fail.  Right now I do have time so I ran it.  Using the default settings in cFiresim of 75/25, portfolio value of 1 million, spending of 40k, etc.  Here are the results.

After 10 years:  37.31% of portfolios survived a 1.33 million drop in year 10.
After 15 years:  44.96% of portfolios survived a 1.33 million drop in year 15.
After 20 years:  52.42% of portfolios survived a 1.33 million drop in year 20.
After 25 years:  52.10% of portfolios survived a 1.33 million drop in year 25.
After 30 years:  47.37% of portfolios survived a 1.33 million drop in year 30.

Looking at the data I can't decide if the % started to fall in the last 2 years because there were less time frames to test against(thanks to the length of the time frames) or because the portfolio was being depleted.
« Last Edit: April 14, 2015, 08:56:30 PM by Indexer »

#### arebelspy

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##### Re: Historical odds of getting &quot;bumped&quot; into a lower WR?
« Reply #17 on: April 14, 2015, 10:17:17 PM »

Thanks for starting it brooklynguy. :)

Re: cFIREsim bug, Bo is in the middle of moving right now, so cFIREsim fixes and improvements are on hold, but I'd imagine he'll take a look in a few weeks. :)

I'll never pooh-pooh pursuit of knowledge-for-knowledge's-sake, but is there any particular insight you hope to gain from this knowledge?

Lots of people get OMY syndrome and hold out for a lower withdrawal rate. If a high percentage of cases get you there anyway, then it's more encouragement to be less conservative and avoid a couple extra years of working.

Bingo. If I have doubts of the validity of the 4% rule for a long ER (since it was based around 30 years), but don't want to wait for 3%, this might make me feel better knowing that I may get to 3% after FIRE.  Of course then you have the problem of "if we're in an environment where 4% doesn't work, we probably are in an environment where your portfolio won't get you to 3% on its own."  And round and round we go.  Who's working on the accurate crystal ball app?
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#### TomTX

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##### Re: Historical odds of getting &quot;bumped&quot; into a lower WR?
« Reply #18 on: April 15, 2015, 05:41:09 AM »

Bingo. If I have doubts of the validity of the 4% rule for a long ER (since it was based around 30 years), but don't want to wait for 3%, this might make me feel better knowing that I may get to 3% after FIRE.  Of course then you have the problem of "if we're in an environment where 4% doesn't work, we probably are in an environment where your portfolio won't get you to 3% on its own."  And round and round we go.  Who's working on the accurate crystal ball app?

Vanguard's Monte Carlo simulator will run to 50 years.

#### velocistar237

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##### Re: Historical odds of getting &quot;bumped&quot; into a lower WR?
« Reply #19 on: April 15, 2015, 05:49:50 AM »
Bingo. If I have doubts of the validity of the 4% rule for a long ER (since it was based around 30 years), but don't want to wait for 3%, this might make me feel better knowing that I may get to 3% after FIRE.  Of course then you have the problem of "if we're in an environment where 4% doesn't work, we probably are in an environment where your portfolio won't get you to 3% on its own."  And round and round we go.  Who's working on the accurate crystal ball app?

Here is a pretty robust setup: If the stash dips below the original amount, adjusted for inflation, then work instead of drawing down the stash.

I'm sure there are other ways to factor in part-time work.

Corollary questions: Based on historical data, what are the statistics on how many years you would have to work, and how much each year? What happens at a withdrawal rate of 5%? What approaches minimize the average, maximum, or total amount of work going forward from the present, including what's left of your full-time career?

Who's working on the accurate crystal ball app?

Vanguard's Monte Carlo simulator will run to 50 years.

I couldn't find the check box options for nuclear war, total economic collapse, or alien invasion.

#### brooklynguy

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #20 on: April 15, 2015, 06:42:43 AM »
Bingo. If I have doubts of the validity of the 4% rule for a long ER (since it was based around 30 years), but don't want to wait for 3%, this might make me feel better knowing that I may get to 3% after FIRE.  Of course then you have the problem of "if we're in an environment where 4% doesn't work, we probably are in an environment where your portfolio won't get you to 3% on its own."  And round and round we go.  Who's working on the accurate crystal ball app?

It would really just be a mental trick to make you feel better, though.  If you already know the historical success rate, knowing the historical chances of being bumped to a lower WR doesn't change the overall historical odds of success.  Although, I suppose this could be a way of addressing the insufficient historical data problem -- there aren't enough super-long periods in the historical record to allow us to draw statistically significant conclusions, so it could be helpful to know the historical odds of ending up in a low WR situation at the end of shorter periods.  Still, like skyrefuge said, the portfolio ending value data and other info already given by cFIREsim probably already gets us to the same place.

Vanguard's Monte Carlo simulator will run to 50 years.

Monte Carlo simulators, in my view, are an inferior tool for predicting the future, because they ignore the correlation that exists in the real world between market performance and time periods.

Here is a pretty robust setup: If the stash dips below the original amount, adjusted for inflation, then work instead of drawing down the stash.

I'm sure there are other ways to factor in part-time work.

Corollary questions: Based on historical data, what are the statistics on how many years you would have to work, and how much each year? What happens at a withdrawal rate of 5%? What approaches minimize the average, maximum, or total amount of work going forward from the present, including what's left of your full-time career?

These are the kinds of questions we started asking in the "Oh Shit Percentage" thread.  We asked Bo if it would be possible to implement a feature in cFIREsim that lets it tell you the historical probability of encountering a likelihood of success below a specified threshold, and he said it may not be practical in the current iteration but maybe in the new cFIREsim he is working on.

#### brooklynguy

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #21 on: April 15, 2015, 11:30:07 AM »
Anyway if the goal is to see if the portfolio grows to 133% that is pretty easy to figure as well.  If you start with 1 million just add in an extraordinary expense for 1.33 million at different times and then set the end year right after(if you do it in the same year nothing happens).  This will tell you how many portfolios had over 1.33 million at that time because all other portfolios will fail.  Right now I do have time so I ran it.  Using the default settings in cFiresim of 75/25, portfolio value of 1 million, spending of 40k, etc.  Here are the results.

After 10 years:  37.31% of portfolios survived a 1.33 million drop in year 10.
After 15 years:  44.96% of portfolios survived a 1.33 million drop in year 15.
After 20 years:  52.42% of portfolios survived a 1.33 million drop in year 20.
After 25 years:  52.10% of portfolios survived a 1.33 million drop in year 25.
After 30 years:  47.37% of portfolios survived a 1.33 million drop in year 30.

Looking at the data I can't decide if the % started to fall in the last 2 years because there were less time frames to test against(thanks to the length of the time frames) or because the portfolio was being depleted.

This was a clever hack to approximate the answer.  For some reason when I try to replicate it I get slightly different results, though (whether I use 1.33M or 1.333333M for the one-time extraordinary expense).  For 30 years, using 1.333333M, I get a success rate of 48.7% (slightly above the 47.37% you reported).

Either way, it appears that historically a person retiring on a 4% WR (using cFIREsim's default parameters for asset allocation, etc.) got bumped to a 3% WR slightly over half of the time if their retirement period was at least 20 years long.

However, this answer doesn't seem to match up with an eyeball review of the cFIREsim output graph in a default simulation.  Although it's hard to tell from the jumble of lines, it looks to me as if significantly more than half of the cases crossed the 133.33% mark at some point during their trajectories, no?  Or maybe it's just that the density of lines converged around the \$1M mark is deceiving my eyes...

EDIT:  Actually I just realized that velocistar already said that the FIREcalc data gives us the answer (I must have been blinded by my bias in favor of cFIREsim), which is that 88.6% of cases (101/114) over a 30 year period hit the 3% WR mark.  So why the discrepancy between this answer and the one produced by Indexer's method?  I know FIREcalc and cFIREsim have some differences in their default parameters and underlying data, but I wouldn't think those are big enough to cause this kind of discrepancy.
« Last Edit: April 15, 2015, 11:37:15 AM by brooklynguy »

#### skyrefuge

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #22 on: April 15, 2015, 12:56:52 PM »
EDIT:  Actually I just realized that velocistar already said that the FIREcalc data gives us the answer (I must have been blinded by my bias in favor of cFIREsim), which is that 88.6% of cases (101/114) over a 30 year period hit the 3% WR mark.  So why the discrepancy between this answer and the one produced by Indexer's method?

They're two different things. Indexer's method looks at a snapshot in time to see if at that moment you're at a 3% (or lower) WR (so it's really not surprising that there's no real trend to be found in the 5-year sample points that he chose).  FIREcalc's method checks if you reached a 3% WR at any moment over a 30-year period.

So then it should be obvious why FIREcalc's numbers are much greater than Indexer's. I think the FIREcalc method is what you were originally looking for, but then Indexer's method highlights how arbitrary it is to focus on a 3% "bump", since that bump doesn't have any special stickiness; a one-time 3% WR may have easily fallen back to a 4% WR by the time you measure.

#### brooklynguy

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #23 on: April 15, 2015, 01:14:37 PM »
They're two different things. Indexer's method looks at a snapshot in time to see if at that moment you're at a 3% (or lower) WR (so it's really not surprising that there's no real trend to be found in the 5-year sample points that he chose).  FIREcalc's method checks if you reached a 3% WR at any moment over a 30-year period.

Yeah, I just assumed that Indexer's sampling was frequent enough to establish a relatively accurate trend (after all, cFIREsim's own sample size is only 5x greater, since it uses 1-year sample points--or am I wrong about that?  Does cFIREsim track intra-year market returns?), but guess not.

Quote
but then Indexer's method highlights how arbitrary it is to focus on a 3% "bump", since that bump doesn't have any special stickiness; a one-time 3% WR may have easily fallen back to a 4% WR by the time you measure.

Yeah, but that's kinda the point -- that's equally true of the WR at the commencement of retirement, hence velocistar's and arebelspy's point that the knowledge that a 4% WR will (based on history) very likely turn into a 3% WR can psychologically help people to pull the trigger.

#### skyrefuge

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #24 on: April 15, 2015, 02:27:25 PM »
Yeah, I just assumed that Indexer's sampling was frequent enough to establish a relatively accurate trend (after all, cFIREsim's own sample size is only 5x greater, since it uses 1-year sample points--or am I wrong about that?  Does cFIREsim track intra-year market returns?), but guess not.

Even if Indexer's method did establish a trend, it wouldn't be close to the FIRECalc number. Indexer's method is like asking "for each day in June, what is the chance of the temperature being 90F at 5pm in NYC?" There might be a trend there, with the answer linearly rising from 5% on June 1, to 10% on June 30, as the season gets warmer. But that 5-10% number would be nowhere near the answer for the FIRECalc question, which would be "for the entire month of June, what is the chance of the temperature being 90F at 5pm on at least one day?" That answer would be more like 80-90%, and would be related to Indexer's number by some probability function I've long-ago forgotten. Increasing the number of samples (measuring the temperature at every hour on every day) doesn't make those two different numbers converge.

Yeah, but that's kinda the point -- that's equally true of the WR at the commencement of retirement, hence velocistar's and arebelspy's point that the knowledge that a 4% WR will (based on history) very likely turn into a 3% WR can psychologically help people to pull the trigger.

From one of your previous posts, I got the feeling we kind of agree on this: playing a psychological trick (under the smokescreen of mathematical logic) to cure people of OMY syndrome may result in the correct "end", but I'm not super-comfortable with saying that end justifies those means. While such a trick might be convincing to people who have only a superficial knowledge of SWRs, it would be far better for them to understand the true nature of SWRs (e.g., the 4% SWR is already a pessimistic number because it is derived from the worst-performing year in history, not because your actual WR is likely to sometime fall below 4%). If I had a young kid, and that kid kept throwing iPhones on the ground, I might eventually resort to some story about a fat man in a red suit to get him to stop, but it certainly wouldn't be my first or preferred strategy.

So sure, you can tell someone "dude, don't wait 'til you have a 3% WR before retiring, because you can retire right now at 4% and there's still an 88.6% chance you'll automatically hit a 3% WR during retirement!"  Maybe that convinces him to stop being a wuss, but if he then digs deeper into the math and learns "wait...but now you're telling me that even if I do get lucky and hit that 3% WR in retirement, there's a 50% chance that I'll just fall back to a 4% WR?! brooklynguy is a fuckin' liar, I'm dooooomed!!"

#### arebelspy

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #25 on: April 15, 2015, 02:36:36 PM »
So sure, you can tell someone "dude, don't wait 'til you have a 3% WR before retiring, because you can retire right now at 4% and there's still an 88.6% chance you'll automatically hit a 3% WR during retirement!"  Maybe that convinces him to stop being a wuss, but if he then digs deeper into the math and learns "wait...but now you're telling me that even if I do get lucky and hit that 3% WR in retirement, there's a 50% chance that I'll just fall back to a 4% WR?!

It'd make me feel better, cause even if it "fell back," at least it's probably closer to 3 than 4% at that point.

The "fall forward" stats of how often you rise to a 5 or 6% WR scare me.  ;)

brooklynguy is a fuckin' liar, I'm dooooomed!!"

I am a former teacher who accumulated a bunch of real estate, retired at 29, spent some time traveling the world full time and am now settled with three kids.
If you want to know more about me, this Business Insider profile tells the story pretty well.
I (rarely) blog at AdventuringAlong.com. Check out the Now page to see what I'm up to currently.

#### brooklynguy

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #26 on: April 15, 2015, 03:35:35 PM »
Even if Indexer's method did establish a trend, it wouldn't be close to the FIRECalc number. Indexer's method is like asking "for each day in June, what is the chance of the temperature being 90F at 5pm in NYC?" There might be a trend there, with the answer linearly rising from 5% on June 1, to 10% on June 30, as the season gets warmer. But that 5-10% number would be nowhere near the answer for the FIRECalc question, which would be "for the entire month of June, what is the chance of the temperature being 90F at 5pm on at least one day?" That answer would be more like 80-90%, and would be related to Indexer's number by some probability function I've long-ago forgotten. Increasing the number of samples (measuring the temperature at every hour on every day) doesn't make those two different numbers converge.

Ah, yes, I see the logic error now.  In my mind I was conflating Indexer's approach with cFIREsim's normal characteristic of testing for "failure" at any point over the entirety of the period, but Indexer's method is forcing cFIREsim to test for the specific failure we are interested in only at specific snapshots in time (and, as you pointed out, even taking so many "snapshots" that they become a "moving picture" won't fix the flaw in this approach because it's answering the wrong question).

From one of your previous posts, I got the feeling we kind of agree on this: playing a psychological trick (under the smokescreen of mathematical logic) to cure people of OMY syndrome may result in the correct "end", but I'm not super-comfortable with saying that end justifies those means. While such a trick might be convincing to people who have only a superficial knowledge of SWRs, it would be far better for them to understand the true nature of SWRs (e.g., the 4% SWR is already a pessimistic number because it is derived from the worst-performing year in history, not because your actual WR is likely to sometime fall below 4%). If I had a young kid, and that kid kept throwing iPhones on the ground, I might eventually resort to some story about a fat man in a red suit to get him to stop, but it certainly wouldn't be my first or preferred strategy.

So sure, you can tell someone "dude, don't wait 'til you have a 3% WR before retiring, because you can retire right now at 4% and there's still an 88.6% chance you'll automatically hit a 3% WR during retirement!"  Maybe that convinces him to stop being a wuss, but if he then digs deeper into the math and learns "wait...but now you're telling me that even if I do get lucky and hit that 3% WR in retirement, there's a 50% chance that I'll just fall back to a 4% WR?! brooklynguy is a fuckin' liar, I'm dooooomed!!"

Yeah, we do agree on this:  it's merely a psychological trick.  But I also agree with velocistar and rebs that it can be helpful, since we are emotional, not-entirely-rational creatures.  I'm not viewing it as smoke and mirrors to fool the uninformed, but as a way of viewing the same thing from another angle that could be helpful in getting you over the psychological hump.  Personally, I get more mental comfort from the "93.04% historical success rate" metric than the "88.6% historical odds of being bumped into a 3% WR, which itself has a 100% historical success rate" metric, but I can see how someone could still find the latter psychologically comforting.

Also, as I said before, knowing the chances of hitting a lower WR during relatively-short periods (like 30-year periods) which have occurred relatively often in the historical record may have application towards addressing the problem of the lack of relatively few ultra-long periods (like 70-year periods) in the historical record.  Or maybe that would just be a flawed attempt to bootstrap statistically significant conclusions out of statistically insignificant data?  (Like I said before, I do realize that exercises like what we're doing in this thread are already piling false precision on top of false precision, but that still doesn't want to make me stop :-))

[awesome animated gif]

Wow, that may have been the coolest animated gif I've ever seen in the forum.  Was that Bullet Bill from Mario Bros.?

#### arebelspy

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #27 on: April 15, 2015, 03:46:52 PM »
Yeah, we do agree on this:  it's merely a psychological trick.  But I also agree with velocistar and rebs that it can be helpful, since we are emotional, not-entirely-rational creatures.  I'm not viewing it as smoke and mirrors to fool the uninformed, but as a way of viewing the same thing from another angle that could be helpful in getting you over the psychological hump.

Right.  I want to use it to help MYSELF get over irrational concerns, by seeing another view of how safe the 4% WR actually is.

Wow, that may have been the coolest animated gif I've ever seen in the forum.  Was that Bullet Bill from Mario Bros.?

I am a former teacher who accumulated a bunch of real estate, retired at 29, spent some time traveling the world full time and am now settled with three kids.
If you want to know more about me, this Business Insider profile tells the story pretty well.
I (rarely) blog at AdventuringAlong.com. Check out the Now page to see what I'm up to currently.

#### velocistar237

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #28 on: April 15, 2015, 08:18:49 PM »
It's true that someone might be encouraged by their initial 4% withdrawals turning into 3% withdrawals, but it's a bit of a convoluted explanation. MMM's post on the 4% rule was much more direct, showing that you don't need to reach 4% in most cases. Retiring right before the Great Depression would have only required a 5% withdrawal rate. For \$40K expenses, that's \$800K, about what MMM had when he quit full-time employment.

Another difficulty is that it ignores the difference between amassing 3% in a random year vs. reaching 3% after having amassed 4% in a random year. The latter case means that you're statistically in a favorable year, as opposed to the former case, where you're in a random year. All the information about reaching 3% in some year after starting at 4% is already contained in the fact that you start at 4%.

All this talk about withdrawal rate makes me want to shift mine up toward 5%.

#### arebelspy

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #29 on: April 15, 2015, 09:08:07 PM »
All this talk about withdrawal rate makes me want to shift mine up toward 5%.

Sol made some really good posts arguing for this during your time away from the forums.  Worth looking up, IMO.
I am a former teacher who accumulated a bunch of real estate, retired at 29, spent some time traveling the world full time and am now settled with three kids.
If you want to know more about me, this Business Insider profile tells the story pretty well.
I (rarely) blog at AdventuringAlong.com. Check out the Now page to see what I'm up to currently.

#### brooklynguy

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #30 on: April 16, 2015, 08:27:22 AM »
Another difficulty is that it ignores the difference between amassing 3% in a random year vs. reaching 3% after having amassed 4% in a random year. The latter case means that you're statistically in a favorable year, as opposed to the former case, where you're in a random year. All the information about reaching 3% in some year after starting at 4% is already contained in the fact that you start at 4%.

I'm not following what you meant by the bolded statement.  As long as you're ignoring valuation metrics or other market environment indicators (which is what cFIREsim-style history-based prediction always does), then there is no difference between amassing 3% in a random year and amassing 3% after having amassed 4% in a random year.  All years are randmon -- if you amass a portfolio equal to 33.33x your WR, your historical odds of success are what they are, period.  Unless you're talking about the odds of success for the remainder of the retirement period that commenced when you amassed 4% (rather than the odds of success of a new retirement period commencing the moment you amass 3%)?  Maybe that's what you meant by the information about reaching 3% after starting at 4% already being contained in the fact that you start at 4%?  If so, I agree, and I think that's another way of stating what we said above that this exercise is just another way of viewing the same thing from a different angle.

#### velocistar237

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #31 on: April 16, 2015, 08:37:52 AM »
All this talk about withdrawal rate makes me want to shift mine up toward 5%.

Sol made some really good posts arguing for this during your time away from the forums.  Worth looking up, IMO.

Like this post?

I hadn't tried that option, but wow, that does pretty well even with a higher initial withdrawal rate. Much reduced chance of asset runaway, though.

That thread in general is great. I like this:

Instead of trying to quantify the precision, apply a better algorithm derived from weapons engineering.  Shoot at the target as soon as you have it in range and can track a decent solution, then depend on mid-course guidance and terminal homing.

MMM says that after FI, these mid-course corrections keep getting easier.

#### velocistar237

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #32 on: April 16, 2015, 09:11:07 AM »
Another difficulty is that it ignores the difference between amassing 3% in a random year vs. reaching 3% after having amassed 4% in a random year. The latter case means that you're statistically in a favorable year, as opposed to the former case, where you're in a random year. All the information about reaching 3% in some year after starting at 4% is already contained in the fact that you start at 4%.

I'm not following what you meant by the bolded statement.  As long as you're ignoring valuation metrics or other market environment indicators (which is what cFIREsim-style history-based prediction always does), then there is no difference between amassing 3% in a random year and amassing 3% after having amassed 4% in a random year.  All years are randmon -- if you amass a portfolio equal to 33.33x your WR, your historical odds of success are what they are, period.

I think I see what you mean. Because the market is random, then what happens up to a certain point should be independent from what happens after that point, so how you get to 3% shouldn't matter. My gut disagrees with this. Take it to the extreme. If you start at 4% and then the market takes you to 1%, will your future returns be the same on average as starting at 1% in a random year? I guess I question whether the historical returns are actually independent. I'll look at the data sometime.

Unless you're talking about the odds of success for the remainder of the retirement period that commenced when you amassed 4% (rather than the odds of success of a new retirement period commencing the moment you amass 3%)?  Maybe that's what you meant by the information about reaching 3% after starting at 4% already being contained in the fact that you start at 4%?  If so, I agree, and I think that's another way of stating what we said above that this exercise is just another way of viewing the same thing from a different angle.

Right, the odds of success for starting at 4% are lower than from starting at 3%, and the fact that you're likely to reach 3% after starting at 4% doesn't change the initial starting success. If you do reach 3% after starting at 4%, then that's a good sign.

#### arebelspy

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #33 on: April 16, 2015, 10:17:16 AM »
All this talk about withdrawal rate makes me want to shift mine up toward 5%.

Sol made some really good posts arguing for this during your time away from the forums.  Worth looking up, IMO.

Like this post?

I hadn't tried that option, but wow, that does pretty well even with a higher initial withdrawal rate. Much reduced chance of asset runaway, though.

That thread in general is great. I like this:

Instead of trying to quantify the precision, apply a better algorithm derived from weapons engineering.  Shoot at the target as soon as you have it in range and can track a decent solution, then depend on mid-course guidance and terminal homing.

MMM says that after FI, these mid-course corrections keep getting easier.

Yup, like that, and also philosophical ones (about why we can shoot for a 50% success rate, not the 95% that 4% hits).
I am a former teacher who accumulated a bunch of real estate, retired at 29, spent some time traveling the world full time and am now settled with three kids.
If you want to know more about me, this Business Insider profile tells the story pretty well.
I (rarely) blog at AdventuringAlong.com. Check out the Now page to see what I'm up to currently.

#### brooklynguy

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #34 on: April 16, 2015, 10:31:07 AM »
I think I see what you mean. Because the market is random, then what happens up to a certain point should be independent from what happens after that point, so how you get to 3% shouldn't matter. My gut disagrees with this. Take it to the extreme. If you start at 4% and then the market takes you to 1%, will your future returns be the same on average as starting at 1% in a random year? I guess I question whether the historical returns are actually independent. I'll look at the data sometime.

Yes, but that's because when we use SWR-speak we're referring to the actual historical success rates of retiring in general -- that is, the total number of actual historical success cases divided by the total number of actual historical cases, without regard to market valuation levels or any other factor.  So, as of today, the "chances" of success (in that sense of the term) for someone starting their retirement in 1966 (the absolute worst time in history to commence a 30-year retirement and one of the few actual failure cases to have occurred for someone using a 4% WR) were exactly the same as the "chances" of someone retiring in in 1982 (a phenomenal year to start a 4%-WR-based 30-year retirement) -- namely, 93.04% (using cFIREsim's default parameters).  But in reality, because it is now 2015 and we have the benefit of hindsight, we know that the actual chances of success for the 1966 retiree were 0% and for the 1982 retiree were 100%.  This "problem" inherent in SWR-style prognostication about the chances of future retirement success is discussed in detail in the "Do cFIREsim and FIREcalc both lie?" thread you linked to.

We also know that there is some historical correlation between market-environment-indicators (like CAPE, for example, most recently discussed in this thread) and portfolio returns/success.  We all realize this, either explicitly or implicitly (like your gut is currently intuiting).  Our schizophrenia about simultaneously believing in the randomness of the market and the non-randomness of the market has been a bit of a recurring theme in the forums lately (see here, for example).  I think that is a major contributing factor behind our desire to obtain what could otherwise be described as absurd levels of safety in our retirement planning and our inclination towards OMY syndrome:  if we truly, honestly believed that our own odds of retirement success were north of 95%, as impervious to current market conditions as a spinning roulette wheel or a rolling pair of dice, even before factoring in any external levels of safety margin or flexibility to take corrective action, then would any of us have any hesitation whatsoever about pulling the FIRE trigger?

#### Doulos

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #35 on: April 16, 2015, 02:56:53 PM »
“Don’t store up treasures here on earth, where moths eat them and rust destroys them, and where thieves break in and steal.
Store your treasures in heaven, where moths and rust cannot destroy, and thieves do not break in and steal."

I am a 5%+ SWR kind of guy.
My security does not come from a pile of money in investments.

I would suggest this cFIREsim run for the kind of information you are looking for.
Set your 4% spending using constant % instead of a SWR.  750k and 4% for instance (that would be my 30k normal budget)
Set your inflation adjusted floor and ceiling (low and high), to whatever "Defined value" seems reasonable to you.  20k and 42k in my case for my broke and rich budgets.
Then run your numbers for 30 years.
I get 100%.

This says I could spend my 4% with Zero risk, which is of course a lie.

Looking at the graph gives you a solid idea of how much time you spend in the Broke budget and how much time you spend in the Rich budget.
In this case I get an average of \$36,034.14.  Well above the 4% SWR really at 4.8%.

#### brooklynguy

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #36 on: April 16, 2015, 03:22:12 PM »
I would suggest this cFIREsim run for the kind of information you are looking for.

Uh, not sure what "kind of information" you mean.  The information I was looking for was a method of determining the historical odds of getting bumped from X% to Y%, which your cFIREsim run does not do.

Quote
Set your 4% spending using constant % instead of a SWR.  750k and 4% for instance (that would be my 30k normal budget)
Set your inflation adjusted floor and ceiling (low and high), to whatever "Defined value" seems reasonable to you.  20k and 42k in my case for my broke and rich budgets.
Then run your numbers for 30 years.
I get 100%.

This says I could spend my 4% with Zero risk, which is of course a lie.

No, this says that every retiree in history who would have followed this approach would not have run out of money, which is not a lie.  I would also extrapolate this to mean that you have a very, very good chance of not running out of money in the future if you follow this approach.  This cFIREsim result is not surprising -- you are a using a fixed percentage variable withdrawal plan with quite a low floor (2.7% of the original portfolio value) and a not-crazy-high ceiling (5.6% of the original portfolio value), so of course it has staggeringly high historical success.

#### Doulos

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #37 on: April 16, 2015, 04:52:56 PM »
What does getting bumped from 4% to 3% mean to you?
To me it can mean multiple things.

SWR is always relative to your original number.  So it seems like you are asking how often do you get cases where you need to spend less later.  Like the sol & arebelspy conversation in the linked threads.  It is a matter of perspective.

Do you plan to spend less, then spend more when the market goes up?
Do you plan to spend more, then mitigate market drops with lower budgets?
Do you do both?

I am coming at this from this angle right here.  You budget is variable.  You plan for the good times and the bad.
Getting bumped into a lower withdraw rate is a "bad time" if you mean you are changing your budget to lower your withdraw rate; which is how this question sounds.
If you mean the opposite, your net worth changed giving you a fuzzy warm feeling that you are not doing anything about, that would be a 'good time'.

Are you thinking about 3% vs 4% over the course of the raiseing and falling market prices and values?  How do you know if that 30% gain you just got is real or crazy?

If you look at it that way, you are talking I started with \$1M now, and 40k spending.  Now I have \$1.33M.  That makes your current spending % 3% at that point.
That does not guarantee a success.  Getting the likelyhood of ever hitting the 1.33M does not really get you anywhere practical.

It seems that throughout this thread people are going in both directions as if they are both the question.

#### skyrefuge

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #38 on: April 16, 2015, 05:12:30 PM »
It seems that throughout this thread people are going in both directions as if they are both the question.

"Whoa, LOL, why are there naked people dancing around at this funeral?" --Lone Naked Man Dancing Around At A Funeral

As far as I can tell, you're the only one in this thread who interpreted the question to mean "what are the odds of me lowering my spending amount?" Yes, there was some ambiguity in the question, but everyone else understood brooklynguy's meaning. And it appears that you do now too (except that he wasn't looking for any kind of guarantee of success. Since, you know, he's not dumb.)

#### Doulos

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##### Re: Historical odds of getting "bumped" into a lower WR?
« Reply #39 on: April 16, 2015, 06:43:32 PM »
"Whoa, LOL, why are there naked people dancing around at this funeral?" --Lone Naked Man Dancing Around At A Funeral

Well, I have to admit.  If I have been partying too hard.
I do tend to be naked dancing guy.