### Author Topic: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)  (Read 28306 times)

#### SnackDog

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##### If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« on: March 24, 2015, 11:58:38 AM »
With wild market fluctuations the last few years, I keep thinking about the implications of a changing net investment vs SWR.  If one blindly locked in to 4% in 2009 and adjusted by inflation each year, they could really under spend over 30 years.  What I plan to do is watch the investments the first 5-10 years.  If 4% (or whatever you choose) of the current year investment is greater than the current year planned withdrawal (which would be initial SWR plus annual inflation adjustments), simply reset to 4% as if you had just retired this year.  You are good to go for 30 years at that rate.

Put it another way, anytime your investment grows to the point where the current year withdrawal amount is less than 4% of your investments, simply reset to 4% and year 0.

A work colleague of mine retired in 1995.  By 2005, he had spent about \$2MM (\$200K/year).  But he had more principle than he started with in 1995.  He was either under-spending or had amazing investment performance.  His CPA kept urging him to step up the spending, but he couldn't figure out how.  Haha.

Converse is not true. If the indices sink, historically you will survive without reducing below the 4% rate + annual inflation adjustments.

#### Eric

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #1 on: March 24, 2015, 12:21:40 PM »
Put it another way, anytime your investment grows to the point where the current year withdrawal amount is less than 4% of your investments, simply reset to 4% and year 0.

Isn't that just inviting extra sequence of return risk?

#### Exflyboy

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #2 on: March 24, 2015, 12:46:57 PM »
Your colleague couldn't figure out how to spend more than \$200k a year.. I think we have just hit on the ultimate first world problem..:)

#### Bob W

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #3 on: March 24, 2015, 01:01:30 PM »
One thing to consider is what inflation actually is.  There are at least 10 ways to measure it and the ones the Government uses such as the CPI are minimized.

So what is your personal inflation rate?   i.e. what do you spend money on?

Fixed mortgage --- no inflation there.  (if you don't have one, why not?  Great inflation hedge)
Insurance ---  yep how much did that go up on average the last 5 years for you?     (let's say \$200 month)
Utilities --  Hell water alone is running 10-20% in some areas.  What is your 5 year trend?   (lets say \$200 month)
Food -- A biggy for most folks.  I'm guessing our food inflation is in the 7-10% range.   (let's say \$400 month)
Cars/gas --- Maybe not so big for you and hard to predict?  (let's say \$300 month)
Travel and entertainment? --- totally flexible category

So your "let's say" category might be around 12K per year.   What is your core inflation there?

So yeah,  figure out your own inflation rate to make an accurate call on your SWR.   The hard part is predicting the future.  That is why a mortgage is so powerful a hedge.   Prices may quadruple on food in the next 30 years (likely) but my mortgage will remain the same at worst or go down with cash out at best.

Then on the income side consider if you are gambling in the market or investing in real estate.   You really have no idea what the market will do but you will have a pretty good idea that real estate will provide X amount per year and self adjust for inflation.

Then and lord don't forget the impact of Social Security.

I'm guessing for folks with over 2 million in assets most of this is not worth their time?

#### brooklynguy

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #4 on: March 24, 2015, 01:29:02 PM »
Isn't that just inviting extra sequence of return risk?

Exactly.  This proposal of setting a floor (but no ceiling) on withdrawals sounds like a great way to substantially increase the risk of portfolio failure.  Let's take it as given that the future will be no worse than the past and we can therefore use historical data as a perfect predictive tool for the future.  So using the standard 4% WR has a 95% chance of succeeding, if you stick with the 4% inflation-adjusted withdrawals for the entirety of the 30-year period.  But every time you reset your WR upwards by "marking it to market," you are starting a new plan with a higher than 5/100 chance of failing.  So you've taken your 95/100 odds of success and reduced them to something lower.  If cfiresim were working right now, we could see exactly what the historical success rate was for this plan, looking at it as a single 30-year period (rather than rolling continuous 30-year periods).

#### arebelspy

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #5 on: March 24, 2015, 02:03:56 PM »

Part of the reason why 4% worked is that sometimes the portfolio had grown before it hit the crash times, which let it survive (and only couldn't survive if it hit it too early).  If you constantly reset upwards, you're not letting it grow as it might need to in order to survive, increasing your odds of failure.

All in all though, the idea of continually monitoring and deciding if you need to cut spending or if you can raise it is a good idea for FIRE.  I just wouldn't set a rigid rule on either direction, but be flexible.
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#### SnackDog

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #6 on: March 24, 2015, 04:23:11 PM »
What several of you are suggesting is that if I retire today and start down my merry way at 4% and adjust the for inflation annually (I plan to just use CPI, since someone asked; I don't care what my personal inflation rate is since I can control it), I will make it 30 years.  However, if I reset at year 5, according to the logic I presented, I would have a reduced chance of making it the last 25 years, to say nothing of another 30.

At the same time, if my neighbor retired with the same net worth I had in year 5, he would be good to go at 4% from that day and he would not only make it my last 25 years, but another 5.

What you are missing is that 4% of any principle is enough to start at and will last 30 years, adjusted annually for inflation.  You can start or restart that 30 years and 4% any time you want.  The math is the same.  Under most scenarios, the inflation increases after a few years will have you needing more than the 4% so resetting would give you less, which is no good.

#### arebelspy

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #7 on: March 24, 2015, 04:40:29 PM »
What you are missing is that 4% of any principle is enough to start at and will last 30 years, adjusted annually for inflation.

No, what we are saying is that the reason why 4% works as often as it does (93% of the time) is that when the crash happens, often the portfolio has built up enough that your WR is actually below 4% by that point, even though you've adjusted for inflation, because it outgrew inflation, and that outgrowing allows it to last.

Let me make up numbers to illustrate the point.

Lets say a crash happens at year X.

If you FIRE one year before that (at X-1) at 4% WR, you probably won't make it the 30 years.  You'll be in the small handful of failure cases.  Ditto at X-2.  Maybe at X-3.. But maybe at X-4, X-5, etc. your portfolio has gained enough from those 4-5 years that when the crash happens at X, you last through it (in a way you wouldn't if you FIRE'd only 1 year before, at X-1).

But if you do your plan to reset every year, you're constantly risking a crash happening next.  Thus -- like Eric said -- you're increasing your sequence of returns risk.

There are failure cases with the 4% rule, and by constantly resetting and potentially inflating your spending to 4% (but never reducing), you're vastly increasing your chance of being a failure case, because no longer do you have to get past the first few years of FIRE, but you have to continually do it.
We are two former teachers who accumulated a bunch of real estate, retired at 29, spent some time traveling the world full time and are now settled with two kids.
If you want to know more about us, or how we did that, or see lots of pictures, this Business Insider profile tells our story pretty well.
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#### livingthedream

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #8 on: March 24, 2015, 05:00:28 PM »
Here's a good article on the subject -Retirement Distributions: How Much Can You Afford? - http://paulmerriman.com/retirement-distributions-how-much-can-you-afford-2/

I also like the free flexible retirement planner because you can run all the different scenarios.

#### AlwaysBeenASaver

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #9 on: March 24, 2015, 05:01:34 PM »
I think just the opposite might need to be done. My understanding is the 4% rule is calculated for a 30 year retirement period, while many people here are potentially facing a much longer time period. So I think each year you could recalculate how much you're planning to withdraw, and compare that to 4% of your stashe. If you still have over 30 years left in your expected lifespan, reduce your spending/budget so you're withdrawing no more than 4%, until you get inside that 30 year window.

#### RyanAtTanagra

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #10 on: March 24, 2015, 07:26:22 PM »
Excellent explanation by ars.  If you still find yourself disagreeing, re-read that.  As an alternative, since it sounds like what you're wanting is to be able to spend more as your stache grows, is you can just do 4% of current the stache, whether up or down.  This lets you spend more as it grows, and also has a 0% failure rate.  It can make down years a little lean, however.

#### downtownshuter

• Posts: 29
##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #11 on: March 24, 2015, 08:13:22 PM »
Interesting question. I agree with ars and the others though, it doesn't work that way. When you retire with a 4% swr you're accepting a ~5% chance that you retired during a bad year that will result in a FIRE failure. By resetting your SWR, you're effectively re-retiring and taking an additional 5% risk of failure.

Even simpler analogy: you're playing Russian roulette with 100 chambers and 5 bullets. When you retire, you pull the trigger once. Each time you reset your SWR to a higher level, you're pulling the trigger one more time. Eventually you find a bullet.

#### electriceagle

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #12 on: March 24, 2015, 08:19:06 PM »
What you are missing is that 4% of any principle is enough to start at and will last 30 years, adjusted annually for inflation.

No, what we are saying is that the reason why 4% works as often as it does (93% of the time) is that when the crash happens, often the portfolio has built up enough that your WR is actually below 4% by that point, even though you've adjusted for inflation, because it outgrew inflation, and that outgrowing allows it to last.

Let me make up numbers to illustrate the point.

Lets say a crash happens at year X.

If you FIRE one year before that (at X-1) at 4% WR, you probably won't make it the 30 years.  You'll be in the small handful of failure cases.  Ditto at X-2.  Maybe at X-3.. But maybe at X-4, X-5, etc. your portfolio has gained enough from those 4-5 years that when the crash happens at X, you last through it (in a way you wouldn't if you FIRE'd only 1 year before, at X-1).

But if you do your plan to reset every year, you're constantly risking a crash happening next.  Thus -- like Eric said -- you're increasing your sequence of returns risk.

There are failure cases with the 4% rule, and by constantly resetting and potentially inflating your spending to 4% (but never reducing), you're vastly increasing your chance of being a failure case, because no longer do you have to get past the first few years of FIRE, but you have to continually do it.

Bingo on the increased sequence of return risk. Suppose that the 4% SWR produces a 95% chance of success over your time period. Since the cause of failure happens at the start of the time period, chance of success can be estimated as 0.95^y, where "y" is the number of resets + 1.

Thus:
0 resets -> 95%
1 reset -> 90%
2 resets -> 86%
3 resets -> 81%

That said, the approach that you are considering might work if you went with a 3.5% SWR (98% chance of success). There you get:

0 resets -> 98%
1 reset -> 96%
2 resets -> 94%
3 resets -> 92%

You are even more free to do this if you reduce yourself to a 3% SWR.

#### Exflyboy

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #13 on: March 24, 2015, 09:28:51 PM »
I like it.. My strategy looks a lot like yours but I have not written it down like that.. But I too was planning 2.1% to 4%.

We have measured our spending to be slightly under \$30k per year so our \$1.5M stash gives us about a 2% WR... Of course thats a 3 week roadtrip as a vacation.. i.e not with the foreign travel.. so I can see that spiking up significantly.

Is your house paid off? or are you renting.. what size of stash are you working with?

#### Tyler

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #14 on: March 25, 2015, 11:11:42 AM »
IMHO, the best way to avoid "under spending" is to establish your maximum happiness for the dollar ratio far before FIRE and to simply continue that lifestyle after you retire.  If adjusting up based on returns is on your radar, then to me that's a sign that either you still believe more spending creates more happiness, or you're perhaps tempted to pull the trigger too soon and hope to make up the shortfall with investments.  Neither are particularly healthy retirement mindsets.

#### DoubleDown

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #15 on: March 25, 2015, 02:59:19 PM »
You can start or restart that 30 years and 4% any time you want.  The math is the same.

I'm not sure (but can't yet prove without some more thought) that that's true. I'm reaching back really far into my math days (did undergrad and grad in math), but I recall expectation (probability) being different between a sequence of events, and a sequence of events given a prior set of events (which you are describing). Might be the Bernoulli theorems/equations???

That is, you can't just reset the clock, as it were, on a sequence and calculate the expectation going forward in the same way, and certainly not for dependent events. Since market events almost certainly have some dependency built in, the events preceding where you are -- that is, where you are in the sequence -- matters. That doesn't imply you can foresee the events (time the market), but the is dependency there (unlike, say, flips of a coin where each flip has nothing to do with prior flips).

I think this is what others are arguing from an intuitive standpoint.

#### DoubleDown

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #16 on: March 25, 2015, 03:02:58 PM »
IMHO, the best way to avoid "under spending" is to establish your maximum happiness for the dollar ratio far before FIRE and to simply continue that lifestyle after you retire.

+1

#### brooklynguy

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #17 on: March 25, 2015, 03:33:37 PM »
I'm not sure (but can't yet prove without some more thought) that that's true. I'm reaching back really far into my math days (did undergrad and grad in math), but I recall expectation (probability) being different between a sequence of events, and a sequence of events given a prior set of events (which you are describing).

Right, that's exactly what downtownshuter's apt Russian roulette analogy demonstrates and what electriceagle described.  It is true that each time you pull the trigger, you have a 95/100 chance of not being shot:  even if you've done it 95 times and not been shot, on the 96th trigger pull, you still have a 95/100 chance of not being shot.  But your chances of repeatedly pulling the trigger over and over again and not being shot are not 95/100; if you do it three times, your chances are (95/100) x (95/100) x (95/100) = 85.74%.  The more times you repeat it, the lower your chances of not being shot every single time in the sequence.

#### beltim

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #18 on: March 25, 2015, 03:43:16 PM »
I'm not sure (but can't yet prove without some more thought) that that's true. I'm reaching back really far into my math days (did undergrad and grad in math), but I recall expectation (probability) being different between a sequence of events, and a sequence of events given a prior set of events (which you are describing).

Right, that's exactly what downtownshuter's apt Russian roulette analogy demonstrates and what electriceagle described.  It is true that each time you pull the trigger, you have a 95/100 chance of not being shot:  even if you've done it 95 times and not been shot, on the 96th trigger pull, you still have a 95/100 chance of not being shot.  But your chances of repeatedly pulling the trigger over and over again and not being shot are not 95/100; if you do it three times, your chances are (95/100) x (95/100) x (95/100) = 85.74%.  The more times you repeat it, the lower your chances of not being shot every single time in the sequence.

I don't think that's a valid analogy, and the math is certainly wrong.  The analogy describes a simple binary scenario - yes or no, and then you can repeat.  But the valid comparison for this analogy would be successive 30-year periods, with the withdrawal rate recalculated every 30 years, not a reevaluation of the withdrawal rate after, say, 5 years.

You could certainly test this type of strategy – if not in a simulator like cFIREsim, then using Excel spreadsheets and a lot of work.

#### arebelspy

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #19 on: March 25, 2015, 03:49:22 PM »
I'm not sure (but can't yet prove without some more thought) that that's true. I'm reaching back really far into my math days (did undergrad and grad in math), but I recall expectation (probability) being different between a sequence of events, and a sequence of events given a prior set of events (which you are describing).

Right, that's exactly what downtownshuter's apt Russian roulette analogy demonstrates and what electriceagle described.  It is true that each time you pull the trigger, you have a 95/100 chance of not being shot:  even if you've done it 95 times and not been shot, on the 96th trigger pull, you still have a 95/100 chance of not being shot.  But your chances of repeatedly pulling the trigger over and over again and not being shot are not 95/100; if you do it three times, your chances are (95/100) x (95/100) x (95/100) = 85.74%.  The more times you repeat it, the lower your chances of not being shot every single time in the sequence.

I don't think that's a valid analogy, and the math is certainly wrong.  The analogy describes a simple binary scenario - yes or no, and then you can repeat.  But the valid comparison for this analogy would be successive 30-year periods, with the withdrawal rate recalculated every 30 years, not a reevaluation of the withdrawal rate after, say, 5 years.

You could certainly test this type of strategy – if not in a simulator like cFIREsim, then using Excel spreadsheets and a lot of work.

The reason why it doesn't have to be separate 30 year periods is that a crash in the middle of the 30-year period wouldn't necessarily be doom for someone whose stache had built up enough to ride it out.  But the person who reset the year before that crash couldn't necessarily do so.

So it's more like "hope there's no sequence of returns risk -- crash or large inflation -- during any point of my retirement" rather than the current "hope there's no sequence of returns risk -- crash or large inflation -- at the beginning of my retirement"
We are two former teachers who accumulated a bunch of real estate, retired at 29, spent some time traveling the world full time and are now settled with two kids.
If you want to know more about us, or how we did that, or see lots of pictures, this Business Insider profile tells our story pretty well.
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#### brooklynguy

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #20 on: March 25, 2015, 03:52:00 PM »
The way the OP set up it up, it's rolling 30-year periods (the clock restarts with each "reset"), so it's a valid analogy if we assume that the chances of success at the start of each reset are 95% (which we can't really assume because we don't know the actual chances of success, but it's roughly what we do when we talk about a given SWR having an X% chance of success), no?

Is the math wrong?  What's the correct math?  (I guess I need a refresher on probabilistic math too.)

#### DoubleDown

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #21 on: March 25, 2015, 05:22:36 PM »
Is the math wrong?  What's the correct math?  (I guess I need a refresher on probabilistic math too.)

My simplistic answer would probably be to recalculate the Trinity calculations every year, using all of the prior years available to give an ever-refined SWR based on all the history we have. That way, your new calculated SWR takes into consideration all the prior events. It seems this is what Pfau and others are already doing, and why he's pointing to the current SWR being more in the 3.x% range nowadays given the latest market events. And, of course, you're always still left with the inevitable "past performance is no guarantee of future results."

#### brooklynguy

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #22 on: March 25, 2015, 05:45:39 PM »
It seems this is what Pfau and others are already doing, and why he's pointing to the current SWR being more in the 3.x% range nowadays given the latest market events.

I don't think that's quite right, because inclusion of the most recent data (the long bull market) in the historical dataset should increase the history-based success rate, not decrease it.  Pfau is just looking at the indicators in the current market climate and predicting below-historical-average returns on that basis.

But I was just asking about the math still keeping with the Russian roulette analogy.  (I've learned that when beltim says something, he's usually right.)  If there are 100 chambers and 5 bullets, how do you calculate the odds of not getting shot in a sequence of three trigger pulls?

#### arebelspy

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #23 on: March 25, 2015, 09:47:03 PM »
It seems this is what Pfau and others are already doing, and why he's pointing to the current SWR being more in the 3.x% range nowadays given the latest market events.

I don't think that's quite right, because inclusion of the most recent data (the long bull market) in the historical dataset should increase the history-based success rate, not decrease it.  Pfau is just looking at the indicators in the current market climate and predicting below-historical-average returns on that basis.

But I was just asking about the math still keeping with the Russian roulette analogy.  (I've learned that when beltim says something, he's usually right.)  If there are 100 chambers and 5 bullets, how do you calculate the odds of not getting shot in a sequence of three trigger pulls?

You had that math right, 0.95^3.  But I think he was arguing the analogy isn't correct, so that math is the wrong math to use.
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#### brooklynguy

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #24 on: March 26, 2015, 06:56:00 AM »
You had that math right, 0.95^3.  But I think he was arguing the analogy isn't correct, so that math is the wrong math to use.

Ah, got it.  Thanks.

#### pom

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #25 on: March 26, 2015, 08:09:07 AM »
You had that math right, 0.95^3.  But I think he was arguing the analogy isn't correct, so that math is the wrong math to use.

Ah, got it.  Thanks.

Depends if you re-roll the cylinder. If you don't, the answer is (1-5/100)x(1-5/99)x(1-5/98) = 0.8560 chance of survival. If you pull the trigger 96 times, you are 0% chance of survival, not 0.95^96.

Sorry for the anal retentive response.

#### arebelspy

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##### Re: If (SWR+inflation &lt; 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #26 on: March 26, 2015, 08:11:45 AM »
Good point Pom.  Clearly the second isn't right (not EVERY 30 year period had a failure, so your success rate shouldn't be 0), but I think the first is not quite right either, as they're not completely independent.

Somewhere in the middle, perhaps.
We are two former teachers who accumulated a bunch of real estate, retired at 29, spent some time traveling the world full time and are now settled with two kids.
If you want to know more about us, or how we did that, or see lots of pictures, this Business Insider profile tells our story pretty well.
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#### brooklynguy

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #27 on: March 26, 2015, 08:22:28 AM »
Yes, I was assuming that you re-roll the cylinder after each trigger-pull.  Isn't that how Russian roulette is played?  I'm by no means an expert, but it seems like that's got to be the way it works -- I sure as hell wouldn't pull the trigger after 95 trigger pulls with no shot fired if the cylinder doesn't get re-rolled :-)

Also, now I see beltim's point -- the Russian roulette analogy would require consecutive fully-elapsed 30 year periods for the analogy to correctly apply.

#### DoubleDown

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #28 on: March 26, 2015, 11:11:49 AM »
I had my theorem name wrong when trying to remember -- it's Bayes, not Bernoulli (hey I got the first letter right!!). I suggest this is the appropriate methodology for looking at a sequence of data and "starting over." It is a conditional probability problem, and the theorem shows that the probability of an outcome can/will change depending on the prior conditions known.

It's a bit paradoxical, but if you step out of the sequence, you must then acknowledge the updated, prior conditions to get a new, accurate computation. Bayes' theorem would be the appropriate computation for playing Russian Roulette without spinning the chamber each time (for example, "What are the odds I will be shot (with a 6-chamber revolver) on the fourth attempt given that the trigger has already been pulled twice without firing?"):

http://en.wikipedia.org/wiki/Bayesian_inference

http://en.wikipedia.org/wiki/Bayes'_theorem

Quote
In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule) relates current probability to prior probability.

It is important in the mathematical manipulation of conditional probabilities.[1] Bayes' rule can be derived from more basic axioms of probability, specifically conditional probability.
...
Bayesian inference is a method of statistical inference in which Bayes' rule is used to update the probability for a hypothesis as evidence is acquired. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data.

Bayes' theorem is stated mathematically as the following equation:[6]

P(A|B) = (P(B | A) * P(A)) / P(B)

where A and B are events.

P(A) and P(B) are the probabilities of A and B independent of each other.
P(A|B), a conditional probability, is the probability of A given that B is true.
P(B|A), is the probability of B given that A is true.

#### beltim

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #29 on: March 26, 2015, 11:41:03 AM »
The way the OP set up it up, it's rolling 30-year periods (the clock restarts with each "reset"), so it's a valid analogy if we assume that the chances of success at the start of each reset are 95% (which we can't really assume because we don't know the actual chances of success, but it's roughly what we do when we talk about a given SWR having an X% chance of success), no?

Is the math wrong?  What's the correct math?  (I guess I need a refresher on probabilistic math too.)

The OP set up rolling 30 year periods, but the math on the analogy is only valid for consecutive year periods.  Put another way, there are 0 historical cases of a 4% withdrawal rate failing in the first 5 years.  Thus, we know that a 5% failure rate for the first period is wrong, and any analogy that uses that calculation is therefore wrong.

The question then becomes, is it accurate to use the 95% success rate if we start a new 30 year clock with a 4% withdrawal rate.  Intuitively, I think it does, as long as you also allow for the possibility of your withdrawals decreasing.  If you only have the possibility of increasing withdrawals, I don't think the 95% success rate is valid anymore – you'd have to recompute your success rate, based on what the market did over the last 5 years.

#### arebelspy

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##### Re: If (SWR+inflation &lt; 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #30 on: March 26, 2015, 11:42:29 AM »
But that's what 4%, and the OP's post is based on, only increasing.

I agree one should be flexible, including decreasing spending. But that's not what the proposed rule is.
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#### beltim

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##### Re: If (SWR+inflation &lt; 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #31 on: March 26, 2015, 11:51:06 AM »
But that's what 4%, and the OP's post is based on, only increasing.

I agree one should be flexible, including decreasing spending. But that's not what the proposed rule is.

Well, right.  But I'm interested in trying to figure out the success rate of that strategy would be.  I know it's not just .95^(# of resets) for the reasons I described above.  I also know it's not a flat 95% because the sequence of returns matters.  I'm trying to figure out if there's an easy way to find the actual probability.

#### brooklynguy

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #32 on: March 26, 2015, 11:52:00 AM »
The OP set up rolling 30 year periods, but the math on the analogy is only valid for consecutive year periods.  Put another way, there are 0 historical cases of a 4% withdrawal rate failing in the first 5 years.  Thus, we know that a 5% failure rate for the first period is wrong, and any analogy that uses that calculation is therefore wrong.

The question then becomes, is it accurate to use the 95% success rate if we start a new 30 year clock with a 4% withdrawal rate.  Intuitively, I think it does, as long as you also allow for the possibility of your withdrawals decreasing.  If you only have the possibility of increasing withdrawals, I don't think the 95% success rate is valid anymore – you'd have to recompute your success rate, based on what the market did over the last 5 years.

Yes, you are correct, I realized the logic error (as I noted in reply # 28).  The proper analog to Russian roulette would be consecutive, fully-elapsed 30-year periods (where each 30 year period starts off with a portfolio having a 95% chance of success).  So that's not the proper analogy for this situation.

The OP's proposed rule would require resets upwards and not downwards (i.e., it sets a spending floor but not a spending ceiling).

Doubledown's "Bayes" method sounds like the right approach if the OP's proposed rule applied for the duration of a single 30-year period (and you can easily see the historical success rate of this approach in cfiresim by setting a variable spending plan with a floor but no ceiling).

But the OP's actual proposal is rolling 30-year periods, starting the clock over at each reset (but I don't think it really makes sense set it up that way or to view it from that perspective).

#### beltim

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #33 on: March 26, 2015, 12:12:44 PM »
Alright, so I have a dataset for the S&P 500 that goes back to 1928.  Using cFIREsim for all 30 year periods since 1928 gives a success rate of 51/58 or 88%.  The failure years are:
1929
1965
1966
1967
1968
1969
1973
Let's restrict ourselves to only 30 year periods that start after a 5 year period with annualized returns in excess of 5% (to model cases where the OP might increase spending to a new 4%).  That's 36 out of 53 periods ending in 1984.  By comparing those to the starting failure years, we can get historical information on the success rate of this strategy.  Notably, 1965, 1966, 1967, and 1968 all came after 5-year periods where greater than 5% annual returns.  So, in the historical data set of 36 periods, 4 resulted in failure using the OP's idea (put into practice by 5% annual gains over the preceding 5 years).  Note that the inflation rate in each of the failure times was less than 5%.  So that's a historical success rate of 32/36 or 89%, statistically indistinguishable from the original, full data set.

#### beltim

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #34 on: March 26, 2015, 12:44:36 PM »
Yes, you are correct, I realized the logic error (as I noted in reply # 28).  The proper analog to Russian roulette would be consecutive, fully-elapsed 30-year periods (where each 30 year period starts off with a portfolio having a 95% chance of success).  So that's not the proper analogy for this situation.

Yes, I saw that, sorry about that - I was just quoting the most relevant point in order to frame my comment appropriately.

Quote
Doubledown's "Bayes" method sounds like the right approach if the OP's proposed rule applied for the duration of a single 30-year period (and you can easily see the historical success rate of this approach in cfiresim by setting a variable spending plan with a floor but no ceiling).

But the OP's actual proposal is rolling 30-year periods, starting the clock over at each reset (but I don't think it really makes sense set it up that way or to view it from that perspective).

I think your analysis of Bayesian statistics is right.  I'm trying to figure out the right stats for what the OP is actually suggesting - basically, how the probability of the 4% WR succeeding varies depending on the previous x years of market returns.  I think it's an interesting question, particularly in that it has applications beyond the OP's question.  The market returns in the few years before retiring certainly affect your probability of success, and it would be interesting to know how.  Unfortunately, I suspect there isn't enough data in the historical record to get a statistically significant answer.

#### brooklynguy

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #35 on: March 26, 2015, 01:24:30 PM »
Unfortunately, I suspect there isn't enough data in the historical record to get a statistically significant answer.

I would tend to agree.  I had thought cfiresim's variable spending plan options allowed you to set floors and/or ceilings based on a percentage of the running portfolio value (which would allow us to model the historical success rate of the proposed plan over a desired period length, like, say, 60 years), but looking at the options it seems that only defined values are available as floor/ceiling options.  I would imagine that cfiresim could be revised to create this option (though I know bo_knows already has a lot on his plate at the moment).

#### frugalnacho

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #36 on: March 26, 2015, 08:12:19 PM »
This sounds like a terrible plan.  It guarantees that you will "retire" into a bear market without an adequate buffer.  If you happen to live through any semi major crash in your retirement life time you are guaranteeing that you are going to be one of those few failures.

#### Malaysia41

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #37 on: March 26, 2015, 10:20:45 PM »
Alright, so I have a dataset for the S&P 500 that goes back to 1928.  Using cFIREsim for all 30 year periods since 1928 gives a success rate of 51/58 or 88%.  The failure years are:
1929
1965
1966
1967
1968
1969
1973

When doing cFIREsim and calculating our success rate (over and over) before deciding at last to FIRE, I couldn't help but imagine what it'd be like retiring in those years 65-69.  Many people back then retired with pensions, so they were likely okay.  Others, given the life expectancy at the time, maybe didn't need a 30 year stash.  Still others, like my dad's parents, retired with only their savings.  My grandparents, despite their timing, seemed to do great.

In large part their success was because of my Grandma.  She managed the stash.  When I was still in single digits, she explained to me how she picked stocks: "I buy what I know, and look for value".   She explained what a balance sheet was and that she made sure any stock she picked had a healthy balance sheet.  She kept on the look-out for the 'must have' items her friends raved about.  Then, rather than buying those items, she bought the stock (after a full review of the public books).

Later, when I read Berkshire Hathaway annual reports and interviews with Warren Buffet I couldn't help but think of my Grandma.

Of course now-a-days, indexing is the pretty clear way to go.  But she did great.

As for resetting your spend rate to 4% every year the stash ticks up?  Shudder!  You're just asking for problems.  Our FIRE needs to last 60 years if everything goes to plan.  Upticking to 4% would terrify me.
« Last Edit: March 27, 2015, 02:38:03 AM by Malaysia41 »

#### deborah

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #38 on: March 27, 2015, 12:21:47 AM »
Many people back then retired with pensions, so they were likely okay.  Others, given the life expectancy at the time, maybe didn't need a 30 year stash.
I remember people who retired at that time. They didn't have pensions. They were poor.

#### arebelspy

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #39 on: March 27, 2015, 08:12:50 AM »
Many people back then retired with pensions, so they were likely okay.  Others, given the life expectancy at the time, maybe didn't need a 30 year stash.
I remember people who retired at that time. They didn't have pensions. They were poor.

You are correct, at least as far back as 1979 (and probably further), and if we're only counting private workers.

http://www.ebri.org/publications/benfaq/index.cfm?fa=retfaq14

Looks like 38% of private sector workers had pensions (28% with only pensions and 10% with both db and dc plans), down to 14% today (3% with only pensions, 11% with both) today.  Of course, you have to add public workers in, so that might push it over the 50% mark to "most" retiring with pension.

Still, the point remains, somewhere around half, even back then, didn't have pensions.  The numbers are much lower today.
We are two former teachers who accumulated a bunch of real estate, retired at 29, spent some time traveling the world full time and are now settled with two kids.
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#### brooklynguy

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #40 on: March 27, 2015, 01:04:02 PM »
Alright, so I have a dataset for the S&P 500 that goes back to 1928.  Using cFIREsim for all 30 year periods since 1928 gives a success rate of 51/58 or 88%.  The failure years are:
1929
1965
1966
1967
1968
1969
1973
Let's restrict ourselves to only 30 year periods that start after a 5 year period with annualized returns in excess of 5% (to model cases where the OP might increase spending to a new 4%).  That's 36 out of 53 periods ending in 1984.  By comparing those to the starting failure years, we can get historical information on the success rate of this strategy.  Notably, 1965, 1966, 1967, and 1968 all came after 5-year periods where greater than 5% annual returns.  So, in the historical data set of 36 periods, 4 resulted in failure using the OP's idea (put into practice by 5% annual gains over the preceding 5 years).  Note that the inflation rate in each of the failure times was less than 5%.  So that's a historical success rate of 32/36 or 89%, statistically indistinguishable from the original, full data set.

Ok, I've now focused on this post and taken the time to digest the methodology you used here (which was frankly brilliant).

If we put aside for a moment the fact that there probably just isn't enough data to allow us to draw statistically significant conclusions (which I agree is a real problem), then what your analysis tells us is that retiring after a large market run-up (on an annualized basis) does *not* result in decreased chances of portfolio success.  That is an incredibly counterintuitive result.

#### UnleashHell

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #41 on: March 27, 2015, 01:38:25 PM »
if you only ever take 4% then you'll always have a stash.
as long as you adjust on the way down as well as the way up.

There is 0% chance of failure. of course you have to make sure that 4% of the bottom of the cycle is enough to cover your expenses...

#### arebelspy

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #42 on: March 27, 2015, 01:57:01 PM »
if you only ever take 4% then you'll always have a stash.
as long as you adjust on the way down as well as the way up.

There is 0% chance of failure. of course you have to make sure that 4% of the bottom of the cycle is enough to cover your expenses...

Yes, cFIREsim has an option like this, to reduce your spending but set a "floor" (to make sure the amount doesn't go below the minimum you need).
We are two former teachers who accumulated a bunch of real estate, retired at 29, spent some time traveling the world full time and are now settled with two kids.
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#### Spork

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #43 on: March 27, 2015, 02:02:03 PM »
Okay, so I've been silently reading along...  The OP's suggestion sounded reasonable... and the counter arguments to it have convinced me it isn't.

But...  I've been probably over saving.  I probably over state my expenses and I a think I am being ultra conservative with everything I estimate.

So my follow up here is: what *is* a viable method to re-evaluate and reset spending?  (And I know: this is such a pissy first world problem.  If I die with a big pile of cash -- that's not a terrible problem to have.)

#### arebelspy

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #44 on: March 27, 2015, 02:57:59 PM »
Okay, so I've been silently reading along...  The OP's suggestion sounded reasonable... and the counter arguments to it have convinced me it isn't.

But...  I've been probably over saving.  I probably over state my expenses and I a think I am being ultra conservative with everything I estimate.

So my follow up here is: what *is* a viable method to re-evaluate and reset spending?  (And I know: this is such a pissy first world problem.  If I die with a big pile of cash -- that's not a terrible problem to have.)

Depends on how conservative you want to be - in other words, what success rate is acceptable to you.

And also how flexible you are with your spending, and if you're willing to take a cut from year to year if the market is down.

IMO, just run cFIREcalc each year with your current parameters.  You can use the "investigate" function to determine your max SWR at the present time based on the success rate you feel comfortable with (i.e. plug in 90% or 95% or 100% or whatever) and see what is the max spending you could do for the year, and cap at that (or lower, again, if you want to feel comfortable).

Setting rigid "rules" seems silly - pick what makes you comfortable and adjust based on that.
We are two former teachers who accumulated a bunch of real estate, retired at 29, spent some time traveling the world full time and are now settled with two kids.
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#### brooklynguy

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #45 on: March 29, 2015, 02:02:17 PM »
Alright, so I have a dataset for the S&P 500 that goes back to 1928.  Using cFIREsim for all 30 year periods since 1928 gives a success rate of 51/58 or 88%.  The failure years are:
1929
1965
1966
1967
1968
1969
1973
Let's restrict ourselves to only 30 year periods that start after a 5 year period with annualized returns in excess of 5% (to model cases where the OP might increase spending to a new 4%).  That's 36 out of 53 periods ending in 1984.  By comparing those to the starting failure years, we can get historical information on the success rate of this strategy.  Notably, 1965, 1966, 1967, and 1968 all came after 5-year periods where greater than 5% annual returns.  So, in the historical data set of 36 periods, 4 resulted in failure using the OP's idea (put into practice by 5% annual gains over the preceding 5 years).  Note that the inflation rate in each of the failure times was less than 5%.  So that's a historical success rate of 32/36 or 89%, statistically indistinguishable from the original, full data set.

Ok, I've now focused on this post and taken the time to digest the methodology you used here (which was frankly brilliant).

If we put aside for a moment the fact that there probably just isn't enough data to allow us to draw statistically significant conclusions (which I agree is a real problem), then what your analysis tells us is that retiring after a large market run-up (on an annualized basis) does *not* result in decreased chances of portfolio success.  That is an incredibly counterintuitive result.

Beltim, did the data you used for historical S&P 500 returns include reinvestment of dividends?  And was it for returns in nominal terms?

The result seemed so counterintuitive as to almost defy explanation.  But given that the starting years for the failure cases are so clustered around the second half of the 1960s (meaning that almost all the failures resulted from the same single 34-year period of poor real market performance), do you think it would be a useful exercise to do the same analysis using a more failure-prone WR (like maybe 5%)?  Perhaps once there are more failure cases in the dataset, the analysis will show that the market returns in the short period leading up to retirement did have a statistically meaningful effect on the probability of success (though there's probably still not enough data in the overall historical record for the answer to really have statistical significance).

#### arebelspy

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #46 on: March 29, 2015, 02:29:39 PM »
Alright, so I have a dataset for the S&P 500 that goes back to 1928.  Using cFIREsim for all 30 year periods since 1928 gives a success rate of 51/58 or 88%.  The failure years are:
1929
1965
1966
1967
1968
1969
1973
Let's restrict ourselves to only 30 year periods that start after a 5 year period with annualized returns in excess of 5% (to model cases where the OP might increase spending to a new 4%).  That's 36 out of 53 periods ending in 1984.  By comparing those to the starting failure years, we can get historical information on the success rate of this strategy.  Notably, 1965, 1966, 1967, and 1968 all came after 5-year periods where greater than 5% annual returns.  So, in the historical data set of 36 periods, 4 resulted in failure using the OP's idea (put into practice by 5% annual gains over the preceding 5 years).  Note that the inflation rate in each of the failure times was less than 5%.  So that's a historical success rate of 32/36 or 89%, statistically indistinguishable from the original, full data set.

Ok, I've now focused on this post and taken the time to digest the methodology you used here (which was frankly brilliant).

If we put aside for a moment the fact that there probably just isn't enough data to allow us to draw statistically significant conclusions (which I agree is a real problem), then what your analysis tells us is that retiring after a large market run-up (on an annualized basis) does *not* result in decreased chances of portfolio success.  That is an incredibly counterintuitive result.

Beltim, did the data you used for historical S&P 500 returns include reinvestment of dividends?  And was it for returns in nominal terms?

The result seemed so counterintuitive as to almost defy explanation.  But given that the starting years for the failure cases are so clustered around the second half of the 1960s (meaning that almost all the failures resulted from the same single 34-year period of poor real market performance), do you think it would be a useful exercise to do the same analysis using a more failure-prone WR (like maybe 5%)?  Perhaps once there are more failure cases in the dataset, the analysis will show that the market returns in the short period leading up to retirement did have a statistically meaningful effect on the probability of success (though there's probably still not enough data in the overall historical record for the answer to really have statistical significance).

At some point of course the years you retire will matter more, but I think one potential takeaway is that 4% seems safe enough in those circumstances, even when nearing a market peak.
We are two former teachers who accumulated a bunch of real estate, retired at 29, spent some time traveling the world full time and are now settled with two kids.
If you want to know more about us, or how we did that, or see lots of pictures, this Business Insider profile tells our story pretty well.
We (rarely) blog at AdventuringAlong.com. Check out our Now page to see what we're up to currently.

#### brooklynguy

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #47 on: March 29, 2015, 03:07:19 PM »
At some point of course the years you retire will matter more, but I think one potential takeaway is that 4% seems safe enough in those circumstances, even when nearing a market peak.

Yes, I agree that's an important takeaway.  I just find it extremely interesting that the data seems to say that retiring after a steep market run-up had zero effect on historical chances of success, which might mitigate the concern expressed in this thread regarding the presumed greater likelihood of hitting your retirement-commencement-trigger portfolio value at a time with higher-than-average probability of portfolio failure.

#### beltim

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #48 on: March 29, 2015, 11:56:57 PM »
Ok, I've now focused on this post and taken the time to digest the methodology you used here (which was frankly brilliant).

If we put aside for a moment the fact that there probably just isn't enough data to allow us to draw statistically significant conclusions (which I agree is a real problem), then what your analysis tells us is that retiring after a large market run-up (on an annualized basis) does *not* result in decreased chances of portfolio success.  That is an incredibly counterintuitive result.

Hey, thanks!

Beltim, did the data you used for historical S&P 500 returns include reinvestment of dividends?  And was it for returns in nominal terms?

Yes on both - it included dividends, and was in nominal terms.  However, the inflation in each 5 year period below that was less than 5% annualized.

Quote
The result seemed so counterintuitive as to almost defy explanation.  But given that the starting years for the failure cases are so clustered around the second half of the 1960s (meaning that almost all the failures resulted from the same single 34-year period of poor real market performance), do you think it would be a useful exercise to do the same analysis using a more failure-prone WR (like maybe 5%)?  Perhaps once there are more failure cases in the dataset, the analysis will show that the market returns in the short period leading up to retirement did have a statistically meaningful effect on the probability of success (though there's probably still not enough data in the overall historical record for the answer to really have statistical significance).

I like the idea, but I wonder about the relevance of using a 5% withdrawal rate to look into the success rate of a 4% withdrawal rate.

#### beltim

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##### Re: If (SWR+inflation < 4% of stash, reset to 4%, spend SWR+inflation)
« Reply #49 on: March 30, 2015, 12:08:32 AM »
Unfortunately, I suspect there isn't enough data in the historical record to get a statistically significant answer.

I would tend to agree.  I had thought cfiresim's variable spending plan options allowed you to set floors and/or ceilings based on a percentage of the running portfolio value (which would allow us to model the historical success rate of the proposed plan over a desired period length, like, say, 60 years), but looking at the options it seems that only defined values are available as floor/ceiling options.  I would imagine that cfiresim could be revised to create this option (though I know bo_knows already has a lot on his plate at the moment).

I was playing around with cFIREsim and I think the "Retire Again & Again Method" is a pretty good simulation.  Set to a 4% withdrawal rate, and increases any time the market goes up 3% (a crude method for inflation), with a floor in constant dollars of 4% of the initial starting value, the success rate falls from 107/115 to 105/115 or, from 93% to 91.3%.