The 4% Rule – A Castle in the Air

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M
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Joined: Wed Sep 29, 2010 7:34 pm

Re: The 4% Rule – A Castle in the Air

Post by M »

You know - really - this seems less of an academic exercise and more of a - how much risk are you willing to tolerate exercise.

I know people who quit their job, while renting, with no savings. In fact, I know a few people who did this during my unskilled labor work days. It was almost a running joke. They had no plan - they just quit...after a couple weeks they ran out of money to buy cigarettes and we would find them working at the fast food restaurant right next to us. Then we would trade our burgers for their pizza, or chicken, or whatever...If you asked them what their withdrawal rate was they would assume you are talking about a new pull out method for sex.

Sometimes this did not work out - and they didn't find a new job in time and were evicted from their apartment. Then they simply moved back in with their parents usually, or with their brother, or cousin, or friend. One girl simply started flirting with a guy and moved in with him a few days later. Somedays I wish I was born a beautiful girl instead...

In some ways - these people were more free than some of the people on this forum. Sure - they had no money...but if they did not want to be somewhere, they just quit, or moved, or whatever.

If you have money but have mental blocks to freedom then you still aren't free. Just like the person who will not read has no particular advantage over someone who cannot read, someone with money who never uses it for freedom purposes is no more free than someone without money.

Of course there is the security aspect of it but - It's impossible to prove the future. Literally all of our theories and knowledge and predictive power of the future is based on the past, and there is nothing that proves the future will behave like the past, since the future has not occurred yet.

Even a 1% withdrawal rate - we want to use this now because it is the global safe withdrawal...which is again based on history. There were a lot of very rich Jews during world war 2 who lost everything. I'm sure some of them had a 1% withdrawal rate. That did not save them. At the end of the day they were forced into prison camps at the point of a gun. Literally all of their money and assets were seized.

If you really are aiming for a 1% withdrawal rate I would argue you are overestimating just how secure financial assets are, in general. There is only so much security that can be found in money. Everything can be taken by the government or an invading army.

If you are under a 2% withdrawal rate instead of investing more in financial markets I would invest in other things. For example, I would move somewhere that is not likely to lose a world war, or is not likely to be involved in a world war. I would develop good social relationships, especially with people who will share housing and food with you. I would develop gardening shooting and cooking skills, and perhaps adopt The Alpha strategy, have solar panels for your own energy production, etc. If your goal is security I would invest in other things.

But really - there is no 100% security. We all die someday - I have yet to hear about anyone living past 125 years or so. Most of the worst case scenarios an ere level expense person who runs out of money is going to involve...going back to work when they run out of money to buy cigarettes, or food, or whatever. Just like the fast food workers I used to work with. Except I doubt there is anyone on this forum who smokes cigarettes.

Of course - I have a 2.5% withdrawal rate and wonder if that is even safe these days or not. So I may just be writing this post for myself in a way. I don't know what a safe withdrawal rate really is moving forward, but I know if I keep working I will start investing in other things that are not financial in nature.

ertyu
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Re: The 4% Rule – A Castle in the Air

Post by ertyu »

M wrote:
Wed Sep 14, 2022 6:02 pm
I don't know what a safe withdrawal rate really is moving forward, but I know if I keep working I will start investing in other things that are not financial in nature.
Yeah, completely right -- we're coming back a full circle here -- that's why our goal here on this forum isn't to arrive at a certain amount of savings and lean back, it's to acquire a broad web of skills that create redundancies

zbigi
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Re: The 4% Rule – A Castle in the Air

Post by zbigi »

M wrote:
Wed Sep 14, 2022 6:02 pm
But really - there is no 100% security. We all die someday - I have yet to hear about anyone living past 125 years or so. Most of the worst case scenarios an ere level expense person who runs out of money is going to involve...going back to work when they run out of money to buy cigarettes, or food, or whatever. Just like the fast food workers I used to work with. Except I doubt there is anyone on this forum who smokes cigarettes.
Unfortunately, the scenario when one offs oneself is also on table. I doubt there will be any work available for 80 or 90 year olds.

M
Posts: 350
Joined: Wed Sep 29, 2010 7:34 pm

Re: The 4% Rule – A Castle in the Air

Post by M »

zbigi wrote:
Thu Sep 15, 2022 2:31 am
Unfortunately, the scenario when one offs oneself is also on table. I doubt there will be any work available for 80 or 90 year olds.
Well - that is certainly an option...I have trouble even comparing these sorts of doomsday scenarios with modern day reality though. Maybe it is my location in America, maybe this is different in other countries.

I know several old people who are retired in this age range and situation. None of them have any money and few have the ability or willingness to work much.

There are several food banks in the area who hand out food, for free, to anyone. You don't have much choice in the food - you get what they give you. It is in a cardboard box, and one of my neighbors gives me the excess of her food because they give her too much food for herself. It's literally free food - no questions asked. It comes in these giant cardboard boxes. She goes there twice a week but I think the limit is once a day. If you tell them you have a family they will give you more food.

In addition there are food stamps that she qualifies for which she barely uses. So she already has redundancy in her system. If the food banks shut down she would simply switch over to using her food stamps at a traditional grocery store.

In addition - there is a third level of redundancy in the system because, like the average older American she gets social security checks of around $1,500 a month. She doesn't even need most of this money - she wastes it on brand new suvs, partying, vacations and whatnot. She does not save it at all. But if the food banks shutdown and the food stamps were taken away she would use this to buy food and buy used suvs instead.

Now - there is a fourth level of redundancy built into her system - because she has children who would certainly keep her from starving to death. They would not pay for her new SUV or partying, but they would give her housing and food.

Of course there is a fifth level of redundancy...I know another lady..well she is actually related to me. Anyway she has never worked in her entire life. Always lived off of family or boyfriends, so she had no money, no social security or Medicare either since she never worked. She was not pleasant to be around - always lied and cheated and stole from everyone. Eventually when she was 70 years old her dad died and her family was done supporting her. Everyone had enough of her nonsense over the decades and she wound up homeless. I thought she was done for sure. That was the end...

Eventually the police found her, and drove her to a nursing home. Since she had no job Medicaid paid for the nursing home.Now she spends her days eating steak dinners and playing bingo. It is disgusting. A lady with no plans, no money, no job, whom most everyone hated because she lied and stole from people her whole life, this was the worst case scenario for her.

Of course there is a sixth level of redundancy which is getting a job. I know a couple people in this age range who amazingly still work. One worked..well he worked - he is dead now - but he worked at a grocery store. The other works at a nursing home still. He is older than most of the residents. We joke that someday he will go to work and never come back.

But yes - there may not be any jobs available. And the 4% rule might fail. And the 3% rule. And maybe in this case the 1% rule might save them.

What are the odds though? I really don't know. Anyone want to guess what are the odds all of these systems fail, and 2% withdrawal rate fails, so it really makes sense to have a 1% withdrawal rate?

prudentelo
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Re: The 4% Rule – A Castle in the Air

Post by prudentelo »

Biggest use for WR is to decide if you're on the zero/infinity side of the line.

For example 5% WR is exactly what I do NOT want. It is only just on side of zero line. So for saving little extra work, good chance I go to zero even without some unaccountable disaster.

But 10% might be OK because I might prefer to live a different (better?) life than keep working "worse" life for 3x as much money. Of course will have to work again at some point. But that is "known" because 10% always fails, so part of plan.

Also 2% might be OK because why work more for 1% when, as you (M) say rightly, chance of "normal" failure at 2% probably lower than chance of ""extraordinary one time loss"".

3.5%? Well, only quit if you really don't like your job. (I did, on similar but more prudent reasoning than your friends who quit with the no savings at all)

One thing is also to ask how much of the life is about getting security, in any form? Is it ever wise to do things that are dangeorus deliberately? You're probably going to die at 80 (not 800) whatever you do. There are worse things than 10 year holiday when young followed by the return to work. Plenty of workers die at 62 wishing they did that. Of course running out of money at 62 with blank resume may be another story.

ertyu
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Re: The 4% Rule – A Castle in the Air

Post by ertyu »

Following up on running out of money at 62 with blank resume: it is likely that the best thing one can do to acquire "life security" besides accumulating wealth is making sure one's body stays fit, healthy, and thus able to work with minimal suffering as one ages. I don't know where I read this, but I remember something along the lines of, a fit 65 y/old is capable of around 60% of the physical effort/strength/exertion as a fit 25 y/o. Enough to flip burgers, should it come to that - or to grow one's own tomatoes.

zbigi
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Re: The 4% Rule – A Castle in the Air

Post by zbigi »

ertyu wrote:
Thu Sep 15, 2022 6:13 pm
Following up on running out of money at 62 with blank resume: it is likely that the best thing one can do to acquire "life security" besides accumulating wealth is making sure one's body stays fit, healthy, and thus able to work with minimal suffering as one ages. I don't know where I read this, but I remember something along the lines of, a fit 65 y/old is capable of around 60% of the physical effort/strength/exertion as a fit 25 y/o. Enough to flip burgers, should it come to that - or to grow one's own tomatoes.
Yeah, 62 with no job history is likely not a problem. I.e. you will get a shitty and exploitative job for minimum wage, but it will be a job. The problems starts around 80 (or earlier, for people with less luck), when almost everyone is worn down to the degree that holding down a physical job is not an option anymore.

zbigi
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Re: The 4% Rule – A Castle in the Air

Post by zbigi »

M wrote:
Thu Sep 15, 2022 7:28 am
That's a good writeup, thanks for showing the US perspective. I guess it comes down to US having way more safety nets that the less developed countries, but at the cost of it being much harder to reach 1-2% WR. Whereas in for example Poland, it's the opposite - safety net is shitty (e.g. state nursing homes are essentially sad warehouses for old people, with crappy food, but still you have to be really sick or give a bribe to get there without a couple years of waiting), but, thanks to geoarbitrage, you can get to 2% WR in a reasonable time.

prudentelo
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Re: The 4% Rule – A Castle in the Air

Post by prudentelo »

Organizing life to optimize quality when (if) 80 is "planning to fail"

steveo73
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Re: The 4% Rule – A Castle in the Air

Post by steveo73 »

prudentelo wrote:
Fri Sep 16, 2022 6:12 am
Organizing life to optimize quality when (if) 80 is "planning to fail"
In Australia we have a pension that when you get to 67 you get 37k per couple. We spend a bit more than that but we have 3 kids. 37k for myself and my wife would be fine. You get more if you don't own your house but you also have to pay rent and rent is expensive. You also get additional benefits with the pension like cheaper public transport. So basically if you own your own house you should be fine if you don't live large and we don't.

We also have good health care if you are prepared to shop around a tiny bit. The past say 2 months I've had two blood tests and an x-ray along with say 3-4 trips to the doctor. This has cost me nothing. We have no health insurance.

So basically in Australia if you get to 67 and own your own house you should be pretty good.

I don't believe Australia is perfect or anything but to me it shows how poorly managed other developed countries are if they don't have these safety nets.

If my 5% fails prior to 67 I have the following backups

1. Return to work/apply for social security.
2. Sell my house (a 4 bedroom house) and downsize. The proviso here is I need to own some form of property to avoid rent and the fees on that property can't be too expensive. This is definitely achievable.

Post 67 assuming I own the property I live in there should be no problems even if my money runs out.

I wonder why the systems in other developed countries are so poor ? Your question about failing at 80 isn't really an option for me. The social system shouldn't allow it. I know the counter argument is you can't rely on the government blah blah blah and I sort of get that because I don't rely on the government but if the system in a developed country isn't good enough there is something wrong with the system. That argument is in my opinion way too pessimistic. If you are living with that fear you are in my opinion not living well.

I think in Australia we need to pay more taxes because there is too much pressure right now (mostly too much debt from pandemic payments) but I think other developed countries really should consider increasing taxes to create a better system. It just sounds wrong in principle to me.

chenda
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Re: The 4% Rule – A Castle in the Air

Post by chenda »

steveo73 wrote:
Fri Sep 16, 2022 7:49 am
I wonder why the systems in other developed countries are so poor ?
It sounds like Australia's system is very similar to most developed countries.

M
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Re: The 4% Rule – A Castle in the Air

Post by M »

chenda wrote:
Fri Sep 16, 2022 11:05 am
It sounds like Australia's system is very similar to most developed countries.
+1

As an example, In America, my wife and I will get 30k a year USD from social security as a couple plus medicare (government subsidized healthcare) when we are 67. This converts to around 45k Australian dollars at current exchange rates. It doesn't sound like our Medicare system is quiet as good as the Australian healthcare system, so most likely 6k of that will go to healthcare for us. So it sounds like it compares well to the Australian system overall. This is what we currently live on with four kids and a paid off 5 bedroom house. Millions of retirees live off this system in America with no money or invested assets and live perfectly fine.

I have worked for 16 years full time. This assumes I quit tomorrow and never work. My wife has never worked in her life. This assumes she never works. If either of us work more in the future these figures go higher.

There are various other social safety nets that catch a ton of people in America from truly failing:

Poor disabled young people get picked up by SSDI (Payments to disabled people) and SNAP (food stamps to pay for food) if they have low income.

Pregnant women or women with kids 0-5 age get picked up by WIC (Women Infant and Children) which pay for diapers, formula, food, etc

Low income Americans qualify for many things, including:
-Section 8 housing (heavily subsidized housing)
-Low income Home Energy Assistance Program (subsidized electric and natural gas)
-SNAP (Supplemental Nutrition Assistance Program to pay for food)
-Medicaid (free medical)
-Lifeline (free cell phone)
-ACP (Affordable Connectivity Program - free internet).
-And if they have kids - Free school lunches for children, and CHIP (Child Health Insurance program - subsidized healthcare for kids for families who make too much to qualify for medicaid)
-Earned income tax credit (Refundable tax credit, around 6k max, for low income Americans who work. Refundable just means they get the money regardless of if they owe taxes or not, i.e. free money to reward work)

Old people who never worked, and never paid into social security or medicare, and have no assets or income qualify for medicaid which will pay for a nursing home. So the truly worst case situation is playing bingo and eating steak dinners in a nursing home.

Of course - our government could take these things all away tomorrow. My counter argument to this is - we live in a country founded by rebels who overthrew our previous government by force over smaller matters. Everyone has the legal right to own firearms, and if you tell a few tens of millions of people you are taking away their source of food, some of them might have just enough money left to go buy a sniper rifle and 50 rounds of ammo or something. Some of the politicians in America are scared of the voters for reasons beyond just getting voted out, and it's not uncommon to find armed militias marching right outside government buildings even in normal times.

Frankly - given the US governments standard operating procedure for dealing with most major crisis so far (Great depression, recession of 2008, pandemic etc) is to expand out more social safety net programs and spend more money, I struggle to imagine a scenario where:

A) The government is still functional
B) These social safety net programs are all gone
C) 2% Withdrawal rate fails
D) 1% Withdrawal rate succeeds

The most likely doomsday scenario I can think of is some kind of slow, long term economic collapse with many crisis sparking the government to intervene over and over to expand out social safety nets to ever increasing amounts causing excessive inflation and/or excessively taxing everyone with financial assets to pay for the repeated bailouts.

If this occurs I kind of view the government as my last stop-loss order. E.G. I will let my financial assets run down then sign up for the same programs most of my neighbors already rely on today who never prepared financially at all.

If entire US government fails I am in the same boat as everyone else, and I would imagine all my US denominated dollar assets would be worth about the same as how much confederate dollars were worth after the war. Even a 0.001% withdrawal rate would not matter much then, since all financial assets would be gone. All I would have left is my physical body, possessions, and relationships.

Hopefully this forum would still be operational though. Instead of discussing safe withdrawal rates I would then be wondering how many acres I need per person to perpetually sustain oneself, or how many tomatoes plants to plant per person so I have enough canned tomatoes to last through the winter.

Maybe safe withdrawal rate discussions would turn into safe minimum acres per person of prime agricultural land is needed for perpetual sustainability discussions. :lol:

zbigi
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Re: The 4% Rule – A Castle in the Air

Post by zbigi »

M wrote:
Fri Sep 16, 2022 3:22 pm
+1

As an example, In America, my wife and I will get 30k a year USD from social security as a couple plus medicare (government subsidized healthcare) when we are 67.

I have worked for 16 years full time. This assumes I quit tomorrow and never work. My wife has never worked in her life. This assumes she never works. If either of us work more in the future these figures go higher.
That sounds pretty amazing. Over here in Poland, your wife wouldn't get anything and you'd get back the amount of money you paid in social security contributions (part of employment taxes), portioned into monthly payments (basically a state-run annuity).
On the other hand, from what I gather, the system in UK is way less generous than in US. Over there, if you work for 40 (?) years of your life, you will qualify for around 1000 pounds per month of pension. If you've worked less years, you'll be getting proportionally less. Sounds almost too bad to be true for a developed country, so maybe I'm missing something.

flying_pan
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Re: The 4% Rule – A Castle in the Air

Post by flying_pan »

M wrote:
Fri Sep 16, 2022 3:22 pm
Of course - our government could take these things all away tomorrow. My counter argument to this is - we live in a country founded by rebels who overthrew our previous government by force over smaller matters. Everyone has the legal right to own firearms, and if you tell a few tens of millions of people you are taking away their source of food, some of them might have just enough money left to go buy a sniper rifle and 50 rounds of ammo or something. Some of the politicians in America are scared of the voters for reasons beyond just getting voted out, and it's not uncommon to find armed militias marching right outside government buildings even in normal times.
I agree that social nets will only expand in the US. The main reason being that so many people rely on them that phasing out is nearly impossible, and while they'll need to either adjust taxes for SS, raise the max bracket or just lower payments, they will never get rid of it. The biggest social net issue in USA is healthcare, and even that is covered through ACA or Medicaid if you have low income; and for seniors, healthcare is covered through Medicare.

I don't even think any threat will be needed, anybody who proposes to cut it out will be voted out and the next person will be very careful not to propose something like that.

As for the main topic, I guess 4% will work well until it doesn't. But as M said before, it is sort of a risk tolerance: how much are willing to bet that this will be enough. Many people already have elaborate protections, be it house equity, family connections, various local programs, access to part-time jobs, an option to lower expenses. E.g. in the US, I bet for many even "failed" 4% would mean easy lasting until 62/67/60 (whatever is more convenient to apply for Social Security) and then it would supplement them back to below 4%.

WFJ
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Re: The 4% Rule – A Castle in the Air

Post by WFJ »

There appear to be two issues with any 4% discussion. 1. Is it robust? 2. Are there exceptions?

1. Set up a hypothesis test

Ho = 4% rule is not a viable retirement strategy for a 50 yr duration
Ha = 4% is a viable retirement strategy for a 50 yr duration

Then test the statements and determine what level of significance you are comfortable with. At the 10%, 5% and 1%, I fail to reject Ho, and thus it is not a viable retirement strategy. With strict assumptions, the significance level is around 20%, meaning there is an 80% chance it works and 20% chance it does not. Mainly due to the duration of the estimate, small changes in the assumptions reduces this level of significance to completely random for a 50-year duration.

A more valuable way to approach the issue would be to create a confidence interval estimate rather than a point estimate SWR. Something like "The 90% confidence for a 50 yr SWR, would be between -0.5% to 7%" but requires more work than the relatively easy point estimate provided by 4% rule and why point estimates are favored by FIRE believers. One would need a 99% interval that did not include a negative number (meaning one has to return to work) to have a good estimate for an SWR.

2. As some learn the hard way, having a card that says "healthcare" does not always provide actual care, kind of like playing the lottery, some win but most lose. Some go broke and end up in pleasant retirement homes with great food, activities in amazing locations, others end up in less desirable situations. One has to assume that these lucky opportunities will still be available 40+ years in the future and one will have the ability to locate these, which is a little risky.

M
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Re: The 4% Rule – A Castle in the Air

Post by M »

zbigi wrote:
Fri Sep 16, 2022 3:57 pm
That sounds pretty amazing. Over here in Poland, your wife wouldn't get anything and you'd get back the amount of money you paid in social security contributions (part of employment taxes), portioned into monthly payments (basically a state-run annuity).
On the other hand, from what I gather, the system in UK is way less generous than in US. Over there, if you work for 40 (?) years of your life, you will qualify for around 1000 pounds per month of pension. If you've worked less years, you'll be getting proportionally less. Sounds almost too bad to be true for a developed country, so maybe I'm missing something.
Yes - you are missing something...The 16 years I have worked I have made slightly more money, and thus paid more into social security than a typical American has made during their entire working career. Also my wife and I have been married over ten years, which means she qualifies for 50% of my amount without impacting the amount I get, despite never working.

I have read somewhere that the average social security check in America is around $1,500 USD /month, so my situation might appear slightly better than average. We do have to pay more for healthcare though...Our Medicare does not make healthcare all free - it is more like a limited heavily subsidized healthcare. People often buy additional insurance as well. So probably on average we may get more per month but in America we also pay more for medical care, even in old age, so I think it evens out to be similar to other developed countries.

Also I should mention - before anyone gets confused. In America we have several different distinct systems to help pay for medical care. Even Americans get two of them confused all the time.

-Medicare is a limited heavily subsidized form of healthcare available to old people who worked at least ten years or who is married to someone for ten years who has worked at least ten years. It reduces the cost of healthcare but the healthcare itself is not free. Thus old people may still pay a high amount for healthcare compared to other countries.

-Medicaid is a free healthcare for low income Americans regardless of age. This is typically free, or virtually free, but not all medical providers will accept it and service may be free but also...sub optimal. For example, I have noticed that doctors where I live who accept Medicaid have months long waiting lists, vs doctors who do not you can get in next week.

steveo73
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Re: The 4% Rule – A Castle in the Air

Post by steveo73 »

chenda wrote:
Fri Sep 16, 2022 11:05 am
It sounds like Australia's system is very similar to most developed countries.
Why the extreme pessimism then ?

My opinion is that this is all about false expenses and it has nothing at all to do with WR's being unsafe below say 5%.

steveo73
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Re: The 4% Rule – A Castle in the Air

Post by steveo73 »

M wrote:
Fri Sep 16, 2022 3:22 pm
I struggle to imagine a scenario where:

A) The government is still functional
B) These social safety net programs are all gone
C) 2% Withdrawal rate fails
D) 1% Withdrawal rate succeeds
Those WR figures are way way way (I could keep going here) too high based on your post.

I wonder if you guys have any idea what the assumptions of the 4% rule are.

Assumptions:-

1. No social security.
2. No future earnings.
3. No decrease in spending ever.

In 95% of cases your money lasted 30 years.

There has to be something else going on here.

It's extreme pessimism or something else like:-

1. Your expenses are so tight they are unrealistic.
2. You are investing in some sort of customized portfolio.

In other words you aren't arguing against the 4% rule you are arguing against your implementation of a retirement plan.

It'd be good to get to the real issue here because it ain't the data surrounding the 4% rule.
Last edited by steveo73 on Fri Sep 16, 2022 8:20 pm, edited 3 times in total.

steveo73
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Re: The 4% Rule – A Castle in the Air

Post by steveo73 »

flying_pan wrote:
Fri Sep 16, 2022 3:58 pm
Many people already have elaborate protections, be it house equity, family connections, various local programs, access to part-time jobs, an option to lower expenses. E.g. in the US, I bet for many even "failed" 4% would mean easy lasting until 62/67/60 (whatever is more convenient to apply for Social Security) and then it would supplement them back to below 4%.
Exactly.

I understand there may be specific situations that don't work out but those have to be articulated and they have to be specific to your situation. It can't be a blanket rule which appears to be the default line of thinking here.

It's like this - the thread title of this thread is clearly irrational. It might be specific for your situation but there would have to be some good reasons. It clearly isn't true at all based on living in developed countries based on the details that have been provided.
Last edited by steveo73 on Fri Sep 16, 2022 5:51 pm, edited 1 time in total.

steveo73
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Re: The 4% Rule – A Castle in the Air

Post by steveo73 »

WFJ wrote:
Fri Sep 16, 2022 4:35 pm
Ho = 4% rule is not a viable retirement strategy for a 50 yr duration
Ha = 4% is a viable retirement strategy for a 50 yr duration
Who is retiring for 50 years and why is this is the case ?

That is a big time frame.

Just to put it in perspective. I'm 49 and I retired at say 46. My money doesn't have to last to 50. It has to last to 67. So in effect it's a 20 year time frame.

Let's use a realistic hypothesis. The 4% rule is over a 30 year time frame with pretty harsh assumptions.
WFJ wrote:
Fri Sep 16, 2022 4:35 pm
One has to assume that these lucky opportunities will still be available 40+ years in the future and one will have the ability to locate these, which is a little risky.
Yep but we are talking 40+ years into the future. If you want to keep working to protect yourself against all sorts of potential issues you can do it but that is an endless cycle.

I think this is more about setting yourself up for failure. If you stick to trying to manage extreme events you fail because you work too long. I'll add you might not even be able to manage those extreme events anyway.

Then when people are using really tight expenses to complete their calculations it just sounds like a whole bunch of mental gymnastics to try and convince yourself you are somehow right and everyone else is wrong.

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