Inverse to the 4% Rule
Inverse to the 4% Rule
So this is a purely theoretical question that has been on my mind for the past couple of days. The way I understand the 4% rule is that it's basically the average of the market return, discounted for sequence of returns risk, high valuations, etc. Is there an inverse to the rule during accumulation? Should I assume a higher than average return because I am adding money from my paycheck rather than withdrawing it? It feels like that should be the case mathematically, but I'm not really sure how to think through the problem.
Re: Inverse to the 4% Rule
The calculation of the savings rate during the accumulation phase should account for an increasing bonds glide path and portfolio size risk (which is the risk you won't get average returns when your portfolio is larger and you most need them).
The simplest way I know, and what I tell my kids, is to save a percentage equal to half your age. Edit: Not an inverse but the nearest thing I know to a percent rule for accumulation.
I'm sure there are Monte Carlo tools that can calculate the likelihood a particular savings rate will work. The FIRE community would be a good place to look for these tools.
The simplest way I know, and what I tell my kids, is to save a percentage equal to half your age. Edit: Not an inverse but the nearest thing I know to a percent rule for accumulation.
I'm sure there are Monte Carlo tools that can calculate the likelihood a particular savings rate will work. The FIRE community would be a good place to look for these tools.
Last edited by L84SUPR on Mon Sep 13, 2021 1:14 pm, edited 1 time in total.
Re: Inverse to the 4% Rule
That's not what it is.
The 4% rule is the result of a study that showed that in most past 30year periods they looked at, withdrawing 4% of your portfolio each year would allow the portfolio to last the full 30 years. This is also how people came up with the goal of retiring with at least 25x anticipated annual spending saved up.
If you think you'll need to have a smaller withdrawal rate than 4% in the future, then you would need to up the goal. For instance, with a 3% withdrawal rate, you'd want 33x annual spending saved.
"The only thing that makes life possible is permanent, intolerable uncertainty; not knowing what comes next." ~Ursula LeGuin
Re: Inverse to the 4% Rule
Beensabu wrote: ↑Mon Sep 13, 2021 12:44 pmThat's not what it is.
The 4% rule is the result of a study that showed that in most past 30year periods they looked at, withdrawing 4% of your portfolio each year would allow the portfolio to last the full 30 years. This is also how people came up with the goal of retiring with at least 25x anticipated annual spending saved up.
If you think you'll need to have a smaller withdrawal rate than 4% in the future, then you would need to up the goal. For instance, with a 3% withdrawal rate, you'd want 33x annual spending saved.
It is not 4% of your portfolio each year.
The "4% rule" studied withdrawing 4% of the initial portfolio value the first year of retirement, and then adjusting the withdrawal amount by inflation each year, regardless of what the portfolio does. In each subsequent year, this could end up being much less of your portfolio (like 3% or less) if markets do well, or it could end up being much more of your portfolio (like 5% or more) if markets perform poorly. The idea was to study what level of constant purchasing power could be maintained by a portfolio.
Once in a while you get shown the light, in the strangest of places if you look at it right.

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Re: Inverse to the 4% Rule
A key aspect of rule is having a nonnegative balance after 30 years. What do you want the balance to be after how many years of accumulation?
Re: Inverse to the 4% Rule
Right.Beensabu wrote: ↑Mon Sep 13, 2021 12:44 pmThat's not what it is.
The 4% rule is the result of a study that showed that in most past 30year periods they looked at, withdrawing 4% of your portfolio each year would allow the portfolio to last the full 30 years. This is also how people came up with the goal of retiring with at least 25x anticipated annual spending saved up.
OP, there's an excellent writeup describing the analysis that generated the 4% rule over at the FIRECalc site: https://www.firecalc.com/intro.php
A similar kind of analysis could be done with synthetic data, using a Monte Carlo simulation to generate randomly varying economic conditions and market returns, but basic the concept would be the same: Produce a whole bunch of historically real or simulated retirements, and statistically analyze them to see how much spending a given portfolio over a given retirement duration could support, within a specified confidence interval.
"Discipline matters more than allocation.” ─William Bernstein
Re: Inverse to the 4% Rule
No. Not right. Please see my comment above.iceport wrote: ↑Mon Sep 13, 2021 1:03 pmRight.Beensabu wrote: ↑Mon Sep 13, 2021 12:44 pmThat's not what it is.
The 4% rule is the result of a study that showed that in most past 30year periods they looked at, withdrawing 4% of your portfolio each year would allow the portfolio to last the full 30 years. This is also how people came up with the goal of retiring with at least 25x anticipated annual spending saved up.
OP, there's an excellent writeup describing the analysis that generated the 4% rule over at the FIRECalc site: https://www.firecalc.com/intro.php
A similar kind of analysis could be done with synthetic data, using a Monte Carlo simulation to generate randomly varying economic conditions and market returns, but basic the concept would be the same: Produce a whole bunch of historically real or simulated retirements, and statistically analyze them to see how much spending a given portfolio over a given retirement duration could support, within a specified confidence interval.
Once in a while you get shown the light, in the strangest of places if you look at it right.
Re: Inverse to the 4% Rule
That's not at all how the "4% rule" was derived.
If you really want to know, search for "Bengen Safemax".
No. That doesn't follow.Should I assume a higher than average return because I am adding money from my paycheck rather than withdrawing it?
Just remember: it's not a lie if you believe it.
Re: Inverse to the 4% Rule
Right. The constant 4% is wrong.marcopolo wrote: ↑Mon Sep 13, 2021 1:05 pmNo. Not right. Please see my comment above.iceport wrote: ↑Mon Sep 13, 2021 1:03 pmRight.Beensabu wrote: ↑Mon Sep 13, 2021 12:44 pmThat's not what it is.
The 4% rule is the result of a study that showed that in most past 30year periods they looked at, withdrawing 4% of your portfolio each year would allow the portfolio to last the full 30 years. This is also how people came up with the goal of retiring with at least 25x anticipated annual spending saved up.
OP, there's an excellent writeup describing the analysis that generated the 4% rule over at the FIRECalc site: https://www.firecalc.com/intro.php
A similar kind of analysis could be done with synthetic data, using a Monte Carlo simulation to generate randomly varying economic conditions and market returns, but basic the concept would be the same: Produce a whole bunch of historically real or simulated retirements, and statistically analyze them to see how much spending a given portfolio over a given retirement duration could support, within a specified confidence interval.
But the writeup at FIRECalc is still excellent. And the rest of the comment is still valid, without getting into specifics.
"Discipline matters more than allocation.” ─William Bernstein
Re: Inverse to the 4% Rule
I would also question whether Monte Carlo simulation truly generate realistic economic conditions. Unless, one does some pretty complex things in their Monte Carlo, each subsequent year is a completely independent event, so when you generate large number of trials, you end up with some very long strings of good and poor performing years, the likes of which have never been seen, and might even be physically impossible. The result is that most Monte Carlo simulation end up with heavier tails (on both ends) than is likely to be realistic. That does not mean they are without value, but this point should be taken into account when considering the results.iceport wrote: ↑Mon Sep 13, 2021 1:10 pmRight. The constant 4% is wrong.marcopolo wrote: ↑Mon Sep 13, 2021 1:05 pmNo. Not right. Please see my comment above.iceport wrote: ↑Mon Sep 13, 2021 1:03 pmRight.Beensabu wrote: ↑Mon Sep 13, 2021 12:44 pmThat's not what it is.
The 4% rule is the result of a study that showed that in most past 30year periods they looked at, withdrawing 4% of your portfolio each year would allow the portfolio to last the full 30 years. This is also how people came up with the goal of retiring with at least 25x anticipated annual spending saved up.
OP, there's an excellent writeup describing the analysis that generated the 4% rule over at the FIRECalc site: https://www.firecalc.com/intro.php
A similar kind of analysis could be done with synthetic data, using a Monte Carlo simulation to generate randomly varying economic conditions and market returns, but basic the concept would be the same: Produce a whole bunch of historically real or simulated retirements, and statistically analyze them to see how much spending a given portfolio over a given retirement duration could support, within a specified confidence interval.
But the writeup at FIRECalc is still excellent. And the rest of the comment is still valid, without getting into specifics.
Once in a while you get shown the light, in the strangest of places if you look at it right.
Re: Inverse to the 4% Rule
It is indeed true that market volatility, the reason for sequence of return risk, affects you during the accumulation phase. Consider two situations:
1. market returns 20% in year 1 and 0% in year two. Market CAGR is 9.5%. You invest $1000 at the beginning of each year. At the end you have $2200.
2. market returns 0% in year one and 20% in year two. Same CAGR. But now at the end you have $2400
Same CAGR but more money in case 2.
Basically, for the same CAGR, you do better if there are below average returns when your portfolio is small and above average returns when your portfolio is big.
1. market returns 20% in year 1 and 0% in year two. Market CAGR is 9.5%. You invest $1000 at the beginning of each year. At the end you have $2200.
2. market returns 0% in year one and 20% in year two. Same CAGR. But now at the end you have $2400
Same CAGR but more money in case 2.
Basically, for the same CAGR, you do better if there are below average returns when your portfolio is small and above average returns when your portfolio is big.
Re: Inverse to the 4% Rule
I think jj45 is closest to understanding what I'm asking about.
I totally agree with the rest of ya'll that in the drawdown period, it should be based on the original amount withdrawn adjusted for inflation or one of the other rules (VPW, CAPE based changes, etc). What I was getting at is that the reason that the 4% rule is less than the average return of the market is due to SOR risk, because if there is a recession in the early years, and you withdraw money, you can't regain that, even if the market has normal average returns over your retirement. So it seems to me that it would follow that if you are doing the inverse of withdrawing, which is contributing, you should get "higher than average" returns because of the inverse of SOR risk.jj45 wrote: ↑Mon Sep 13, 2021 2:31 pm It is indeed true that market volatility, the reason for sequence of return risk, affects you during the accumulation phase. Consider two situations:
1. market returns 20% in year 1 and 0% in year two. Market CAGR is 9.5%. You invest $1000 at the beginning of each year. At the end you have $2200.
2. market returns 0% in year one and 20% in year two. Same CAGR. But now at the end you have $2400
Same CAGR but more money in case 2.
Basically, for the same CAGR, you do better if there are below average returns when your portfolio is small and above average returns when your portfolio is big.
Re: Inverse to the 4% Rule
Yes. No.
During withdrawals you withdraw less than you would if returns were constant. During contributions you contribute more than you would if returns were constant. See this thread.
Sequence of returns risk while accumulating
Ron
Money is fungible 
Abbreviations and Acronyms
Re: Inverse to the 4% Rule
Thanks, this is exactly what I was looking for, the SOR risk is basically the same, but at the end of accumulation rather than the beginning of retirement, right? The transition is the scary partOicuryy wrote: ↑Mon Sep 13, 2021 3:32 pmYes. No.
During withdrawals you withdraw less than you would if returns were constant. During contributions you contribute more than you would if returns were constant. See this thread.
Sequence of returns risk while accumulating
Ron
 firebirdparts
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Re: Inverse to the 4% Rule
Very true.
The original question is an unusually good question; I've not seen as much quantitative work on it. I never got much past "save all you can" early on. I had seen lots of rules of thumb, you know. "Pay yourself first" and 10% might have been a rule of thumb. 15% is certainly a wellknown rule of thumb. It's pretty challenging when you're young and trying to fill your house with furniture and window treatments.
When I started working, 401k's had just been invented and I always faced limitations on how much I could add. They've changed a lot. the limits don't mean anything, really, but they've been a curiously effective guideline in my experience.
The original question is an unusually good question; I've not seen as much quantitative work on it. I never got much past "save all you can" early on. I had seen lots of rules of thumb, you know. "Pay yourself first" and 10% might have been a rule of thumb. 15% is certainly a wellknown rule of thumb. It's pretty challenging when you're young and trying to fill your house with furniture and window treatments.
When I started working, 401k's had just been invented and I always faced limitations on how much I could add. They've changed a lot. the limits don't mean anything, really, but they've been a curiously effective guideline in my experience.
A fool and your money are soon partners
Re: Inverse to the 4% Rule
To me the inverse of the 4% rule would be given a savings rate and a desired asset balance (25x of expenses for example) how long historically would it take to get that much money 95% of the time. I am not sure I have seen that study. People normally go 15% savings rate, 7% return, and you get there in about 30 years. I am guessing that the historical spread of results for contribution isn't as great as for withdrawal as the dollar cost averaging smooths out a lot of the variance AND since you aren't taking money out of the portfolio, you will recover from most market drops in a couple of years. It would be interesting to see what the spread is in reality. Would some people get to retire in 25 years and others have to work 35? Or is the spread greater than that. It would be interesting to see.
Realistically nobody has a remotely constant saving rate. Life happens...
Realistically nobody has a remotely constant saving rate. Life happens...
 vanbogle59
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Re: Inverse to the 4% Rule
I'm gonna guess this is what you are asking: "If I intend to live by the 4% rule when retired, what rule do I live by when accumulating?"Treefly wrote: ↑Mon Sep 13, 2021 12:20 pm So this is a purely theoretical question that has been on my mind for the past couple of days. The way I understand the 4% rule is that it's basically the average of the market return, discounted for sequence of returns risk, high valuations, etc. Is there an inverse to the rule during accumulation? Should I assume a higher than average return because I am adding money from my paycheck rather than withdrawing it? It feels like that should be the case mathematically, but I'm not really sure how to think through the problem.
As others have pointed out, the 4% rule comes with a few assumptions (length or retirement, % success, AA...)
If you know your assumptions for the accumulation phase, you can use the same "calculator".
Go here: https://firecalc.com/
put in your current portfolio, how long till retirement, AA....
Then keep adding to your periodic contributions until you get to 95% success of accumulating 25X (i.e. a onetime withdrawal of 25X in Y years)
THAT number is your "inverse 4%"

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Re: Inverse to the 4% Rule
duplicateTreefly wrote: ↑Mon Sep 13, 2021 3:39 pmThanks, this is exactly what I was looking for, the SOR risk is basically the same, but at the end of accumulation rather than the beginning of retirement, right? The transition is the scary partOicuryy wrote: ↑Mon Sep 13, 2021 3:32 pmYes. No.
During withdrawals you withdraw less than you would if returns were constant. During contributions you contribute more than you would if returns were constant. See this thread.
Sequence of returns risk while accumulating
Ron
Last edited by WyomingFIRE on Tue Sep 14, 2021 3:02 am, edited 1 time in total.

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Re: Inverse to the 4% Rule
http://pages.stern.nyu.edu/~adamodar/Ne ... retSP.html
the comment that the sequence of returns during the transition period from accumulation and the first few years of drawdown is so very true. i looked at this table of historical returns quite often when trying to decide if had enough or not to retire as got closer to that date. hope it helps you or others here. i did have a number of clients who got laid off during this period of time and a number just didn't have enough in their retirement accounts and ended up taking minimum wage jobs with no benefits to survive till social security became available . this lost decade for the S&P 5OO was painful for those that retired 12/31/1999 and starting drawing down in January 2000. the beginning and ending values for the S&P 500 was almost the same as started and would have been reduced further by the 10 years of withdrawals. observing that, i came to the conclusion one should be able to withstand that 50% bear market or another "lost decade" on the day you retire and start drawing down the assets earmarked for retirement needs.
the comment that the sequence of returns during the transition period from accumulation and the first few years of drawdown is so very true. i looked at this table of historical returns quite often when trying to decide if had enough or not to retire as got closer to that date. hope it helps you or others here. i did have a number of clients who got laid off during this period of time and a number just didn't have enough in their retirement accounts and ended up taking minimum wage jobs with no benefits to survive till social security became available . this lost decade for the S&P 5OO was painful for those that retired 12/31/1999 and starting drawing down in January 2000. the beginning and ending values for the S&P 500 was almost the same as started and would have been reduced further by the 10 years of withdrawals. observing that, i came to the conclusion one should be able to withstand that 50% bear market or another "lost decade" on the day you retire and start drawing down the assets earmarked for retirement needs.
Re: Inverse to the 4% Rule
The theoretical inverse would be current salary times 25 divided by years worked, adjusted for raises and inflation and then adjusted for compounded interest over those years.
Easy enough to calculate if you make a few key assumptions, but I'm guessing those assumptions are what the heart of your question is.
But I suppose you can get a very rough idea if you simply assume zero growth.
Easy enough to calculate if you make a few key assumptions, but I'm guessing those assumptions are what the heart of your question is.
But I suppose you can get a very rough idea if you simply assume zero growth.
Re: Inverse to the 4% Rule
The closest I've seen is this paper by Wade Pfau that looks at the "Safe Savings Rate" that met the retirement savings goal over a 30year accumulation even in the worst case. It focuses too much on replacing income for my tastes, as I think your portfolio size relative to annual retirement spending is the more informative metric. But it's an interesting way to think about it, for sure.
Re: Inverse to the 4% Rule
Worst case years to retire don't occur only because the return for the period of retirement occurs in a bad sequence. Bad years to retire can also occur because the entire period of the retirement has poor real returns on average.
More specifically, a sequence of returns problem occurs when for a given average return for a period the lowest returns occur early and the higher returns occur late, while withdrawing money. It can also be that one is experiencing a retirement for which the average return is poor compared to a retirement during some other period. It would also be likely that both effects would plague the same retirement compared to one at a different time. Also bad sequence of returns does not have to mean and probably usually isn't a market crash but rather just a secular bear market.
The classic historical example of a bad time to retire is early to midsixties. Someone can characterize the litany of problems plaguing a retirement started that year. A comparison can be made to a classic good year to retire, such as 1982. The latter probably illustrates a good sequence of returns, but I don't know how 19822012 stands for average return for the period compared to 19661996.
More specifically, a sequence of returns problem occurs when for a given average return for a period the lowest returns occur early and the higher returns occur late, while withdrawing money. It can also be that one is experiencing a retirement for which the average return is poor compared to a retirement during some other period. It would also be likely that both effects would plague the same retirement compared to one at a different time. Also bad sequence of returns does not have to mean and probably usually isn't a market crash but rather just a secular bear market.
The classic historical example of a bad time to retire is early to midsixties. Someone can characterize the litany of problems plaguing a retirement started that year. A comparison can be made to a classic good year to retire, such as 1982. The latter probably illustrates a good sequence of returns, but I don't know how 19822012 stands for average return for the period compared to 19661996.
Re: Inverse to the 4% Rule
Decades ago I saw a calculation from a small investor group that showed investing 20% in the S&P500 for 20 years allowed you to retire in 40 years (not investing anything additional for the last 20 years) at the same income you retire at. I cannot vouch for those numbers, and they did not consider SORR, but these seem to be the right type of inversequestions.Tyler9000 wrote: ↑Mon Sep 13, 2021 9:52 pmThe closest I've seen is this paper by Wade Pfau that looks at the "Safe Savings Rate" that met the retirement savings goal over a 30year accumulation even in the worst case. It focuses too much on replacing income for my tastes, as I think your portfolio size relative to annual retirement spending is the more informative metric. But it's an interesting way to think about it, for sure.

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Re: Inverse to the 4% Rule
Very different mathematical problems. For distributions, compounding increases your nest, while withdrawals decrease them. That's why it's interesting to find an 'optimal'. In contributions, your nest only increases.
4% rule is usually calculated for 30 years. But you could come up with a PWR (3%?) independent of time.
For contributions, there is not such a concept of permanent. The more time you invest, the biggest nest you'll have.
4% rule is usually calculated for 30 years. But you could come up with a PWR (3%?) independent of time.
For contributions, there is not such a concept of permanent. The more time you invest, the biggest nest you'll have.
Re: Inverse to the 4% Rule
Do you want to backtest constant real annual contributions? See this post by siamond and the two following posts in the thread I linked to above.
Ron
Ron
Money is fungible 
Abbreviations and Acronyms
Re: Inverse to the 4% Rule
In real life, isn't it saveallyoucan for as long as is necessary? Save pay raises since your mortgage is a fixed rate, and just absorb the inflation of your other expenses i.e. keep driving the same car after it is paid off. Buy knowntobereliable used vehicles to reduce that cost.
OP, my suggestion is to not strive to find the minimum amount to periodically save for retirement, but to look for ways to boost savings, knowing you only have to work until you have saved enough to retire.
OP, my suggestion is to not strive to find the minimum amount to periodically save for retirement, but to look for ways to boost savings, knowing you only have to work until you have saved enough to retire.
 willthrill81
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Re: Inverse to the 4% Rule
And while it's perhaps counterintuitive, a good sequence of returns for retirees is actually (relatively) bad for accumulators. Retirees want the best returns in the beginning and the worst returns in the end, but accumulators would rather have the worst returns first and followed by the best returns.Oicuryy wrote: ↑Mon Sep 13, 2021 3:32 pmYes. No.
During withdrawals you withdraw less than you would if returns were constant. During contributions you contribute more than you would if returns were constant. See this thread.
Sequence of returns risk while accumulating
Ron
In reality, the two factors at work are (1) the average returns over a given period and (2) the specific sequence of those returns. In the thread linked to above, I showed that over at least one historic period, the average returns accounted for 64% of the variance in the final portfolio balance, and the sequence of the returns accounted for the other 36% in the variance. So yes, sequence of returns is a sizable factor for accumulators.
“Good and ill have not changed since yesteryear; nor are they one thing among Elves and Dwarves and another among Men.” J.R.R. Tolkien, The Lord of the Rings
Re: Inverse to the 4% Rule
Does the 15% guideline have any basis in math and history or is just a number someone pulled out of a hat as something achievable that would give ok results on average?

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Re: Inverse to the 4% Rule
Thanks for the link. Figure 5 and the text preceding it gives a simple answer based on historical returns and inflation: use a savings rate of 16.62%. Using that rate, the balance of the portfolio at the end of accumulation would have been just enough to support 30 years of inflationadjusted withdrawals.Tyler9000 wrote: ↑Mon Sep 13, 2021 9:52 pm The closest I've seen is this paper by Wade Pfau that looks at the "Safe Savings Rate" that met the retirement savings goal over a 30year accumulation even in the worst case. It focuses too much on replacing income for my tastes, as I think your portfolio size relative to annual retirement spending is the more informative metric. But it's an interesting way to think about it, for sure.
Unfortunately, it would be necessary to know at the end of accumulation what initial withdrawal rate resulted in portfolio depletion at 30 years. For example, when starting withdrawals in 1980, one would need to know that the maximum sustainable withdrawal rate at that time was 8%, as indicated on Figure 3
Re: Inverse to the 4% Rule
I was also going to mention the Safe Savings Rate paper. One caveat: he assumes that Social Security will cover 50% of your spending, so your portfolio only needs to make up the other 50%. That seems unlikely to be exactly true for very many people, so his exact conclusion should be seen more as an example rather than The Answer.Tyler9000 wrote: ↑Mon Sep 13, 2021 9:52 pmThe closest I've seen is this paper by Wade Pfau that looks at the "Safe Savings Rate"
I think a better approach is Waring & Siegel's "The Only Saving Rate Article You Will Ever Need"[1]. It is basically the accumulation version of a variable withdrawal strategy. For anyone familiar with VPW or other PMTbased withdrawal strategies....you just do the same thing but for accumulation.
One "downside" to Waring & Siegel's approach is that people are likely to have some sticker shock at exactly how expensive it actually is to selffund one's retirement for decades on end. Their approach often calls for you to be saving 25% or so, until equity returns start helping to move the needle. Here's an example from their paper of how it would work for someone with a 60/40 portfolio who started working in the 1942 and retired in 1981.
[1]: https://larrysiegel.org/theonlysaving ... erneed2/
 teen persuasion
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Re: Inverse to the 4% Rule
Started working in 1942 at $100k?
Re: Inverse to the 4% Rule
Ha! They could have retired in 1945. Few yrs at that number and done.

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Re: Inverse to the 4% Rule
That shows the absurdity of the some of the stuff that is being peddled as "research" even by the wellrespected authors such as Larry Siegel. By the way, I loved his latest book and I have tremendous respect for him. I am just saying that applying standard mathematical concepts to stock market is full of traps.
Re: Inverse to the 4% Rule
Ah  thanks for pointing that out! I kept scratching my head trying to figure out where he was coming up with the 50% replacement rate, but assuming the other half comes from social security makes sense. I completely agree that assumptions like that tend to make the numbers less useful in terms of universal application.AlohaJoe wrote: ↑Tue Sep 14, 2021 2:13 am I was also going to mention the Safe Savings Rate paper. One caveat: he assumes that Social Security will cover 50% of your spending, so your portfolio only needs to make up the other 50%. That seems unlikely to be exactly true for very many people, so his exact conclusion should be seen more as an example rather than The Answer.
 willthrill81
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Re: Inverse to the 4% Rule
That would be an annual income of nearly $1.7 million in 2021 dollars.
The problem here wasn't applying math concepts to stocks; it was a completely erroneous starting salary. Heck, even today, exceptionally few workers start out making $100k.wrongfunds wrote: ↑Tue Sep 14, 2021 8:27 am That shows the absurdity of the some of the stuff that is being peddled as "research" even by the wellrespected authors such as Larry Siegel. By the way, I loved his latest book and I have tremendous respect for him. I am just saying that applying standard mathematical concepts to stock market is full of traps.
“Good and ill have not changed since yesteryear; nor are they one thing among Elves and Dwarves and another among Men.” J.R.R. Tolkien, The Lord of the Rings
Re: Inverse to the 4% Rule
And? You realise the numbers can be scaled, right?
Re: Inverse to the 4% Rule
It doesn't matter. You can make the salary 2k and have that be 4k in 1981 (~25k nominal) and nothing changes. But much like VPW this scheme is absurd because it makes you a slave to recent market conditions. It is absurd to not save much in your 50s after saving like made in your 30s,40s and then doing the same thing in your 60s. And the good case is equally bad. Scrimping in 30s, 40s so you don't have to save in your 50s,60s also makes about zero sense. It is easy to write down equations. Doesn't mean the output they generate makes sense.willthrill81 wrote: ↑Tue Sep 14, 2021 9:47 amThat would be an annual income of nearly $1.7 million in 2021 dollars.
The problem here wasn't applying math concepts to stocks; it was a completely erroneous starting salary. Heck, even today, exceptionally few workers start out making $100k.wrongfunds wrote: ↑Tue Sep 14, 2021 8:27 am That shows the absurdity of the some of the stuff that is being peddled as "research" even by the wellrespected authors such as Larry Siegel. By the way, I loved his latest book and I have tremendous respect for him. I am just saying that applying standard mathematical concepts to stock market is full of traps.
 firebirdparts
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Re: Inverse to the 4% Rule
I actually like the idea of it, because it appeals to my profession, but in the end, you can only do that if you have money that’s not invested. Slavery and absurdity are not really the answer.
A fool and your money are soon partners

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Re: Inverse to the 4% Rule
Other sources of retirement income, such as Social Security, is not the only justification for using 50% replacement rate. Some preretirement expenses will no longer occur, such a contributing to a retirement portfolio. On the other hand, there can be additional expenses, such as the cost of medical insurance that is no longer subsidized by an employer.Tyler9000 wrote: ↑Tue Sep 14, 2021 9:09 am Ah  thanks for pointing that out! I kept scratching my head trying to figure out where he was coming up with the 50% replacement rate, but assuming the other half comes from social security makes sense. I completely agree that assumptions like that tend to make the numbers less useful in terms of universal application.
 teen persuasion
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Re: Inverse to the 4% Rule
But the scale makes no sense.
I did the same as willthrill, I googled what $100k in 1942 would be worth today, and got $1,675k. So in 80 years it doubled roughly 4 times, or roughly every 20 years to double once. The worker worked 40 years, so just from inflation his salary should have doubled twice, to $400k, and with more experience it should be even higher. And yet at retirement his ending salary is only about $200k.
Re: Inverse to the 4% Rule
I don't understand what any of that has to do with Waring & Siegel's paper. It seems clear you didn't read it.teen persuasion wrote: ↑Tue Sep 14, 2021 12:32 pmBut the scale makes no sense.
I did the same as willthrill, I googled what $100k in 1942 would be worth today, and got $1,675k. So in 80 years it doubled roughly 4 times, or roughly every 20 years to double once. The worker worked 40 years, so just from inflation his salary should have doubled twice, to $400k, and with more experience it should be even higher. And yet at retirement his ending salary is only about $200k.
All amounts are in inflationadjusted terms so your attempt to say they did the salary "wrong" are nonsensical.
Arguments that a $100,000 salary in 1942 are implausible just show they didn't read the paper and missed the point. The point is that you can plug in your actual salary to the methodology provided and then reevaluate every year. The way the math works you can divide the numbers in their example by 100 or 1,000 or 752 and everything still remains exactly the same.
Re: Inverse to the 4% Rule
No from inflation alone her salary would still be 100k 40 years later. Or 400 years. That is the whole point of doing the math using real dollars. 2% real growth is a pretty solid estimate.teen persuasion wrote: ↑Tue Sep 14, 2021 12:32 pmBut the scale makes no sense.
I did the same as willthrill, I googled what $100k in 1942 would be worth today, and got $1,675k. So in 80 years it doubled roughly 4 times, or roughly every 20 years to double once. The worker worked 40 years, so just from inflation his salary should have doubled twice, to $400k, and with more experience it should be even higher. And yet at retirement his ending salary is only about $200k.
 teen persuasion
 Posts: 1658
 Joined: Sun Oct 25, 2015 1:43 pm
Re: Inverse to the 4% Rule
Apologies, I have not yet read the paper. I was reacting purely to the chart posted.
I'm reading on a tablet, and have learned to NOT click on links likely to autodownload documents, been burned too many times when I expect to be redirected to a webpage.
I did suspect some normalization of the $ figures, with the $100k starting number. But the specific year references seemed to contradict that idea. Trying to map it mentally to our situation, it was counterintuitive (to me) to adjust historical income numbers for inflation.
I'm reading on a tablet, and have learned to NOT click on links likely to autodownload documents, been burned too many times when I expect to be redirected to a webpage.
I did suspect some normalization of the $ figures, with the $100k starting number. But the specific year references seemed to contradict that idea. Trying to map it mentally to our situation, it was counterintuitive (to me) to adjust historical income numbers for inflation.
 firebirdparts
 Posts: 2803
 Joined: Thu Jun 13, 2019 4:21 pm
Re: Inverse to the 4% Rule
It was assumed that the reader is not an idiot, and the text says so without drama. If you're working in constant 2021 dollars, lo and behold, the scale is great. But even that is irrelevant.
This is like saying we don't believe any information that was presented because the author misspelled "dollar". It's ridiculous. You don't win a prize for being banal.
A fool and your money are soon partners
Re: Inverse to the 4% Rule
The paper uses the specific year to show how the scheme performs differently given the starting points. There is an example for someone who retires in the 70s and by thier mid 40s never has to contribute again AND ends up with way more money than they need to replace half their income. This shows the poor sequence of returns (i.e. your last 15 years have a ~0% real return) effect.teen persuasion wrote: ↑Wed Sep 15, 2021 6:42 am Apologies, I have not yet read the paper. I was reacting purely to the chart posted.
I'm reading on a tablet, and have learned to NOT click on links likely to autodownload documents, been burned too many times when I expect to be redirected to a webpage.
I did suspect some normalization of the $ figures, with the $100k starting number. But the specific year references seemed to contradict that idea. Trying to map it mentally to our situation, it was counterintuitive (to me) to adjust historical income numbers for inflation.
The 100k is a good because it is a reasonable salary for the reader (i.e. easy for them to map to their situation) and it is pretty easy to do math off. And doing math in real numbers prevents you from thinking you will be absurdly wealthy (1k in 1941 is 6k in 1981) in 40 years.
It would be interesting to know where the persons saving 15% every year ended up with in these cases. Given the almost impossibility of implementing this scheme (i.e. saving 160k out of 216k is going require some very specific tax and living situations. In the standard case you are paying 40k in income tax, 10k in SS, and living on 6k), it doesn't seem very useful to think about implementing. And even if you could do it, it seems like a weird personality that is ok alternating between years of saving 0% and years of saving 20%+.
Re: Inverse to the 4% Rule
This comment really got me thinking, and it inspired me to build a tool that will allow people to find the safe savings rate for any portfolio and financial goal. For example, here's a chart that shows the full spread of savings rates since 1970 that were required for a USbased investor making $100k a year to grow a Classic 60/40 portfolio from $10k to $1mm. Note that all numbers are expressed in today's dollars and are adjusted for inflation.randomguy wrote: ↑Mon Sep 13, 2021 7:43 pm To me the inverse of the 4% rule would be given a savings rate and a desired asset balance (25x of expenses for example) how long historically would it take to get that much money 95% of the time. I am not sure I have seen that study. People normally go 15% savings rate, 7% return, and you get there in about 30 years. I am guessing that the historical spread of results for contribution isn't as great as for withdrawal as the dollar cost averaging smooths out a lot of the variance AND since you aren't taking money out of the portfolio, you will recover from most market drops in a couple of years. It would be interesting to see what the spread is in reality. Would some people get to retire in 25 years and others have to work 35? Or is the spread greater than that. It would be interesting to see.
For more info, here's a detailed explanation. I hope everyone finds it useful.
The Right Savings Rate Will Conquer Any Bear Market

 Posts: 2867
 Joined: Tue Dec 21, 2010 3:55 pm
Re: Inverse to the 4% Rule
A snide comment (just for fun!)
This tells me that even at 100% savings it will take at least 8 years to reach that number! Does that pass reasonableness test?
This tells me that even at 100% savings it will take at least 8 years to reach that number! Does that pass reasonableness test?
Re: Inverse to the 4% Rule
It does to me! But I'm not exactly unbiased.wrongfunds wrote: ↑Mon Sep 20, 2021 3:00 pm A snide comment (just for fun!)
This tells me that even at 100% savings it will take at least 8 years to reach that number! Does that pass reasonableness test?
For clarity, it took between 611 years (with 8 years as the approximate median) to accumulate $1mm saving $100k a year. Markets are messy, and nobody earns the average return every year.
Now is it reasonable to save 100% of your money for many years at a time? Probably not. If anyone can figure that out, I'd like to hear how! IMO, this just shows that some goals really do take time.

 Posts: 2867
 Joined: Tue Dec 21, 2010 3:55 pm
Re: Inverse to the 4% Rule
That 33% SSR for 20 years passes KlangFool's test for moderately high income where 1/3 goes to taxes, 1/3 spent and 1/3 invested.
You chart is interesting and is a must for younger crowd who are just starting to invest.
You chart is interesting and is a must for younger crowd who are just starting to invest.