## The 4% rule

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m@ver1ck
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Joined: Fri Sep 14, 2018 2:18 pm

### The 4% rule

Can someone point me to the math behind it? Or some calculators on how to simulate sequence of return events?
If I just go by a 4% withdrawal starting rate and keep increasing spend by 2% (inflation) every year, and say a conservative 6% return rate, I could go on living on that money forever... - which is probably the wrong way to think about it....

Thesaints
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Joined: Tue Jun 20, 2017 12:25 am

### Re: The 4% rule

The math behind the problem is hard. That's why the 4% is not a "rule", but simply the observation that backtesting a 60/40 portfolio, 4% real withdrawal did not deplete completely the capital over 30 years in 95% (iirc) of the cases.

The first thing to appreciate is that such a portfolio in the past had an average return of ~4.5% real. What it is going to be in the future, with bonds not even yielding 2% real, is another matter.

The second thing to appreciate is that a portfolio yielding 4% annually, supports 4% spending indefinitely. A portfolio yielding 4% on average may instead run out of money.

The third thing to appreciate is that in the backtesting study, portfolios reduced to a couple of hundred dollars on year 30 were considered "successful". Things are quite different in real life. The portfolio owner would get scared and reduce withdrawals (if at all possible) much earlier than that.
Last edited by Thesaints on Wed May 08, 2019 12:47 am, edited 2 times in total.

AlohaJoe
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### Re: The 4% rule

m@ver1ck wrote:
Wed May 08, 2019 12:20 am
Can someone point me to the math behind it? Or some calculators on how to simulate sequence of return events?

www.firecalc.com
If I just go by a 4% withdrawal starting rate and keep increasing spend by 2% (inflation) every year, and say a conservative 6% return rate, I could go on living on that money forever... - which is probably the wrong way to think about it....
Yep, that's the wrong way to think about it. Inflation is often more than 2%. And returns are often less than 6%.

mega317
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### Re: The 4% rule

Thesaints wrote:
Wed May 08, 2019 12:35 am
The math behind the problem is hard. That's why the 4% is not a "rule", but simply the observation that backtesting a 60/40 portfolio, 4% real withdrawal did not deplete completely the capital over 30 years in 95% (iirc) of the cases.
It's a 50/50 portfolio. I'm surprised there are so many pages of discussion on the "4% rule" which yes isn't a rule, with hardly anyone seeming to have read the study.

https://www.researchgate.net/profile/Ph ... tfolio.pdf

student
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### Re: The 4% rule

Take a look at https://www.bogleheads.org/wiki/Inflati ... t_spending and check out the retirement calculator listed there. In addition, personal capital and fidelity also have one that are good. (You have to create an account. Free for PC. I think it is free to create one at fidelity if you are not a customer.)

Wiggums
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### Re: The 4% rule

AlohaJoe
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Location: Saigon, Vietnam

### Re: The 4% rule

mega317 wrote:
Wed May 08, 2019 4:24 am
Thesaints wrote:
Wed May 08, 2019 12:35 am
The math behind the problem is hard. That's why the 4% is not a "rule", but simply the observation that backtesting a 60/40 portfolio, 4% real withdrawal did not deplete completely the capital over 30 years in 95% (iirc) of the cases.
It's a 50/50 portfolio.
Using historical financial market returns, the study suggests that portfolios of at least 75% stock provide 4% to 5% inflation-adjusted withdrawals.

Jack FFR1846
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### Re: The 4% rule

The Trinity Study

That's where the number came from.

Bogle: Smart Beta is stupid

mega317
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### Re: The 4% rule

AlohaJoe wrote:
Wed May 08, 2019 5:32 am
mega317 wrote:
Wed May 08, 2019 4:24 am
Thesaints wrote:
Wed May 08, 2019 12:35 am
The math behind the problem is hard. That's why the 4% is not a "rule", but simply the observation that backtesting a 60/40 portfolio, 4% real withdrawal did not deplete completely the capital over 30 years in 95% (iirc) of the cases.
It's a 50/50 portfolio.
Using historical financial market returns, the study suggests that portfolios of at least 75% stock provide 4% to 5% inflation-adjusted withdrawals.
If you're going to be snarky you should read past the abstract and pay attention to the thread. 4% withdrawal, adjusted for inflation, 30 years, 95% success was 50/50.

Seasonal
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### Re: The 4% rule

If 4% is really a hard and fast rule, you could continue 4% inflation adjusted withdrawals based on initial portfolio size despite massive portfolio declines, while if your portfolio increased you could reset and base 4% on the new larger portfolio size.

On the other hand, this may illustrate the absurdity of considering it a rule rather than a general guideline.

aristotelian
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### Re: The 4% rule

It is not based on any mathematical rule of thumb. It is based on backtested historical data. Your math is a decent way of thinking about it but the sequence of returns is an issue. Returns might average 6% but an early crash with no change in spending could be a problem.

Rudedog
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Joined: Wed Aug 01, 2018 3:15 pm

### Re: The 4% rule

25 years of retirement........4% withdrawals per year. 4% x 25 = 100%. Just a rough guess or rough guideline to follow.

alex_686
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Joined: Mon Feb 09, 2015 2:39 pm

### Re: The 4% rule

Jack FFR1846 wrote:
Wed May 08, 2019 5:43 am
The Trinity Study

That's where the number came from.

To extend a bit, the Trinity study is just a historical observation. It does not present a theory, so there is no math to understand behind the “rule”.
Former brokerage operations & mutual fund accountant. I hate risk, which is why I study and embrace it.

tennisplyr
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### Re: The 4% rule

Rudedog wrote:
Wed May 08, 2019 6:37 am
25 years of retirement........4% withdrawals per year. 4% x 25 = 100%. Just a rough guess or rough guideline to follow.
+1. Exactly
Those who move forward with a happy spirit will find that things always work out.

AlohaJoe
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### Re: The 4% rule

Jack FFR1846 wrote:
Wed May 08, 2019 5:43 am
The Trinity Study

That's where the number came from.
It actually came from William Bengen, not the Trinity Study. The Trinity Study came a few years later and simply replicated Bengen's work.

Jags4186
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### Re: The 4% rule

m@ver1ck wrote:
Wed May 08, 2019 12:20 am
Can someone point me to the math behind it? Or some calculators on how to simulate sequence of return events?
If I just go by a 4% withdrawal starting rate and keep increasing spend by 2% (inflation) every year, and say a conservative 6% return rate, I could go on living on that money forever... - which is probably the wrong way to think about it....
That’s because the 4% rule doesn’t say you can live on this money forever. It says you won’t run out of money after 30 years based on historical returns. Run out of money means you could have \$1 left at the end of year 30 and it was a success.

Wiggums
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### Re: The 4% rule

Rudedog wrote:
Wed May 08, 2019 6:37 am
25 years of retirement........4% withdrawals per year. 4% x 25 = 100%. Just a rough guess or rough guideline to follow.
Here is an article on 4% rule versus 25 times expenses

https://www.thebalance.com/dont-confuse ... umb-453920

elainet7
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### Re: The 4% rule

with very low bond yields, dividends half of what they were, and hi stock valuations, the 4% rule might not work
the Trinity study show nearly 100% success with stocks at 25%

mega317
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Joined: Tue Apr 19, 2016 10:55 am

### Re: The 4% rule

Wiggums wrote:
Wed May 08, 2019 6:59 am
Rudedog wrote:
Wed May 08, 2019 6:37 am
25 years of retirement........4% withdrawals per year. 4% x 25 = 100%. Just a rough guess or rough guideline to follow.
Here is an article on 4% rule versus 25 times expenses

https://www.thebalance.com/dont-confuse ... umb-453920
This from the article makes no sense and is not true.
This rule-of-thumb assumes you'll be able to generate an annualized real return of 4 percent per year.
If the portfolio grows at 4% real, and your withdrawals remain 4% real, that will sustain indefinitely. If that's your assumption then it is a wildly conservative withdrawal rate.

mega317
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### Re: The 4% rule

elainet7 wrote:
Wed May 08, 2019 7:03 am
the Trinity study show nearly 100% success with stocks at 25%
74%

ruralavalon
Posts: 18785
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Location: Illinois

### Re: The 4% rule

m@ver1ck wrote:
Wed May 08, 2019 12:20 am
Can someone point me to the math behind it? Or some calculators on how to simulate sequence of return events?
If I just go by a 4% withdrawal starting rate and keep increasing spend by 2% (inflation) every year, and say a conservative 6% return rate, I could go on living on that money forever... - which is probably the wrong way to think about it....
The "4% rule" is not a rule, it is not a withdrawal strategy, it is a planning tool that helps decide how much of a nest egg you might want to have at the start of retirement (e.g. 25 times annual spending for a 30 year retirement).

It is not calculation, it is an observation of what would have worked in the past. Boglehead's wiki, Trinity Study, "Table 3".
Last edited by ruralavalon on Wed May 08, 2019 7:50 am, edited 2 times in total.
"Everything should be as simple as it is, but not simpler." - Albert Einstein | Wiki article link:Getting Started

TheTimeLord
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### Re: The 4% rule

mega317 wrote:
Wed May 08, 2019 7:15 am
elainet7 wrote:
Wed May 08, 2019 7:03 am
the Trinity study show nearly 100% success with stocks at 25%
74%
From Early Retirement Now's Ultimate Guide to Safe Withdrawal Rates

https://earlyretirementnow.com/2016/12/ ... t-1-intro/

IMHO, Investing should be about living the life you want, not avoiding the life you fear. | Run, You Clever Boy! [9085]

MotoTrojan
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### Re: The 4% rule

elainet7 wrote:
Wed May 08, 2019 7:03 am
with very low bond yields, dividends half of what they were, and hi stock valuations, the 4% rule might not work
the Trinity study show nearly 100% success with stocks at 25%
Buybacks more than make up for the reduction in historical dividends and while yields on bonds have come down their real return may not be as off as you’d think.

MikeG62
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### Re: The 4% rule

m@ver1ck wrote:
Wed May 08, 2019 12:20 am
...and say a conservative 6% return rate
I do not believe that 6% is a "conservative" future return rate on a balanced portfolio (of equities and fixed income).
Real Knowledge Comes Only From Experience

Grt2bOutdoors
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### Re: The 4% rule

MikeG62 wrote:
Wed May 08, 2019 8:04 am
m@ver1ck wrote:
Wed May 08, 2019 12:20 am
...and say a conservative 6% return rate
I do not believe that 6% is a "conservative" future return rate on a balanced portfolio (of equities and fixed income).
Agree. I use 4% as a moderate return, 3% as conservative.
"One should invest based on their need, ability and willingness to take risk - Larry Swedroe" Asking Portfolio Questions

yousha
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### Re: The 4% rule

Does the RMD withdrawal abide by the 4% suggestion?

Grt2bOutdoors
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Location: New York

### Re: The 4% rule

m@ver1ck wrote:
Wed May 08, 2019 12:20 am
Can someone point me to the math behind it? Or some calculators on how to simulate sequence of return events?
If I just go by a 4% withdrawal starting rate and keep increasing spend by 2% (inflation) every year, and say a conservative 6% return rate, I could go on living on that money forever... - which is probably the wrong way to think about it....
Instead of increasing spending by inflation, you should increase it only when the portfolio value has actually increased above the 2% inflation factor. If you continually withdraw at a 6% rate while the portfolio value either stays the same or decreases all you are doing is ensuring the value of the portfolio will decline at a faster rate and cement your way to portfolio failure. An interesting factoid, for NYS/NYC pension holders, the pension will pay a COLA on the first \$18K of pension and only after 5 years has passed and only up to a 3% inflation factor. You may want to consider something like that in your calculations, then its likely your portfolio value could let you live on that money forever.
"One should invest based on their need, ability and willingness to take risk - Larry Swedroe" Asking Portfolio Questions

Grt2bOutdoors
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### Re: The 4% rule

yousha wrote:
Wed May 08, 2019 8:14 am
Does the RMD withdrawal abide by the 4% suggestion?
No, RMD's are based on your expected life expectancy. You can find the RMD table at www.irs.gov
"One should invest based on their need, ability and willingness to take risk - Larry Swedroe" Asking Portfolio Questions

22twain
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### Re: The 4% rule

yousha wrote:
Wed May 08, 2019 8:14 am
Does the RMD withdrawal abide by the 4% suggestion?
I suggest you clarify what you mean by "abide by the 4% suggestion."
Help save endangered words! When you write "princiPLE", make sure you don't really mean "princiPAL"!

JoMoney
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### Re: The 4% rule

yousha wrote:
Wed May 08, 2019 8:14 am
Does the RMD withdrawal abide by the 4% suggestion?
It depends... but generally for a single person over age 70 the RMD would be a larger percentage of the IRA's balance...
But there is no requirement to spend all of your RMD (just reinvest outside of an IRA), no requirement to hold all of your portfolio inside an IRA (or any account subject to RMDs), and a very low probability that a 70 year old will need a portfolio to last 30 years (life expectancy is closer to half that).
"To achieve satisfactory investment results is easier than most people realize; to achieve superior results is harder than it looks." - Benjamin Graham

mega317
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### Re: The 4% rule

TheTimeLord wrote:
Wed May 08, 2019 7:48 am
mega317 wrote:
Wed May 08, 2019 7:15 am
elainet7 wrote:
Wed May 08, 2019 7:03 am
the Trinity study show nearly 100% success with stocks at 25%
74%
From Early Retirement Now's Ultimate Guide to Safe Withdrawal Rates

https://earlyretirementnow.com/2016/12/ ... t-1-intro/

I didn't read your link --what is the methodology? It could be similar because your chart has an 80 where trinity has a 74.

The Wizard
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### Re: The 4% rule

Grt2bOutdoors wrote:
Wed May 08, 2019 8:15 am
yousha wrote:
Wed May 08, 2019 8:14 am
Does the RMD withdrawal abide by the 4% suggestion?
No, RMD's are based on your expected life expectancy. You can find the RMD table at www.irs.gov
Actually, it sort of does "abide".
It starts at 3.65% which isn't far from 4%.
The 4% rule increases withdrawal by inflation each year, while the RMD formula doesn't care about inflation but does care about growth or shrinkage in your remaining portfolio year to year.

Under some conditions, a thirty year graph of the two functions will look rather similar...
Attempted new signature...

TheTimeLord
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### Re: The 4% rule

mega317 wrote:
Wed May 08, 2019 8:38 am
TheTimeLord wrote:
Wed May 08, 2019 7:48 am
mega317 wrote:
Wed May 08, 2019 7:15 am
elainet7 wrote:
Wed May 08, 2019 7:03 am
the Trinity study show nearly 100% success with stocks at 25%
74%
From Early Retirement Now's Ultimate Guide to Safe Withdrawal Rates

https://earlyretirementnow.com/2016/12/ ... t-1-intro/

I didn't read your link --what is the methodology? It could be similar because your chart has an 80 where trinity has a 74.
Here is their explanation. But I suggest you click the link and read the material for yourself. I would hate to mischaracterize their work.
We use monthly total return data (including dividends/interest) for the S&P500 and 10-year Treasury Bonds from January 1871 to September 2016. We realize that some other researchers use slightly higher yielding corporate bonds. Notice, though, that this higher yield comes at the price of higher correlation with equities and thus less diversification. Our analysis yielded that the exposure in the LQD ETF (iShares investment-grade corporate bonds) has roughly the exposure of 75% government bonds (IEF = 7-10-year US Treasuries) and 25% US equities (VTI = Vanguard US Total Equity Market ETF). So, a 60% equities 40% corporate bond portfolio has about the same return characteristics as a 70% equities, 30% government bond portfolio if you like to translate our portfolio weights into a Stock vs. Corporate Bond portfolio. The Barclays Agg (iShares ticker AGG) is somewhere in between.
Monthly returns and monthly CPI inflation are translated into monthly real returns. We assume that the retiree has withdrawn an initial amount equal to one-twelfth of the targeted withdrawal rate at the market closing price of the previous month. The remainder of the portfolio grows at the real market return during the current month. At the end of the month the retiree withdrawals the next monthly installment and rebalances the portfolio weights to the target equity and bond shares. We assume that the portfolio is subject to a 0.05% drag from fees for low-cost mutual funds.
IMHO, Investing should be about living the life you want, not avoiding the life you fear. | Run, You Clever Boy! [9085]

MnD
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### Re: The 4% rule

Thesaints wrote:
Wed May 08, 2019 12:35 am
The first thing to appreciate is that such a portfolio in the past had an average return of ~4.5% real. What it is going to be in the future, with bonds not even yielding 2% real, is another matter.
Grt2bOutdoors wrote:
Wed May 08, 2019 8:09 am
MikeG62 wrote:
Wed May 08, 2019 8:04 am
m@ver1ck wrote:
Wed May 08, 2019 12:20 am
...and say a conservative 6% return rate
I do not believe that 6% is a "conservative" future return rate on a balanced portfolio (of equities and fixed income).
Agree. I use 4% as a moderate return, 3% as conservative.

And conversely, an average 30-year portfolio return of less than 4% real has supported a 4% real withdrawal rate quite nicely. And in the large majority of sequences, the amount that could have withdrawn was much higher than 4%, with 4% leaving an ending portfolio many times larger than what one started with at retirement.

It's increasingly popular on this board for some to imply with authority that "things are different now" and the 4% guideline is now some sort of reckless spending level reserved for drunken sailors and the lot - and 3% or even lower is the "new" conservative withdrawal benchmark. I would do your own research and not rely on pessimistic crystal ball/tea leaves assumptions that condense to "it's different now" and future is going to be worse than anything experienced in the past 100-130 years.

Here's a plot by siamond of this board that show the maximum real withdrawal rate (SWR) for 30-year retirements starting in past years along with the 30-year average returns (CAGR) for those same starting years for a 60/40 portfolio.

I would consider that the very real risk of pessimistic spending assumptions in retirement is working many more years to be able to live off some sort of ultra-low withdrawal rate, and instead ending up dead, disabled or chronically ill such that you don't get any retirement at all or not one that can really be enjoyed at any reasonable standard. Among people with significant retirement assets and common sense about money, I know of zero that have ever run out of money in retirement and I know of dozens that experienced earlier than expected death, disability and chronic major lifestyle limiting illnesses. Especially when you consider it only has to affect one or the other partner in a two-person household to torpedo that hoped for happy, healthy and long retirement.

70/30 AA for life, Global market cap equity. Rebalance if fixed income <25% or >35%. Weighted ER< .10%. 5% of annual portfolio balance SWR, Proportional (to AA) withdrawals.

yousha
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### Re: The 4% rule

The Wizard wrote:
Wed May 08, 2019 8:38 am
Grt2bOutdoors wrote:
Wed May 08, 2019 8:15 am
yousha wrote:
Wed May 08, 2019 8:14 am
Does the RMD withdrawal abide by the 4% suggestion?
No, RMD's are based on your expected life expectancy. You can find the RMD table at www.irs.gov
Actually, it sort of does "abide".
It starts at 3.65% which isn't far from 4%.
The 4% rule increases withdrawal by inflation each year, while the RMD formula doesn't care about inflation but does care about growth or shrinkage in your remaining portfolio year to year.

Under some conditions, a thirty year graph of the two functions will look rather similar...

HomerJ
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### Re: The 4% rule

elainet7 wrote:
Wed May 08, 2019 7:03 am
with very low bond yields, dividends half of what they were, and hi stock valuations, the 4% rule might not work
the Trinity study show nearly 100% success with stocks at 25%
The 4% "rule" was not based on good times, or even average times. It's the withdrawal rate that worked in the past even during BAD times (i.e. low bond yields, high stock valuations).

During an average 30-year period, you could pull 5% or 6%. During the WORST 30-year periods (Great Depression, high inflation of the 70s, etc.), you could still pull 4%.

So, the next 30 years would have to be even WORSE than the Great Depression years for 4% to fail. That's certainly possible, but low bond yields alone aren't going to cause 4% to fail.
A Goldman Sachs associate provided a variety of detailed explanations, but then offered a caveat, “If I’m being dead-### honest, though, nobody knows what’s really going on.”

HomerJ
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### Re: The 4% rule

Grt2bOutdoors wrote:
Wed May 08, 2019 8:09 am
MikeG62 wrote:
Wed May 08, 2019 8:04 am
m@ver1ck wrote:
Wed May 08, 2019 12:20 am
...and say a conservative 6% return rate
I do not believe that 6% is a "conservative" future return rate on a balanced portfolio (of equities and fixed income).
Agree. I use 4% as a moderate return, 3% as conservative.
Are you guys talking real or nominal? His 6% was nominal (or 4% real).

3% real might be conservative, 3% nominal is pretty silly since you can get more than that from CDs.

And like others have said, you don't need 4% real for 4% withdrawals to work. Even 1% real is good enough to let 4% withdrawals last 30 years.

Things have to be really bad for a long time for 4% to not work.
A Goldman Sachs associate provided a variety of detailed explanations, but then offered a caveat, “If I’m being dead-### honest, though, nobody knows what’s really going on.”

alex_686
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### Re: The 4% rule

MnD wrote:
Wed May 08, 2019 9:07 am
It's increasingly popular on this board for some to imply with authority that "things are different now" and the 4% guideline is now some sort of reckless spending level reserved for drunken sailors and the lot - and 3% or even lower is the "new" conservative withdrawal benchmark. I would do your own research and not rely on pessimistic crystal ball/tea leaves assumptions that condense to "it's different now" and future is going to be worse than anything experienced in the past 100-130 years.
So, one of my main criticisms of the Trinity study is that backwards looking and lacks theory. That is, why does the 4% rule work? You suggest that it has worked for the past 100 years, I would suggest it has not worked for the majority of the past 500 years. So hopefully whatever happened for the past few decades - whatever that was - will continue. I would also suggest that we only have 50 years of high quality data.

For the "pessimist" side I will point out that forward looking numbers are lower than historical norms. Low real long term treasury rates and low earning yields (i.e., high P/E ratios) suggest that we will have below normal returns for the next 10 years.
Former brokerage operations & mutual fund accountant. I hate risk, which is why I study and embrace it.

TheTimeLord
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### Re: The 4% rule

alex_686 wrote:
Wed May 08, 2019 10:05 am
MnD wrote:
Wed May 08, 2019 9:07 am
It's increasingly popular on this board for some to imply with authority that "things are different now" and the 4% guideline is now some sort of reckless spending level reserved for drunken sailors and the lot - and 3% or even lower is the "new" conservative withdrawal benchmark. I would do your own research and not rely on pessimistic crystal ball/tea leaves assumptions that condense to "it's different now" and future is going to be worse than anything experienced in the past 100-130 years.
So, one of my main criticisms of the Trinity study is that backwards looking and lacks theory.
Isn't that the same as CAPE 10 and the pessimists love it.
IMHO, Investing should be about living the life you want, not avoiding the life you fear. | Run, You Clever Boy! [9085]

ruralavalon
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Location: Illinois

### Re: The 4% rule

yousha wrote:
Wed May 08, 2019 8:14 am
Does the RMD withdrawal abide by the 4% suggestion?
Required Minimum Distributions (RMDs) start at age 70.5 with a rate of 3.65%.
"Everything should be as simple as it is, but not simpler." - Albert Einstein | Wiki article link:Getting Started

willthrill81
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Location: USA

### Re: The 4% rule

MnD wrote:
Wed May 08, 2019 9:07 am
Thesaints wrote:
Wed May 08, 2019 12:35 am
The first thing to appreciate is that such a portfolio in the past had an average return of ~4.5% real. What it is going to be in the future, with bonds not even yielding 2% real, is another matter.
Grt2bOutdoors wrote:
Wed May 08, 2019 8:09 am
MikeG62 wrote:
Wed May 08, 2019 8:04 am
m@ver1ck wrote:
Wed May 08, 2019 12:20 am
...and say a conservative 6% return rate
I do not believe that 6% is a "conservative" future return rate on a balanced portfolio (of equities and fixed income).
Agree. I use 4% as a moderate return, 3% as conservative.

And conversely, an average 30-year portfolio return of less than 4% real has supported a 4% real withdrawal rate quite nicely. And in the large majority of sequences, the amount that could have withdrawn was much higher than 4%, with 4% leaving an ending portfolio many times larger than what one started with at retirement.

It's increasingly popular on this board for some to imply with authority that "things are different now" and the 4% guideline is now some sort of reckless spending level reserved for drunken sailors and the lot - and 3% or even lower is the "new" conservative withdrawal benchmark. I would do your own research and not rely on pessimistic crystal ball/tea leaves assumptions that condense to "it's different now" and future is going to be worse than anything experienced in the past 100-130 years.

Here's a plot by siamond of this board that show the maximum real withdrawal rate (SWR) for 30-year retirements starting in past years along with the 30-year average returns (CAGR) for those same starting years for a 60/40 portfolio.

I would consider that the very real risk of pessimistic spending assumptions in retirement is working many more years to be able to live off some sort of ultra-low withdrawal rate, and instead ending up dead, disabled or chronically ill such that you don't get any retirement at all or not one that can really be enjoyed at any reasonable standard. Among people with significant retirement assets and common sense about money, I know of zero that have ever run out of money in retirement and I know of dozens that experienced earlier than expected death, disability and chronic major lifestyle limiting illnesses. Especially when you consider it only has to affect one or the other partner in a two-person household to torpedo that hoped for happy, healthy and long retirement.

That chart of Siamond's is absolutely incredible. It demonstrates that the sequence of returns really has mattered at least as much as the returns themselves. This throws a huge monkey wrench into the 'high valuations and low bond yields mean an ever lower SWR than in the past' arguments.

Just to add a little, it will likely take 5-10 additional years of working to go from a 4% withdrawal rate to 3%. When I ran the math not long ago, I believe that for a person with a 20% savings rate who experienced 5% average real returns, it would take 5 more years to go from 25x to 33x. If the real returns were 2%, it would take 10 more years to get to 33x. Those 5-10 years are irrecoverable and for most retirees merely reduce the likelihood of needing to cut back on their discretionary spending from an already small number to an even smaller one. Some clearly think that's a good trade-off, but I view it as being a very poor one.
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

willthrill81
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Location: USA

### Re: The 4% rule

alex_686 wrote:
Wed May 08, 2019 10:05 am
So, one of my main criticisms of the Trinity study is that backwards looking and lacks theory.
I've yet to see a single withdrawal strategy that was not in some way based on history. Some certainly do so more than others, and the '4% rule' is an extreme example of this. Taylor's 'spend what you like' (i.e. 'fly by the seat of your pants') may not be based on history, but it certainly makes implicit assumptions about the future not being too gloomy. Even the time value of money formulaic approach that I really like needs the user to estimate forward returns, and this cannot be done with no reference at all to history unless you believe that an estimate like 0% real returns is not based on history.

But frankly, I really don't know why anyone would want to completely turn their back on 100+ years of market history. You might not be suggesting that, but some around here do.
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

Thesaints
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### Re: The 4% rule

mega317 wrote:
Wed May 08, 2019 7:14 am
Wiggums wrote:
Wed May 08, 2019 6:59 am
Rudedog wrote:
Wed May 08, 2019 6:37 am
25 years of retirement........4% withdrawals per year. 4% x 25 = 100%. Just a rough guess or rough guideline to follow.
Here is an article on 4% rule versus 25 times expenses

https://www.thebalance.com/dont-confuse ... umb-453920
This from the article makes no sense and is not true.
This rule-of-thumb assumes you'll be able to generate an annualized real return of 4 percent per year.
If the portfolio grows at 4% real, and your withdrawals remain 4% real, that will sustain indefinitely. If that's your assumption then it is a wildly conservative withdrawal rate.
Not necessarily if it grows at 4% real on average !

60/40 or 50/50 it is the same, btw. Not a substantial difference in the analysis.

alex_686
Posts: 6505
Joined: Mon Feb 09, 2015 2:39 pm

### Re: The 4% rule

alex_686 wrote:
Wed May 08, 2019 10:05 am
TheTimeLord wrote:
Wed May 08, 2019 10:13 am
So, one of my main criticisms of the Trinity study is that backwards looking and lacks theory.
Isn't that the same as CAPE 10 and the pessimists love it.
As somebody who advocates for CAPE 10, No. It kind of boils down epistemology

For CAPE 10, there is a narrative on why it works, there is a model on how it works, and one can back-test that model to see how accurate it is. Of course, how much do you want to rest on theory, fancy math, and projections? They have failed in the past.

You can't do any of these things with the Trinity study - it is a mere historical observation. The authors don't present how it works and they offer no model, and they don't suggest that it will work in the future. It is just a historical observation. A high quality observation - but that is all. There is of course the story about the turkey, who observes that farmer has come out every day and feed them, so it is reasonable to project forward that the farmer will come out again on Thanksgiving day and feed them again. Historical observation has limits too.

As a pragmatist, I can use more than one mode of though to come to my conclusions. Different approaches have different strengths and weakness.

Going back to the OP, they asked about the math behind the 4% rule. The answer is that there is none, so don't even try it.
Former brokerage operations & mutual fund accountant. I hate risk, which is why I study and embrace it.

Thesaints
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Joined: Tue Jun 20, 2017 12:25 am

### Re: The 4% rule

CAPE 10 does not work either, since it is independent on interest rates. We know for a fact that those have huge effect on the economy, so expecting CAPE 10 to work is kind of surprising.

alex_686
Posts: 6505
Joined: Mon Feb 09, 2015 2:39 pm

### Re: The 4% rule

willthrill81 wrote:
Wed May 08, 2019 10:48 am
I've yet to see a single withdrawal strategy that was not in some way based on history. Some certainly do so more than others, and the '4% rule' is an extreme example of this. ... Even the time value of money formulaic approach that I really like needs the user to estimate forward returns, and this cannot be done with no reference at all to history unless you believe that an estimate like 0% real returns is not based on history.

But frankly, I really don't know why anyone would want to completely turn their back on 100+ years of market history. You might not be suggesting that, but some around here do.
So a few points.

First, most withdrawal strategies I have read are based on investment theory, not history. That being said, most are all back-tested against historical data. Others are on Monte Carlo simulations which may or may not be based on historical inputs. You really have to pull apart the strategies to figure out what the underlying bones are made off.

Second, I think we might be looking at the exact same data and coming to different conclusions. I am very cautious of using historical data. Why use historical data if the trend lines don't revert to the mean? If you look at different time periods you get different structures, different returns on bonds and equities, different equity risk premiums, different volatilities. And these shift every 5 to 10 years. Often, when you pile on more that 10 years worth of information the statistical validity of what you are studding falls thanks to the shifting of the underlying structures. While I think historical analysis can inform, one has to be mindful of its limitations.
Former brokerage operations & mutual fund accountant. I hate risk, which is why I study and embrace it.

Tyler9000
Posts: 543
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### Re: The 4% rule

m@ver1ck wrote:
Wed May 08, 2019 12:20 am
Can someone point me to the math behind it? Or some calculators on how to simulate sequence of return events?
Try this: How Safe Withdrawal Rates Work

It walks through the general theory behind safe withdrawal rates and also offers some tools to calculate them for your own personal portfolio.

alex_686
Posts: 6505
Joined: Mon Feb 09, 2015 2:39 pm

### Re: The 4% rule

Thesaints wrote:
Wed May 08, 2019 11:01 am
CAPE 10 does not work either, since it is independent on interest rates. We know for a fact that those have huge effect on the economy, so expecting CAPE 10 to work is kind of surprising.
Why do you say that? CAPE 10's projections are in real rates, not nominal. And, in theory, it should incorporate the real rates from long term treasuries.

And as a proponent of CAPE 10, I am not saying it is prefect. For such a simple model it delivers 60% power of explanation. There are better models out there - but they tend to be much more complicated, and the power does not increase that much.

So, if not CAPE 10 then what? I will point out that it does a better job than historical results - see my last post for more detail here.
Former brokerage operations & mutual fund accountant. I hate risk, which is why I study and embrace it.

ohai
Posts: 1327
Joined: Wed Dec 27, 2017 2:10 pm

### Re: The 4% rule

alex_686 wrote:
Wed May 08, 2019 11:06 am
willthrill81 wrote:
Wed May 08, 2019 10:48 am
I've yet to see a single withdrawal strategy that was not in some way based on history. Some certainly do so more than others, and the '4% rule' is an extreme example of this. ... Even the time value of money formulaic approach that I really like needs the user to estimate forward returns, and this cannot be done with no reference at all to history unless you believe that an estimate like 0% real returns is not based on history.

But frankly, I really don't know why anyone would want to completely turn their back on 100+ years of market history. You might not be suggesting that, but some around here do.
So a few points.

First, most withdrawal strategies I have read are based on investment theory, not history. That being said, most are all back-tested against historical data. Others are on Monte Carlo simulations which may or may not be based on historical inputs. You really have to pull apart the strategies to figure out what the underlying bones are made off.

Second, I think we might be looking at the exact same data and coming to different conclusions. I am very cautious of using historical data. Why use historical data if the trend lines don't revert to the mean? If you look at different time periods you get different structures, different returns on bonds and equities, different equity risk premiums, different volatilities. And these shift every 5 to 10 years. Often, when you pile on more that 10 years worth of information the statistical validity of what you are studding falls thanks to the shifting of the underlying structures. While I think historical analysis can inform, one has to be mindful of its limitations.
Historical data is crucial, because it often captures a lot of statistical events that you might not model otherwise. For instance, unless they are modeling stochastic volatility and jump diffusion, all those simulations with 10k paths on the internet don't have a 2008 crash in their distributions.

I agree that recent history is much more relevant than past history.

willthrill81
Posts: 19636
Joined: Thu Jan 26, 2017 3:17 pm
Location: USA

### Re: The 4% rule

alex_686 wrote:
Wed May 08, 2019 11:06 am
willthrill81 wrote:
Wed May 08, 2019 10:48 am
I've yet to see a single withdrawal strategy that was not in some way based on history. Some certainly do so more than others, and the '4% rule' is an extreme example of this. ... Even the time value of money formulaic approach that I really like needs the user to estimate forward returns, and this cannot be done with no reference at all to history unless you believe that an estimate like 0% real returns is not based on history.

But frankly, I really don't know why anyone would want to completely turn their back on 100+ years of market history. You might not be suggesting that, but some around here do.
So a few points.

First, most withdrawal strategies I have read are based on investment theory, not history. That being said, most are all back-tested against historical data. Others are on Monte Carlo simulations which may or may not be based on historical inputs. You really have to pull apart the strategies to figure out what the underlying bones are made off.
If you would point them out, that would be great. But how do we know if an investment theory is 'good' if we don't backtest it? So we're still basing our withdrawal strategy at least in part on history; it's just a question of degrees.
alex_686 wrote:
Wed May 08, 2019 11:06 am
Second, I think we might be looking at the exact same data and coming to different conclusions. I am very cautious of using historical data. Why use historical data if the trend lines don't revert to the mean? If you look at different time periods you get different structures, different returns on bonds and equities, different equity risk premiums, different volatilities. And these shift every 5 to 10 years. Often, when you pile on more that 10 years worth of information the statistical validity of what you are studding falls thanks to the shifting of the underlying structures. While I think historical analysis can inform, one has to be mindful of its limitations.
I entirely agree, which is why I espouse flexible withdrawal strategies that take current market conditions, your current portfolio value, and your own personal circumstance into account, like the time-value of money approach.

One of the most prudent and valid ways to use historic data is to examine whether a particular strategy, investment or withdrawal, is at least plausible.
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings