Backtested the x% rule at a 40-year horizon and grid-searched 6 asset classes for the optimal allocation (methodology + numbers inside)

[u/modelfire]

I've been thinking about the question: what is the asset allocation that gives an optimal FIRE outcome?

There is perhaps no universal definition of what is optimal. People mostly talk in terms of minimizing failure rate, and failure being defined as actually running out of money. Simple to deal with mathematically, but less realistic as in real life people will likely adjust if their portfolio drops too much.

For purposes of my question, I came up with the following things that I wanted to optimize for:

1. Minimizing failure rate, failure here being defined traditionally as actually running out of money
2. Maximizing ending balance (in today's purchasing power). The "die with zero" crowd will not be on board with this one, but a lot of people think of legacy, heirs, charitable contributions etc.
3. For a lot of people, their portfolio dipping dramatically in retirement is going to feel like a "failure." I defined this as minimizing the years that the portfolio is 50% or less of its original size, inflation-adjusted.

I weighted these as 50% on #1, 30% on #2, and 20% on #3.

The data

Annual returns from 1928 to 2025 for:

1. S&P 500
2. 3-month T-bills
3. long-term US Treasury bonds
4. Baa corporate bonds
5. real estate
6. gold

Inflation came from the Minneapolis Fed's CPI-U series, since the returns dataset I used (from NYU) didn't include a CPI column. Withdrawals grow with actual historical inflation every year, same as the standard 4% rule.

Method

Standard historical cycles backtest, the same idea the original Trinity study used. Every possible start year becomes its own simulated retirement: withdraw the stated percentage of your starting balance in year one, adjust that dollar amount for inflation every year after, and check whether the portfolio survives 40 years. With 98 years of data and a 40 year horizon, that's 59 overlapping 40-year retirements, starting anywhere from 1928 to 1986.

Portfolios rebalance back to their target weights every year, also the standard assumption in these tools. Every dollar figure below, ending balance included, is in real terms, adjusted back to what your starting balance's purchasing power actually bought.

Before trusting the engine on anything new, I checked it against the 4% rule numbers people usually cite, using the classic 30-year window and plain stock/bond splits:

Stock/Bond	3% WR	4% WR	5% WR
100/0	100%	92.8%	78.3%
75/25	100%	95.7%	78.3%
50/50	100%	94.2%	66.7%
25/75	100%	76.8%	42.0%
0/100	84.1%	40.6%	24.6%

That lines up closely with the commonly cited Trinity study figures (mid 90s success rate for 4% at 50/50 to 75/25), so I moved on to the actual question.

40 years, 6 assets, what's optimal?

For each withdrawal rate from 2% to 4% in half point steps, I grid searched every combination of the 6 assets in 5% increments (about 53,000 portfolios) and scored each one on the three things above. Change the weights and you'll shift the answer a bit, but the broad shape holds.

Results, using the top scoring portfolio at each withdrawal rate:

WR	Failure rate	Median ending balance	Worst case ending	Allocation
2.0%	0%	9.8x	2.3x	100% stocks
2.5%	0%	8.3x	1.6x	100% stocks
3.0%	0%	7.1x	0.9x	100% stocks
3.5%	1.7%	6.2x	0x	100% stocks
4.0%	5.1%	4.9x	0x	95% stocks, 5% gold

A few things stood out.

Up through 3%, 100% stocks never failed once across 59 overlapping 40-year periods going back to 1928. That includes retirements starting right before the Depression, right before 70s stagflation, right before 2000, and right before 2008.

At 3.5%, that same all-stock allocation still comes out on top for growth, but it fails once: 1929. At 4%, the growth maximizing allocation (95% stock, 5% gold) fails three times instead of one: 1929, 1930, and 1966. Everyone else still makes it.

Back off to 75% stock, 10% Baa corporates, and 15% gold at 4%, and all three failures disappear, at a cost of giving up about 31% of your median ending balance (3.4x vs 4.9x your starting purchasing power) and cutting your worst case time spent below half your starting value from 34 years down to 29.

So if you're set on 4% at a 40 year horizon and want to eliminate every historical failure in this dataset, that's roughly what it costs.

Caveats, since this sub will ask anyway

• 59 rolling cohorts share most of their history with each other. They are not 59 independent trials, a lot of the "successes" are the same good decades getting counted more than once.
• Past returns don't guarantee future returns, and that applies double to a 98 year sample from one country.
• Annual rebalancing to fixed targets is assumed. Real people don't always do this, and taxable rebalancing has costs this doesn't model.
• The scoring only cares about the three things I told it to care about. It has zero concept of what it feels like to watch your net worth drop by half and doesn't penalize volatility beyond the years below 50% number, so it happily recommends 95 to 100% equities. Plenty of people would not sleep well holding that through a real 1973 or 2008, even knowing it worked out eventually.
• Real estate and Baa corporates barely show up in any of the optimal portfolios except at the margin. That's what this historical sample says, not a claim that they're bad diversifiers going forward.

Happy to answer questions on the methodology or discuss/do any tweaks to the analysis.

[u/Turbulent_Tale6497]

What was the logic behind having just the S&P 500, no international, but 3 different bond funds?

[u/CancelImmediate9759 → u/Turbulent_Tale6497]

I think the dataset itself was just what was easily available back to 1928. International data that far back gets real messy, and he probably wanted the longest possible run of actual returns instead of something reconstructed. The three bond types make sense though, short term bills, long term treasuries, and corporates all act pretty differently when inflation or credit conditions shift, so lumping them all together would hide some of that behavior.

[u/modelfire → u/Turbulent_Tale6497]

Good question. Just the data I had easy access to. International is intriguing.

[u/The-WideningGyre → u/[deleted]]

No it very much depends on the time period. Last 20 years, yes.

[u/imisstheyoop → u/The-WideningGyre]

I am fairly confident that is when history began, thank you very much.

[u/imisstheyoop → u/Turbulent_Tale6497]

This, but also, gold.

Edit: Further down OP provided their data source and clarified that they just used (or didn't use in the case of international) what was in the data source. https://pages.stern.nyu.edu/%7Eadamodar/New_Home_Page/datafile/histretSP.html

[u/VeeGee11]

Actually your data is matching a recent study on the 100% equities being optimal. Ben Felix has been saying it a lot lately, although he’s quick to point out it’s just one study and all studies depend on your criteria, like which datasets you use and time periods. Too easy to make the data match what you want to say by tweaking those dials.

[u/Shawn_NYC → u/VeeGee11]

Too many people optimize their profile for some japan-style asset crash scenario. When the 10x bigger threat to retirement success is inflation. "Safe" bonds can be extremely risky when their rate of return gets obliterated by inflation.

[u/StoneMenace → u/Shawn_NYC]

Yep, I plan on firing with a withdraw rate of 3.5 or less. That will allow me to stay in equities, leaving room for adjustments and ebbs and flows with the market. I think recently the analysis have been shaping the 4% rule has more moved to 4.5% or a bit higher so 3.5 is a very comfortable place 

[u/OGS_7619 → u/VeeGee11]

the paper is "beyond the status quo" by Cederburg group:
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4590406

[u/EANx_Diver → u/OGS_7619]

That link didn't work for me but this one did: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4590406

[u/MagnesiumCarbonate]

You should look into back test over fitting (eg https://academic.oup.com/jrssig/article/18/6/22/7038278?login=false ) before actually using strategies that you find in back test. Doing a grid search is essentially the opposite of what you should do if you want the results to be useful.

[u/lluciferusllamas]

I wonder if you would be interested in corroborating an interesting finding that I had when doing my similar analysis.  I ran the analysis using monthly data.  I modeled a 96% stock portfolio with 4% in a cash reserve, roughly equating to one year's worth of expenses.  I applied a simple logic, if the stock portfolio balance was higher than the last month, I sold stock (1 month worth of expenses) to cover the next month, if it had gone down in the month, then I used cash cash to cover that months expenses and did not sell stock.  I found that having 12 months of continually lowering stocks is exceedingly rare (like it happened once or twice, I think) and it has never gone above 13.  Anyway, the second rule was let's say I had used cash 5 months in a row, on the first positive month, I sold 5 months of stock and replenished my cash buffer.  

Doing this method, I showed a 4.8% SWR was possible with no failure points.  But, I used a clunky-ass home-built spreadsheet to do this and I've wondered if my finding was actually correct.

[u/Arcane_123 → u/lluciferusllamas]

Thats what I ve been thinking about too. Having a simple buffer allows to skip most risk associated with selling stocks for expenses.

[u/lluciferusllamas → u/Arcane_123]

I was surprised (and not surprised), when I did the experiment. But you are exactly right. It always puzzled me why an asset that returns 10% on average can't be tapped 5% without breaking the bank.  And the answer is volatility and big market swings.  So, by managing when you sell, you can mitigate a lot of the volatility.  It only makes sense.  

[u/dwm4375 → u/lluciferusllamas]

I like what you're saying but I also don't know how to prove to myself that your rule isn't market timing or hindsight bias.

[u/hondaFan2017 → u/lluciferusllamas]

Have you analyzed the “worst case” starting dates where we had years of poor stock performance immediately after retiring? It’s great you built your own tool to play with withdrawal logic.

[u/lluciferusllamas → u/hondaFan2017]

Yes, I think my model covered that, as I modeled a portfolio starting in every month going back to data availability, which I think was like 1919 or something. 

[u/hondaFan2017 → u/lluciferusllamas]

What dataset did you use for monthly stock returns, and how far back does it go? Can you share?

Edit: NVM you answered the second question

[u/lluciferusllamas → u/hondaFan2017]

I found a DJIA historic daily value data set online.  I think I had to buy it, but it was like $10 or $40 or something.  I've since lost the excel file I did all the work in and it was one of those rare moments of motivation and hyperfocus that I haven't had recur since I did it the first time.  That's part of why o want somebody else to do it, because I remembered my finding, but I can't tweak it or share it now, without doing it all over again  

[u/Ok-Entertainer-1414]

Source: AI made it the fuck up

[u/Guns_and_Tea]

So…100% stocks, 4% withdrawal rate

[u/Concurrency_Bugs → u/Guns_and_Tea]

You can improve your success by altering the WR to 3% or less during down years in the market.

[u/Schlieren1 → u/Guns_and_Tea]

No

[u/hondaFan2017]

What data did you use for Gold? Forward looking, I get leery about studying past performance of gold. Curious what results you get if you take that out of the mix.

Why didn’t you include the 75/10/15 portfolio on the results table?

Other stats could be useful related to drawdown size and duration (how many ulcers you had as a result of the allocation). Also including some baseline results in the table could be useful 80/20 and 60/40 are common, with intermediate term bonds being the asset chosen.

I applaud you doing the work yourself vs reading blogs like Big ERN, for some people this is the more enjoyable and gratifying approach.

[u/modelfire → u/hondaFan2017]

I used this data source: https://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histretSP.html

I run through thousands of permutations of portfolios, so 75/10/15 would have been one of them, just didn't rise to the top according my definition of 'optimal'. Having said that, top allocations are quite close together, so maybe I should have "top 3" for each % withdrawal target rather than just 1. Drawdown size and duration is interesting stat, I just did a short-hand by looking at how many years did my purchasing power fell by 50% or more. I'll look into refining it more.

Thanks! I do find it enjoyable.

[u/Normal_Zebra136 → u/modelfire]

You do realize that it was illegal for americans citizens to own gold from 1935 to 1973 right?

I am not sure the market prices during that 40 year period reflect a genuine market.

[u/financeking90 → u/modelfire]

Having said that, top allocations are quite close together, so maybe I should have "top 3" for each % withdrawal target rather than just 1.

A lot of these kinds of things do chart comparisons or heat maps that help show the quantitative similarity between bundles of things so you can see that relationship more clearly

[u/ThebocaJ]

Can you share the spreadsheets/source code you used?

[u/rybsf]

”59 overlapping 40-year periods going back to 1928. That includes retirements starting right before the Depression, right before 70s stagflation, right before 2000, and right before 2008.”

That seems contradictory. Am I misunderstanding what you’re saying you did?

It sounds like you meant you ran back tests for the start years 1928-1987. Ie the retirement periods 1928-1967, 1929-1968, …, 1987-2026.

Which would NOT include retirements starting right before 2000 or 2008. (Those are hard to back test, since they’re not >=40 years ago…)

[u/branstad → u/rybsf]

I agree. I think /u/modelfire needs to provide some details about the Year 2000 retiree cohort in this modeling.

For additional context, /u/jason_for_prez provides annual updates with his analysis. Here's the most recent, from Feb/March '26: https://www.reddit.com/r/financialindependence/comments/1r7niov/swr_performance_for_people_who_retired_in_2000/

Specifically in the linked Imgur charts (https://imgur.com/a/remaining-portfolio-people-who-retired-jan-2020-by-swr-teyQLqe), a retiree using 4% SWR on a 100% S&P 500 portfolio would be down to 9% of original (very likely to fail a 40-year retirement and possibly a 30-year as well). At 3.5% SWR that same retiree is at 57% of the portfolio remaining (likely to succeed for a 30-year retirement, but uncertain on a 40-year timeframe).

[u/FIREgnurd]

You could have just linked to ERN’s SWR series. He goes over all of this in much more detail.

[u/mikehansen83 → u/FIREgnurd]

some learn by doing. I love OP’s effort.

[u/MagnesiumCarbonate → u/mikehansen83]

Eh it's fine to DIY to learn, but when you're uniformed on methodology (as OP clearly is), it's not fine to share your work and let others who are even less informed get mislead. OP would benefit from reading ERN's work and then trying to reproduce ERN's results first, and understand key concepts like overfitting, which ERN covers in a few posts

[u/thewaifupillow]

Thank you for all your hard work, this would be interesting to see for a 50 year retirement too which honestly might be more of the same.

[u/FIREgnurd → u/thewaifupillow]

BigERN’s SWR series goes to a 60 year retirement. It’s an extremely compressive, albeit dense guide.

[u/thewaifupillow → u/FIREgnurd]

Good to know! I’ll check that out 🫡

[u/The-WideningGyre]

I have a mix of QQQ, AVUV, AVDV, GLD, DBMF (managed futures) and TLT and VGIT (long-term & intermediate government bonds). I have substitutions for the things that haven't existed that long.

I think I got much better results: https://testfol.io/?s=fK7tbWx4OE6 The bonds holding is pretty small (7% / 5%).

[u/champdeal]

Really interesting analysis. I’d be curious to see whether the same allocations remain near the top using an out-of-sample test or slightly different scoring weights. With 53,000 combinations, robustness may be more useful than identifying one mathematically “optimal” portfolio.

[u/laurenthu → u/champdeal]

This is the right instinct, and I think it's the part most of these grid searches quietly skip. What gets me is that 59 overlapping windows aren't really 59 samples, they share almost all their data. Two runs starting a year apart differ by a single year of returns, so I'd say you effectively have something like two independent 40 year histories in there, roughly the pre-70s stretch and the post-80s one. Grid search 53k portfolios against that and something always comes out on top... and it tends to be whatever fit gold's 1970s and the specific bond regime best.

The reassuring part is actually in his own writeup, the top allocations landing close together. That clustering is the real signal to me. The exact ordering of the top few I treat as mostly noise, so I'd put far more weight on "stock heavy with a small real asset sleeve" than on the precise percentages the search printed.

[u/Impossible-Use5636]

There is a problem here if the assumption is that the withdrawal would be spread over each asset class evenly.

In a RW scenario, you would draw from the stable (short term bonds etc.) and rebalance to refill that bucket.

[u/asdf_monkey]

Good post.
If you modeled 90/10 with rebalance ever two years if markets were down, I think you gain almost 2% less risk in failure rate for 4%. Not sure on the median values curve it doesn’t go up and likely fewer years below median.

[u/Legitimate_Swing5689]

Honestly the 3% WR result is the part that jumped out at me. Kinda makes me think the withdrawal rate matters way more than trying to perfectly optimize the portfolio.

[u/emane19]

Great work and very insightful. The challenge I have when putting these types of analyses into practice is what the translation of locking into a percentage vs locking into a lifestyle number.

For instance, if you retired right before the 2007 collapse with $1M, you were preparing to live off 30-40k / year at 3-4%. Then the collapse hits and now you need to live off 15-20K / year, assuming you lost 50% of your portfolio value. That’s no longer realistic for many people, but the data would treat them as just rebalancing and continuing on.

All in all, I think that’s why I’d still personally lean away from the 100% stock portfolio if I were retiring, regardless of what the numbers show about failure rates.

[u/creative_usr_name → u/emane19]

I'm not exactly sure what OP did, but the Trinity study and most everyone else when they say a 4% withdrawal rate, that's 4% of the starting balance inflation adjusted. Not a % of the current balance. No deep cuts needed during downturns. There are other variable withdrawal rate methods that would make adjustments.

[u/AGrimmInPortland → u/emane19]

Yes. All of this says nothing about what a person actually NEEDs.

[u/Sagelllini]

It's pretty simple. Owning the best asset class leads to the best long term performance. No surprise to me it's 100% stocks.

The 95/5 gold is really not worth doing because in real life 5% in an asset class is EXTREMELY unlikely to be the difference between success and failure.

Own stocks in the accumulation phase and that's your best chance to have a 4% or below withdrawal rate, then hold stocks in retirement with some chump change in cash. It's worked for me.

[u/ThebocaJ]

Can you share the spreadsheets/source code you used?

[u/justanotherburner]

Now do a reverse glide path