Welcome! You probably landed on this page because you clicked someone’s link to my Safe Withdrawal Rate Series. Thanks for stopping by! This series has now grown to 30+ parts and if you are looking for a less technical summary before jumping into the nitty-gritty details, I recommend you check out the new “landing page” to my series first:
The Safe Withdrawal Rate Series – A Guide for First-Time Readers
But if you got an appetite for the technical details after that I suggest you check out all the other parts as well! Also, I posted the results from parts 1 through 8 as a Social Science Research Network (SSRN) working paper in pdf format:
Safe Withdrawal Rates: A Guide for Early Retirees (SSRN WP#2920322)
But without further ado, here’s Part 1 of the Series:
We just calculated over 6.5 million safe withdrawal rates. Well, not by hand, of course, but by writing a computer program that loops over all possible combinations of retirement dates, and other model parameters. Not a big surprise here, but it took a lot of work to put this together. We can’t possibly fit all results into one single post, so we publish our results in multiple parts. Today, we briefly introduce our research and some baseline results. Stay tuned for more to come in the next few weeks/months:
The plan to work on this research came after one of those moments when we realized that if you want something done right and exactly applicable to our own situation, we just have to do it ourselves. We wanted to do a lot more robustness analysis than we had seen anywhere in the blogging world.
Nonconformist among the nonconformists
Intriguingly, very few early retirement planners or bloggers question the validity of the 4% safe withdrawal rate rule. When you retire in your 30s or even 40s you are by nature nonconformist. You question the consensus, the people with the McMansions and the full-size SUVs in the driveway. People who are otherwise extremely suspicious about everything consensus suddenly eat up the 4% rule without much questioning or checking under the hood:
- People take the Trinity Study at face value and extrapolate the 30-year windows from Trinity to 50+ years for the early retirement crowd (bad, bad, bad idea, see Part 2 of our series!!!),
- It’s probably not a good idea to use a withdrawal rate calibrated to the average retiree since 1926 when today’s equity valuation is much less attractive than the average since 1926, see Part 3 of this series.
- Social Security will also save your behind come age 67 (uuhhhm, good luck with that, see Part 4 of this series!).
- Folks wave their hands about how one can just slow consumption growth (it’s not that easy, see Part 5 of this series!),
- and wave their hands about how the 4% rule did just fine in 2001 and 2008 (believe me, it didn’t; see Part 6 of this series!)
Has anybody actually done some serious simulations that are truly applicable to the FIRE community? Something comparable to the original Trinity Study, but with more bells-and-whistles and robustness checks applicable to the FIRE community? I don’t like the “hand-me-down” research targeted at my parents’ retirement. So, when you want something done, and done right, you gotta do it yourself! Which is what we did with the 6.5 million safe withdrawal rates.
What we do to be more relevant for early retirees
- The study is done at a monthly frequency (not just annual like cFIREsim), starting with equity and bond returns in January 1871 and going through September 2016. It would be unrealistic for us to withdraw funds only once per year at the beginning of the year and have – on average – 6 months of cash sitting around in our checking account.
- We look at the sustainable withdrawal rates over 30, 40, 50, and 60-year windows. It’s still a good idea to keep the 30-year window for comparison, though this window length is simply too short for us in the early retirement community.
- We look at different target final values, i.e., calibrate maximum withdrawal rates to deplete the capital (final value=0), preserve the inflation-adjusted initial capital (final value=100% of initial value) and some steps in between (final value=25%, 50%, 75% of inflation-adjusted initial value). This is useful for retirees who are uncomfortable with the idea of running out of money at some future date and/or plan to leave a bequest to their children, grandchildren, and charitable organizations.
- We extrapolate past the current history and append equity and bond returns after September 2016. To this end, we assume long-term average returns for equities going forward (about 6.6% real p.a.). For bonds, we assume a low real return over the first 10 years: only 0% real p.a., which is actually slightly above the 9/30/2016 10Y yield (1.61%) minus the inflation expectation at the time (~2%). After the initial 10 years, bonds too will return their long-term average of 2.6% real per year. We should note that these return assumptions are likely going to generate higher sustainable withdrawal rates due to the absence of return volatility.
- We study how different the safe withdrawal rates and success probabilities were in various equity valuation regimes. Specifically, how do safe withdrawal rates and success probabilities look like for different Shiller CAPE ratio regimes? We did a similar study before using cFIREsim.com, but now we can rely on our own monthly simulations and easily loop over all sorts of other model parameter values.
- We can study the impact of reducing the monthly withdrawals over time. This mimics the assumption that some people consume less as they age. Or we can take into account the impact of lower withdrawals once retirees start collecting Social Security.
- We study how alternative withdrawal strategies, e.g., dynamic withdrawal rules rates based on equity valuation (Shiller CAPE) would have performed during this time.
Methodology in detail
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.
Why 6.5 Million Safe Withdrawal rates?
We calculate safe withdrawal rates for all possible combinations of 1) starting dates, 2) retirement horizons, 3) equity weights, 4) final asset values and 5) withdrawal patterns:
- 1739 possible retirement start dates between February 1, 1871, and December 1, 2016.
- 4 different retirement horizons: 30, 40, 50, and 60 years
- 21 different equity weights from 0% to 100% in 5% steps (bond weight = 100%-equity weight)
- 5 different final asset value targets: 0%, 25%, 50%, 75% and 100% of real inflation adjusted initial asset value
- 9 different withdrawal patterns. The baseline assumes that withdrawals are adjusted in line with CPI inflation, but we also allow for slower than CPI-growth. We also check how lower withdrawal rates 20 or 30 years after the retirement start date (to account for Social Security income) will impact the maximum sustainable withdrawal rates.
Hence, we calculate 1739 x 4 x 21 x 5 x 9 = 6,573,420 different safe withdrawal rates.
Base Case Results
Here’s a table, roughly the same structure as they use in the Trinity Study. Major changes:
- we use retirement lengths of 30-60 years and
- withdrawal rates only between 3% and 5% in 25 basis point step. No serious long-term retirement planner with a horizon of 50-60 years would ever even consider a withdrawal rate above 5%, anyway, given that equities return “only” about 6.6% and you have to account for volatility and sequence of return risk.
The success criterion is a final asset value of zero as in the Trinity Study.
A few conclusions from this table:
- The success rates for a 30-year horizon are roughly consistent with the Trinity study.
- Success probabilities stay very high at all horizons when using 75-100% equity shares and withdrawal rates of 3.5% and under.
- Success probabilities deteriorate quite a bit when the retirement horizon goes from 30 to 60 years.
- It may be true that for a 30-year horizon, an equity share of 50-100% gives consistently high success rates if the withdrawal rate is 4% or lower. Essentially the main result of the Trinity Study! But for longer horizons, 100% stocks gives the highest success rate. This goes back to our earlier research that showed that over long horizons bonds can have extended drought periods and only equity-like returns are a guarantee for not running out of money over long horizons. For example, a 4% withdrawal rate has a 95% success probability in a 50%/50% over 30 years, but only 65% over 60 years. The failure probability is 7 times higher over the 60-year horizon!
- A 5% withdrawal rate would have an unacceptably low success rate even after 30 years, and certainly after 60 years. As stated above, no early retiree should get anywhere close to a 5% withdrawal rate.
Another way to look at the data: Plot a time series chart of different safe withdrawal rates over time both for 30-year and 60-year horizons. In the chart below I use an 80% equity weight and 20% bond weight, pretty common among bloggers. Unsurprisingly, the 60-year withdrawal rates are significantly below the 30-year rates. There are only a few occasions where the 30-year SWR drops below 4%, but a 60-year retirement horizon has a few stubbornly long episodes with 3.5-4% withdrawal rates. So, 3.5% is the new 4%! What’s worse, in future posts, we will show that you’d likely have to reduce the 3.5% even further to account for a) today’s high CAPE ratio and b) a higher final asset target!!!
Another way to slice the data; same chart but as a scatter plot instead of time series chart, see below. The 30-year safe withdrawal rate is on the x-axis and 60-year withdrawal rate is on the y-axis. The dots are all under the 45-degree line, no surprise here! On average, the 60-year SWR are more than a full percentage point below the 30-year SWR (below the 45-degree line), but in the region where it really matters, when the SWRs are low, the difference is “only” about 0.5%.
Thanks for the analysis of the 4% rule. Very persuasive. In fact, the analysis may actually understate the case against the 4% rule.
In the model, “success” is based on final values of the portfolio and cumulative 30 or 60 year returns — not on what happens to the portfolio over the path. It’s possible that the portfolio could be exhausted at an intermediate date before 30 or 60 years but could still be recorded as a “success” under this methodology. For example, that could happen if there was an early string of very bad returns, followed by a later string of very positive returns.
The possibility of an early exhaustion also raises a question about the robustness of the finding that very high equity shares are beneficial. High equity shares could increase the risk of early portfolio exhaustion which might not be detected using a methodology based on cumulative returns.
Have you done any robustness checks on the risks of early exhaustion?
Unless you have massive supplemental cash flows later in life, it’s unlikely that you exhaust your portfolio at an intermediate date and not run out of money after 60 years.
There is an issue if you have a more stringent criterion, i.e., capital preservation after 30 years, where the portfolio may drop below the final target (just not all the way to zero) and still you make it after 30 years.
Love this robust analysis! I wonder if there’s also a case to be made here that there’s probably a higher likelihood of being able to have a higher SWR if you retire a year or two after a bear market — i.e. after a market crashes and recovers for a year or so, you will likely have lower sequence of return risk since bull markets tend to last ~4 years on average + shortest bull market was 31 months (not guaranteed). I’m curious if your dataset might show when the optimal time &/or minimum recovery requirements to retire post-market crash is – while not 100% guaranteed given past results don’t necessarily predict the future, targeting this type of timeframe could give higher probability of success, especially for those considering lean or normal FIRE, vs. those considering retirement possibly towards the end of a bull market. This also seems to indicate that sequence of returns and market crash risk during early retirement is the biggest risk driving higher SWR’s – if these risks can be reduced, a safe withdrawal rate could be closer to 5%+ (larger pair of shoes maybe :)). Will continue to read through this series — I assume you also have something comparing the leveraged out of the money put-selling strategy with this to see how that adjusts SWR assumptions — with 7%+ tax-adjusted returns, it seems like selling insurance might also increase SWRs to some extent.
Thanks for digging into this hairy problem!
I don’t believe it’s a great idea to tie your retirement safety to strict timelines in terms of months or years after a bear market.
I already do the calculations contingent on the CAPE and the recent drawdown (see the Google Sheet). Fundamental measures like that are more useful in gauging conditional SWRs.
Thanks a lot for this excellent work, it is extremely helpful for the FIRE community. Based on the last ~150 years of US data, these results show that a 3% SWR has a 100% success rate for 60 year retirement horizon in case of 50-100% stock allocation. So assuming the future is similar to the last ~150 years of US data, which is not an unreasonable assumption, a 3% withdrawal rate seems very safe. Still, it will be immensely helpful if you could write a post on what the SWR will be if this assumption did not hold, by looking at countries that have been less fortunate than US. Specifically:
[1] What kind of SWR can generally be expected for a 60 year retirement horizon in case of Emerging Market, Pacific, or Europe? Is the SWR in these markets comparable to the SWR in US, or is it substantially lower than US?
[2] Your plots show what the SWR was in US for someone who reached FIRE during WW2 or near the end of cold war. What was the SWR for someone who reached FIRE during WW2 in Germany/Japan/Italy or near the end of cold war in Russia? i.e., how much does the SWR drop if a country ends up in the losing side of a war instead of the winning side?
[3] US recovered from past stock market crashes relatively quickly, so can you please also look at the effect of relatively long crashes on SWR? What is the SWR for someone who reached FIRE in Japan on Christmas 1989? Since there is only 32 years of data in this case, we can define “success” as say >50% capital preservation after 32 years.
If you could kindly spare some time from your busy schedule, and write a post addressing the above questions it will be immensely helpful for those in the FIRE community who wish to prepare for the possibility that the future may be less fortunate than the last ~150 years in US. If you (or someone else) have already done these analysis and have posted the results, can you please provide some references/links where I can read them? Thanks again for your excellent work.
1+2: I don’t have returns for other markets going far enough back to determine that. Wade Pfau and others have computed non-US SWRs. I don’t plan to spend time digging up the non-US data when others have done the job already. 😉
Another reason to not do the non-US calculations: If you believe that the U.S. will be invaded and destroyed like Western Europe in WW2, then all bets are off. I take my chances with the US believing that we will be stay unscathed like in prior events.
3: Not true. Post-2001, Europe recovered much faster than the US market.
I don’t think that Japan 1989 is a good comparison. We’ve never reached the PE ratios that Japan had back then.
Thanks for suggesting the work of Wade Pfau on non-US SWRs. I will look into it.
I’m not sure if this is exactly what you were referring to, but following is a link to a paper by Wade Pfau that “explores the issue of sustainable withdrawal rates using 109 years of financial market data for 17 developed market countries”: https://www.coronation.com/assets/Coroconnect/An%20International%20Perspective%20on%20Safe%20Withdrawal%20Rates%20from%20Retirement%20Savings.pdf
There are different versions of it, but this seems to be one reference, yes.
ERN — your work is fantastic for those of us who want more precision in our FIRE planning. Thanks for this SWR series which has taken years of work!
Question about how you do inflation adjustments. Let’s use an example. 3% of a 2 million dollar portfolio. You start with an initial withdrawal value of 60,000 or 5,000 per month. In order to calculate how much to withdraw with inflation, do you:
1.) Use your retirement start month as the base and then use an inflation calculator to find out the value of 5,000 in the present (For example, the Bureau of Labor statics one: https://www.bls.gov/data/inflation_calculator.htm). That means you use the same base for every month for the entirety of the withdrawals.
or
2.) Look at the current month’s inflation (https://www.bls.gov/cpi/) and just multiple the 5,000 by (1+ the inflation percent).
or
3.) Something else.
I’m assuming that you do 1 so that the inflation is cumulative (as we want to preserve our purchasing power as compared to our start date). Is that correct? I want to make sure that I understand what you are doing and how we should calculate how much to withdrawal each month in retirement.
Can you let us know your inflation source (where you pull the inflation date from) and method?
You’ve done so much for this community. Thanks again!
Thanks!
Yes, it’s indeed method 1 (though I don’t use the BLS calculator). I calculate the real returns myself.
The inflation numbers come from FRED: https://fred.stlouisfed.org/series/CPIAUCSL
The historical data from Shiller: http://www.econ.yale.edu/~shiller/data/ie_data.xls
Best of luck!
K.
You’re awesome. Thank you!
Karsten,
I was comparing your CPI with that posted by FRED. Up through December 2014 the CPI data matches. From 2015, your CPI is ever so slightly lower than FRED. While insignificant to all your extensive research, from an academic standpoint, I was wondering if FRED had adjusted the CPI calculations or you switched to a different CPI source or perhaps you have developed your own FRED CPI adjustment based on your research? Thank you for all the insights with the SWR series.
Benchmark revisions. The last time I updated the return and macro data was in mid-January. Return Data up to 12/2022 are OK and stay that way. But CPI can undergo revisions and they can go back many years. As we see, all the way back to 2018.
I reloaded the data and copy/pasted the new CPI data into the SWR sheet.. I will also update the return and CPI data up top 3/31/2023 once we have the new CPI data in April.
Also note that the revisions are minor enough that they will have no impact on anything calculated in the SWR sheet! 🙂
Sorry but i did not follow.
Taking original example
“3% of a 2 million dollar portfolio-You start with an initial withdrawal value of 60,000 or 5,000 per month.”
How should we proceed so that we maintain 3% withdrawl ra pa adjusted for inflation? I thought #2 does that
I forgot to mention – Thankyou so much for the detailed series. Ive skimmed through the entire series and now customizing this methodology for my parents who are in a different country 😀
You rock!
Both methods do that
Method 1 calculates all values in real dollars. Withdrawals are constant and returns are CPI-adjusted.
Method 2 uses nominal dollars. Nominal returns and withdrawals that grow by CPI.
I’m using Method 1 in my calculations. But if you like to use Method 2, that’s fine too. It yields the same final (real) results.
Thanks for clarifying. I had a followup question. Id really appreciate if you can clarify.
Approach 1:
Portfolio at T=0; P0=P
Expenses, E0=E
P1= P*(1+inflation_adjusted_return)= P*(1+ (1+return_rate)/(1+inflation_rate)-1) = P*(1+return rate)/(1+inflation_Rate)
E1=E
So inflation adjusted Portfolio Val at T1= P*(1+return/1+inflation)-E
Approach 2:
Expenses, E0=E
P1=P*(1+return_rate)
E1= E*(1+inflation_rate)
Inflation adjusted Porfolio at T1= P*(1+return_rate)-E*(1+inflation_rate)
This is where im getting stuck. Approach 1 creates an additional (1+inflation) in the denominator and they dont seem to match. What am i missing?
Ive taken definition of inflation adjusted return from Investopedia:
https://www.investopedia.com/terms/i/inflation_adjusted_return.asp
I normally prefer to make the withdrawals at the beginning of the month, so the portfolio value is P1=(P0-W)*(1+R1).
But I can run with your assumption too where you withdraw at the end.
In nominal terms:
(I) P1=P0*(1+R)-E(1+i). The withdrawal happens in period t+1, so we adjust the withdrawal by the inflation rate.
In real terms:
(II) p1=P0*(1+R)/(1+i)-E
If we had reclassified everything in real terms, i.e., real returns r=(1+R)/(1+i)-1 then we could also write this as
(III) p1=p0*(1+r)-E
Note that equations (II) and (III) are identical because r=(1+R)/(1+i)-1
It would have been nice of you to detail your rationale for including the historic data from 1871 – 1926, since so many of your posts reference the Trinity Study, data after 1926. I would not think that most investors would care to model their retirement projections on 1800s data, which is not robust or seemingly relevant. Without an explanation, it looks like the data was only included to boost your own model for lower withdrawal rates. The 1800s were a dismal period for stock returns and most of us wouldn’t have been able to retire in that era (or have indoor plumbing). Additionally, I have read that most the returns in the 1800s came from dividends not equity appreciation, although very few people invested in stocks during that era. Did your analysis include the reinvestment of equity dividends? I appreciate your work on safe withdrawal estimates.
In part 28 I introduce a tool where you can simulate your own stuff. And you can also look at the SWR stats only for the 1926-forward era.
Wouldn’t make a huge difference because the all-time worst case scenarios often occur during the 1929-1932 and 1968-1982 time spans.
Your hard work has brought me (and I’m sure so many others) so much peace and clarity for longterm financial plans, it’s been frustrating only finding rules of thumb in general media without seeing the pure math supporting withdrawal strategies, wildly refreshing.
Would there be a large difference in the result using a globally diversified index fund (I hold mostly VT and Vanguard/Fidelity TDFs in various 401ks)? Aiming for a 3-3.5% withdrawal in retirement
For ETFs that don’t quite fit into the schema I provided, there is a new tab (“ETF Factor Exposures”) in the SWR sheet with factor model regression results, where you can see what combination of asset class weights in the toolbox looks like the ETF of your choice. VT is most likely close to the iShares URTH (World ETF). Here are the factor weights to replicate it with the asset classes in the toolkit:
SPX-TR 65.76%
10Y BM 3.87%
30Y BM -0.94%
International 35.12%
Gold -1.59%
SMB 2.77%
HML -1.44%
Cash -2.22%
Oh wow, this is extremely helpful; perfect, thank you so much!
You bet!
Great website. Thanks for all the work you’ve done. If you don’t mind addressing, I’ve read through many of your posts and had a few basic questions:
1. For investing in equities, the implementation is straightforward (buy the appropriate index fund or ETF). However, since you recommend the bond portion of the asset allocation should be in 10-year Treasuries, do you recommend just selling the most long-dated holdings and buying new 10-year maturities when re-balancing? I would imagine you would end up holding 10-year treasuries with varying maturities, so this is unclear to me from a mechanical standpoint.
2. Is there an analytical way of thinking about re-sizing the SWR if the portfolio grows substantially after a number of years? It would seem aggressive to keep up-sizing the base withdrawal amount as the portfolio grows even using the fail safe SWR. On the other hand, never adjusting beyond inflation seems too conservative if your portfolio has seen substantial growth.
3. I read a 2015 paper by Javier Estrada that claims the strategy with the lowest failure rate is to have 100% equities (at the time of retirement!) and glidepath towards more bonds during retirement. He calls it a “Declining Equities” strategy. It sounds crazy, but I thought about an extreme scenario: if you are two years away from dying, you would hold two years of cash with a 50% fail safe SWR. Any allocation to equities would reduce the 50% SWR. This would seem to lead to a strategy where the bond allocation should increase during one’s retirement as you approach your terminal year. What are your thoughts?
1: I have return data on 10-year benchmark bonds. The closest you’d get would be the IEF, 7-10-year US Treasury ETF from iShares. I don’t recommend trading individual bonds as a retail investor. Mutual funds and ETFs are the way to go.
2: Yes. You’d recalculate your SWR as your retirement progresses. See Part 28. You’ll likely bump up your safe withdrawal amount as time progresses.
Another option: A CAPE-based rule. See parts 18 and 54.
3: 100% equities at retirement would have been bad when using US return data. The best approach is to have a high bond share at retirement and then shift back into stocks as retirement progresses. See parts 19+20.
Thanks for the interesting series of articles! However, based on my reading, it seems that the simulated portfolio return values used are unclear because of the extrapolated assumptions for equity and bond returns from Sept 2016 to some unspecified final year (I wonder what is that final year?), as mentioned in point 4 within your article, which I have reproduced below. It seems to me your simulations combined actual historical return values for stocks and bonds in your point number 1 and added to them with some additional extrapolated hypothetical returns in your point 4 for some unspecified number of years. Without the crucial piece of information regarding how many extrapolated years were used for the dataset, it’s hard to know how much I should trust those charts and figures. I hope this can be clarified. Thanks!
“4. We extrapolate past the current history and append equity and bond returns after September 2016. To this end, we assume long-term average returns for equities going forward (about 6.6% real p.a.). For bonds, we assume a low real return over the first 10 years: only 0% real p.a., which is actually slightly above the 9/30/2016 10Y yield (1.61%) minus the inflation expectation at the time (~2%). After the initial 10 years, bonds too will return their long-term average of 2.6% real per year.”
It makes no difference for the 1929 retirement cohort.
The 1964/65 cohorts now have almost the entire 60-year history, so the “calibrated/extrapolated” date is now almost completely rolled out and replaced with actual return data up to Feb 2024.
With later cohorts and very long horizons there may be a small impact but notice that the last few years of retirement have almost no impact on the SWR. It’s called Sequence Risk, see parts 14 + 15. Especially this table:
Linear regression result: SWR on future realized returns. Knowing only the average returns over the next 30 years is not very informative (low R^2). The distribution of returns over the 30 years matters a lot more! Note: Due to overlapping windows the t-stats are Newey-West heteroskedasticity-adjusted.