### Update: We 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)

Welcome back! This is our **50th post**, as I just learned from WordPress. Cheers to that and thanks to our readers for coming back every week! As promised in last week’s introductory post, we present some additional results about safe withdrawal rates for early retirees. Today’s post deals with an important issue that all retirees (whether retiring early or in their mid-60s) should ask themselves:

**Do we want to deplete our savings or maintain a certain minimum real value of the principal to bequeath to our heirs?**

We are amazed by how little discussion there is in the personal finance community about this. Hence, today’s topic:

**Capital Preservation vs. Capital Depletion**

**capital preservation**: target a certain minimum asset level (as % of the initial value) at the end of the retirement horizon. Under full capital preservation we’d aim to keep the real, inflation-adjusted value constant, by consuming “only” the capital gains, dividends, and interest over time, while keeping the principal (plus inflation-adjustment!) in place.**capital depletion**: target a zero (or at least positive) final portfolio value, by consuming gains as well as principal over time

Needless to say, the Trinity Study does its calculations according to strategy 2. In other words, a “success” per Trinity is to not run out of money before the end of year 30. Whether at a 30-year or 60-year horizon, the idea of depleting capital has at least two unsettling features for us:

- We like to leave a bequest to our daughter (and future grandchildren) and several charitable causes.
- We are uncomfortable with the idea of running out of money in our late 80s and being forced to live a less than dignified final years of our retirement or becoming a burden to our daughter.

**The fallacy of extrapolating from 30-year to 60-year windows**

It doesn’t take a rocket scientist to realize that capital preservation allows you to withdraw less than capital depletion. How much? That depends on the portfolio returns and the investment/retirement horizon. We found surprisingly little work in the FIRE community dealing with this issue, hence we got the computer running to do some research on our own.

One advantage of targeting capital preservation is that if your withdrawal strategy *preserves* capital for one 30-year window it will likely do so for a second 30-year window. But, if you *deplete* your capital after 30 years, then you cannot keep the same withdrawal rate for another 30 years. This is almost too trivial to point out, but you’ll be amazed how often you hear folks on the web mixing up the two. The extrapolation fallacy usually works like this:

*“There is a small probability of running out of money after 30 years. But the median final value after 30 years is likely much higher than even the starting value, even adjusted for inflation. So, let’s just extrapolate 30-year window to a 60-year window.”*

Huh? Do you see the fallacy here? The Trinity Study is not about the *median* retiree. It’s about the probability of *tail events*. We already know that a median retiree has nothing to worry about if the real withdrawal rate is roughly the same as the real capital market return. But after 30 years, there will be a significant percentage of retirees who will not be counted as a failure in the Trinity Study (portfolio value >0) but their portfolio might have been compromised enough to run dry after another 5 or 10 years. They are the people who will not be able to do a net worth “reset” back to the median after 30 years. That makes this extrapolation fallacy so dangerous.

**Warmup: Some simple calculations**

Before we even jump into the simulations, let’s do a little warm-up exercise. To gain some insights into why the 60-year withdrawal rates are likely significantly lower than the 30-year rates, let’s do some simple calculations in Excel.

Let’s assume a constant 4% p.a. real (inflation-adjusted) portfolio return. A retiree with a $1,000,000 portfolio withdraws a fixed amount at the beginning of the first month and then inflation-adjusts the withdrawals every month. Let’s calculate how much the retiree can withdraw under the following withdrawal strategies:

- Capital Preservation: 3.92%. Why not 4.00%? That’s because the initial withdrawal takes place at the beginning, not the end of the month. Who knew that such a trivial difference can make a 0.08% difference in the SWR?
- Target 50% remaining net worth after 60 years: 4.12%. Amazing, how a 0.20% difference in the withdrawal rate ($167 in the first month) makes a huge difference after 60 years. But then again, that’s 60 years of compound interest for you!
- Target capital depletion after 60 years: 4.33%. Only another 0.21% increase in the withdrawal rate and we wipe out the capital after 60 years.
- Target 50% remaining net worth after 30 years: 4.79%. If you wonder how long would the remaining half million last at that withdrawal rate: 13 years (to be precise, 160 months, for a total of 520 months).
- Deplete the entire portfolio after 30 years (Trinity Study assumption): 5.66%. That’s a whopping 1.74 percentage points above the capital preservation rate!

What we find intriguing about these numbers is that over a 30-year horizon, the benefit of capital depletion adds 1.74% to your safe withdrawal rate, while over a 60-year horizon depleting your capital adds only 0.41%. That’s one of the reasons we believe the Trinity Study is so flawed when applied to the early retirement community; a 60- year retirement horizon is a completely different animal from the Trinity Study 30-year horizon.

**Simulations**

The calculations above are all nice, but they are really only relevant for the median retiree. We don’t want to commit that same flaw we pointed out above. To determine the *tail event* probabilities, we again have to employ our simulation framework, using monthly asset returns since 1871 to see how different retirement cohorts would have fared under different assumptions. The table below is an extension of the results from last week. We report success probabilities over 30 and 60-year horizons (we leave out the 40 and 50-year figures to keep the table size manageable). The new feature in this table is that we calculate success probabilities not just for a capital depletion target but also for maintaining 25%, 50%, 75%, and 100% of the capital after 30 and 60 years. Note that the success criterion applies only to the *final* period. You could temporarily fall below that target, but as long as you finish above the target, we call it a success.

As we already saw last week, for a 60-year horizon, a withdrawal rate of 3.5% or below and an equity weight of 75% yielded excellent success probabilities. The good news is that targeting a higher final asset value does not mess up our success probabilities much. For example, at 100% stocks and 3.5% withdrawal rate, the success rate drops from 98% to 96% when going from capital depletion to a 100% final target value. Still acceptable! For a 30-year horizon, it’s a very different story. At 4% withdrawal rate and 100% equity weight you have a 97% success rate when targeting capital depletion but only 80% success rate when targeting 100% capital preservation. The intuition goes back to the simple Excel calculations: Over 30 years, capital depletion gives you such a big boost to the allowable withdrawal rate because the horizon is so much shorter. Hence, to achieve capital preservation we’d have to either seriously cut our withdrawal rate or accept much lower success rates.

We also found some interesting insights when plotting the success probabilities of different withdrawal strategies as a function of the equity weight, see chart below. It’s basically some of the same information as in the table above, but easier to visualize. The top chart is for a 3.5% withdrawal rate and the bottom chart for the 4% rate. Each chart has 4 lines for the different combinations of 30-year and 60-year retirement horizons, each with capital depletion (FV=0%) and capital preservation (FV=100%).

The dark blue line (30Y horizon, capital depletion) is what the Trinity Study is all about. And, according to this chart, it’s a completely different animal (probably a different animal from a different continent) from the other three lines:

- Success rates are significantly higher under the Trinity Study assumptions than under the other, FIRE-relevant parameterizations. At 3.5% withdrawal rates, the 30-year, FV=0 rule is pretty much fool-proof even at equity shares significantly below 50%. Not so over the 60-year horizon or for a 30-year horizon with capital preservation. For equity weights between 50% and 100% we face success rates that can be quite a bit lower. For example, look at the 65% success rate vs. 95% success rate for capital depletion, 50% equity weight, and 4% withdrawal rate.
- The retirement horizon has implications for the
**portfolio allocation**. While the Trinity Study suggested that pretty much any equity share between 50% and 100% is close to foolproof (and we confirmed that result) the simulations over 60-year horizons suggest that the success probability is monotonically increasing in the equity weight. Even more importantly, the success probabilities seem to drop off quite significantly when going below 70% equity weight. Over longer horizons, bonds are bad!

Another intriguing result from this chart: The 60-year capital preservation rule had a slightly *higher* (!) success rate than the 30-year capital preservation rule, at least for high enough equity shares. How is that possible? It’s quite intuitive: If your portfolio value was, say, 90% after 30 years, then you would have failed the 30-year capital preservation condition. But with the average portfolio return above 4% for a high enough equity share, you can likely get above the 100% target again over the next 30 years.

**Capital Depletion vs. Preservation Scatter Plots**

Just like last week, let’s create a scatter plot of the maximum allowable withdrawal rates under two different withdrawal strategies. Here are two charts, each with the SWR under capital depletion (FV=0) on the x-axis and under capital preservation (FV=100%) on the y-axis. The first chart for a 30-year horizon and the second chart for a 60-year horizon.

For a 30-year horizon, the dots tend to fall significantly below the 45-degree line. The median distance is about 1.25%. So, to preserve capital over a 30-year horizon you’d have to cut your SWR by about 1.25 percentage points. Ouch! In contrast, over a 60-year horizon, there is only a relatively tiny distance between the dots and the 45-degree line, only about 0.19%. Lowering the withdrawal rate by less than one-fifth of a percentage point can make the difference between running dry after 60 years and capital preservation. That’s good news and bad news at the same time. If you care about leaving a bequest you don’t have to curb your consumption by much to ensure maintaining your portfolio value for 60 years. But the bad news is that over a 60-year horizon, small changes in the withdrawal rate can have huge consequences on final outcomes.

**Summary**

- Safe withdrawal rules
*can*be extrapolated when the success criterion is capital preservation, at least if the equity share is high enough. - If the success criterion is capital depletion, as in the Trinity Study, we should not extrapolate safe withdrawal rules to longer horizons. Our simulations show that your failure rates grow significantly when going from 30 to 60-year horizons. You’d have to apply a 0.50% haircut to the withdrawal rate to achieve the same success rate again.
- Bonds may look attractive in the Trinity Study setting but due to their low expected return (only 2.6% real over the entire time period since 1871), they pose a significant risk of running out of money in the long-run. This is consistent with our earlier post on the long-term risks of low bond returns.

More great stuff here, ERN – amazing analysis as always!

The sensitivity of capital preservation outcomes to that initial withdrawal value is incredible. Peeps best be careful about spending rates, lifestyle inflation, etc… Doesn’t take much to knock over the apple cart.

Since it relates, I’ll link below to an FL post discussing from work from Pfau and portfolio preservation vis-a-vis withdrawal rates. You know I ain’t no fan of all Pfau’s work (or of Kitces’, for that matter), but WP managed to do something pretty useful on this front, and it provides a slightly different and complementary perspective to what you’ve set out here. Basically, the analysis covers what SWRs are for nominal and real wealth preservation over a 30-year horizon, using a 50/50 equity/bond mix, backtested beginning 1926.

Here’s the link: http://www.financialibre.com/the-4-rule-inflation-building-wealth-in-retirement/

Thanks as always for the awesome work…and more museum-worthy graphics!

Thanks FL! Great link! Yes nominal vs real is also something worth studying. We’ll do that in a future post. Cheers!

Very detailed work ERN.

What surprised me most was that we can extrapolate for the capital preservation model. Logically if you take a step back it makes sense, but its hard to wrap the brain around. The capital depletion model however makes complete sense. Just because you succeed to 30 years doesn’t mean you have more then a token amount left at the end of year 30. If that token amount wouldn’t last you for first 30 years how would it for the second? The criteria for success doesn’t change. Even if the safe withdrawal rate is 4%, you have to have enough left after 30 years to start back at 4%.

Thanks!

Yes, exactly. We were surprised too, initially, how the capital preservation rule extrapolates so well. Of course, it depends on the withdrawal rate too. If you set it too high (6%+) then extrapolation doesn’t work any more. But if the withdrawal rate is a little bit below the expected real capital market return it works pretty well.

Cheers!

ERN

Great, great post. I have boomarked as a keeper.

I extrapolated your data to our situation. Leave a 1x legacy fund. 2-2.5% WR. 40-45 yr horizon. 75% equities. I am thinking we will be close to rock solid, if not 100%. Please tell me it to be true!!

I was flabbergasted by the 60 yr vs 30 yr differences and I think any early retiree needs to read this, perhaps twice, and think a little harder. You have convinced me that the Trinity study is not for those with a penchant for pulling the plug at 35 yrs old and sitting back at 4% and enjoying the sunset, even with a fully loaded equity portfolio. That 1 in 10 chance of failing ( with capital depletion) would mean more work to supplement the income which for me defeats the purpose of an early retirement.

Yup, the 2.5%WR, 40Y horizon, 75% equities was 100% safe in the past. With the company pension you’re in excellent shape!

Thanks for stopping by!

ERN

So I am an ultra-conservative planner, and have long eschewed the 4% rule. Your (and FL’s) 3.5% work has been very helpful, however I’d still been leaning on a 3% WR target. This was even after completely discounting our future pension (appears stable), possible SS (who knows), and the likelihood of some enjoyable side work in our early FIRE years (oxymoron?). Given our personal dynamic, the idea of an (0.5 * Initial) endowment in the future is very appealing … I think that concept sub-consciously had pressed me toward a 3% WR number.

All that to say, as an engineer/finance geek, the data you present is quite satisfying. We’ve officially been recruited to the “dark-side” of a 3.25% target WR. Curious to see whether your audience participation analysis might have room to include a (1x equivalent) future pension income. I have a feeling that will drag me even deeper toward the “darker-side” of a 3.5% target, haha! 🙂

Really appreciate your analysis … this series is a really fine piece of work already!

Great, glad you liked our work! We are definitely leaning toward 3.25-3.50% as well in light of the long retirement horizon.

Yes, I will look into the benefit of Social Security/Pension income in a future post!

Cheers!

Thx for doing the math. Helps to understand assumptions and flaws in general studies.

We qould aim for capital preservation, for a period of 50-60 years… We might need to review the SWR… Food for thought…

Thanks ATL! Glad this was helpful! Cheers,

ERN

Thank you for your excellent analysis which I think is right on target. There is another aspect to the retirement numbers that is rarely discussed…the effect of taxes and what in type of account your assets are being held. Having 5 million dollars in a retirement account is very different than having the same 5 million dollars in regular brokerage account. Retirement accounts ( regular IRA, 401k, prension plan, profit sharing plan etc) are taxed at regular rates while money invested outside of these plans is taxed as capital gains only. What matters is what is left after you pay taxes. If you have a Mitt Romney sized IRA you will be paying top tax rates on your RMD.

It would be helpful to develop a chart which could analyze total assets and the relative percentage in retirement/non-retirement accounts and guide us on how to maximize the AFTER TAX returns or at a minimum help us decide how much one would have to spend.

I have no real idea what tax rate to assume when I make my projections. My current rate is

at the max and I assume in retirement it will be lower but I don’t know how much lower.

Clearly a 15% net tax or a 40% tax will have implications for spendable income.

Good points! After tax that 3.5% withdrawal rate might only be a 3.0% withdrawal rate.

Since everybody’s situation is different, we haven’t touched that topic (yet). But I will think about how we can address that issue. Good suggestion!

I can tell you what we envision for ourselves:

In the best possible scenario we can generate close to $100k p.a. in income with zero taxes. About $25k is completely tax-free (standard deduction plus 3 exemptions). $75k in dividends and LT capital gains are tax-free in the first two federal tax brackets. We also plan to live in a zero income tax state.

If your situation is different you’d likely have to apply another haircut to get your net SWR.

Cheers!

25x your annual spending is the often quoted metric for having enough money to retire using the 4% annual withdrawal rule.

Given the work you have done with these simulations and your own situation, how many multiples of your annual retirement spending to you plan to have saved up when you retire? How do you expect possible future lower returns to influence this number since your simulations are based on past market data when average returns may have been higher than future returns? I’m curious too about your answer to Dr. Joe’s question about how RMDs might impact your ability to not deplete your total retirement account balance over time.

Yup, 25x is what’s normally quoted, but we try to target 30x or more. Maybe all the way up to 35x.

You make a really good point about future returns being below the long-term averages. The CAPE ratio is much higher today and signal sub-par equity returns. That’s the topic of the next installment. 🙂

About the RMDs: For us personally, we have only about 1/3 of our net worth in tax-advantaged accounts. Even if we deplete all of them we still have taxable accounts to leave as a bequest. But even with 100% invested in 401(k) and IRAs, recall that the RMD only requires distribution, not consumption of the money. If the RMD is 5% and you want to consume only 3% of your net worth, simply reinvest the 2% leftover in a taxable account.

Cheers!

An idea for post #7

There are quite a few research papers out there from respectable asset managers and consultancies arguing that equity and bond returns going forward will not be close to the 20th century numbers. E.g. a recent report by McKinsey and Company argues that the real equity returns are likely to be ca 2 percent less vs historical for the next 30-40 years due to the slower labor productivity and population growth. It would be interesting to see a simulation which models such a scenario for a 40-60 years long retirement and includes the sequence of return drag

Agree: current equity valuations are expensive and that normally predicts lower than average returns. We plan to address that issue this coming Wednesday in part 3, so stay tuned!

Thanks for stopping by!

Your work has influenced my thinking about ER on so many levels. Thank you for doing it, and a note of thanks to PoF for introducing me to your blog – it should be mandatory reading for anyone considering ER.

Prior to your analysis of capital preservation vs depletion, I hadn’t read much about this issue. But for years, I’ve had a gnawing uneasiness about some of the financial calculator scenarios in which our portfolio “succeeds,” but without much margin. I don’t think I could handle that, psychologically. I feel much more comfortable with the concept of 0.25 – 0.5x capital preservation, and will use your data in our planning as we move forward.

Thanks again!

Thanks a lot. That was exactly our feeling: uneasy about some of the assumptions in the Trinity Study. I’m glad we dug deeper into this. 🙂

Cheers!

What an amazing analysis. Has really given me confidence about early retirement (or complete change in careers).

One question Im not clear on, is the final value for caputal presrvation adjusted by inflation or is it the initial nominal amount?

Thanks so much!

That’s a great question: Everything here is done in real dollars. So withdrawals over time are adjusted for inflation, and final values are also adjusted for CPI and expressed in date zero dollars. That’s such a crucial point because 50% of the nominal value would mean such completely different things over different time periods. That wouldn’t be informative. So the 50% final asset value has to be real!

I don’t know if you realize this but this will be a great segue to next week’s topic dealing with inflation adjustments and getting those right. 🙂

LOVE this post! Been looking for this information for a while. I’m trying to figure out what the withdrawal rate with 100% capital preservation would be after 60 year time horizon with 100% success. Would prefer 50% stocks. Looks like I’d be at 96% with 3% withdrawal rate based on your table. Is it reasonable to think I’d be at 100% success rate with 2.75% withdrawal rate, or is 2.5% a better rate to use? Thank you!!

Thanks! Yes, 3% and below it looks like historical simulations had extremely high success rates. Best of luck!

ERN

This is a great analysis and I very much appreciate the detail and depth of thought that the author has put into this series.

One thing I’m wondering about: Is FV=100% a proper target? Because as mentioned in the article the 60 year preservation rule had slightly better outcomes than the 30 year capital preservation rule, because the 30 year dip was intermittent in several cases. Now in the same vain a 120-year (or even a perpetual) preservation rule would have a better outcome than the 60 year year preservation rule, wouldn’t it?

Now obviously we don’t have enough data for that, but perhaps another way of compensating would be to look at FV around 75% (to pick a number), instead of 100%, to allow for some temporary dip at the endpoint. You show the data for FV=75% in the table of course, but I’m wondering, how much using something like FV=75% instead of FV=100% would have altered the subsequent analysis.

I think the gains from doubling the retirement horizon diminish when you go from 30 vs. 60 to 60 vs 120. There are enough business cycles to average over when you have 60 years and more.

In the post I have the table with 0-100% in 25% steps. The difference in success rates between 75% and 100% is noticeable for the 30Y horizon, but very minor for the 60Y horizon. Not sure what you meant by the question, but keep in mind that the success criterion is only for the final period. A FV=100% after 60Y is still OK even if temporarily you dropped to 50% or less after 30 years. I never calculated the probabilities of NEVER falling below a certain threshold. Only for falling below the threshold at the end of the horizon.

Cheers,

ERN

Great stuff.

So I’m 50 years old. No kids, just me and wife. 50/50 and perhaps now 60/40 portfolio.

If I’m not mistaken you are saying based on your research if I withdrew 3.25% over an approximate 50 year period I should not run out of money or have about 25 to 50% left over?

Looks good to me. Over very long horizons I always recommend higher equity shares. If you want to use 40% bonds, I’d recommend investment grade corporate bonds with a slightly higher yield (but not junk bonds!)

https://earlyretirementnow.com/2016/12/21/the-ultimate-guide-to-safe-withdrawal-rates-part-3-equity-valuation/

See the chart that uses 50% final value target and 3.25% SWR:

Also, keep in mind that you will get some Social Security! That adds another layer of safety. So it looks like you are in excellent shape! Congrats!!!

Bad: Because of reading your thoughtful analysis, my number has just increased. Good: Luckily I’m now aware of the risks of failure and I won’t pull the plug too soon. 3.25% sounds a lot more sensible than 4.00% now. Thank you for your in-depth analysis! Data and science ftw.

Btw is your analysis tool available online so that others or I can play around with it and verify/falsify your conclusions?

Thanks! A limited functionality tool is introduced in Part 7 of this series. Best of luck!