A Different Way to Plan Retirement – Guest Post on “Monte Carlo” Simulations by “Gasem”

Today we have another guest post, this time by our long-time reader “Gasem.” I’m sure most of you who have looked through the comments section here and at a number of other blogs would have noticed his comments. They are always highly insightful. He’s also a prolific writer on his own blog MD on FIRE, which I highly recommend. And if you’re not a Gasem-fan yet, I suggest you check out the What’s Up Next? podcast episode earlier this year where he was featured together with Susan from FIIdeas and VagabondMD

In any case, we had a discussion about using Monte Carlo Simulations to gauge safe withdrawal rates following David Graham’s guest post two weeks ago. And Gasem volunteered to write a guest post here detailing his approach measuring retirement risks. So without further ado, Dr. “Gasem,” please take over…

David Graham recently wrote a great post on this site regarding the 4% rule. What is the 4% rule really? You save 25x your yearly need and put it at some risk in a portfolio and then try to extract 30 years of value from the portfolio by extracting 4%/yr. 25x is the target (initial) principal. You have to inflation-adjust the withdrawal, and then you risk the principal at some interest rate above inflation. Let’s say you have 1M, you pull out 4% above inflation (and SORR doesn’t eat your lunch) you will preserve your capital and thus still have 1M 25 years later. You can re-retire for another 25 years on that 1M (capital preservation!) and still pull out 4%. So if inflation is 2% you need to make 6% on your money to run this money machine. 6% is the leverage on your future, That’s the “math” behind the 4% projection.

What’s the problem you say? The problem is volatility. The problem is the market can not guarantee 6% return and 2% inflation. Return is all over the map as is inflation. One year you may make 12%, the next year lose 20%. One year inflation maybe 2% and 5 years later 13% (1979). If you’re lucky it’ll work out you tell yourself, probably will work out, I read it on the internet! So what’s the probability? That’s where “Monte Carlo Simulations” come in. Let’s take a look…

Monte Carlo Simulations: A primer (by ERN)

Very briefly, this is Karsten/ERN again with a few words on Monte Carlo (MC) methods. You must have noticed that I haven’t written anything on MC yet. So far, I focused on historical simulations only in my Safe Withdrawal Rate Series. Personally, I find that historical returns, despite some limitations (chiefly, the limited amount of data we have to play with) is the most intuitive approach to tackle the two important features retirement researchers have to deal with: 1) time-varying asset class correlations; stocks and bonds sometimes have negative correlations, which is good for diversification and sometimes they have a positive correlation (1970s/80s), which is awful for diversification. And 2) mean-reversion in asset returns which makes asset returns, especially equity returns, look like they deviate from the strict random walk hypothesis, as documented in my blog post last year. Both features are hard (though, not impossible!!!) to replicate with MC!

But just to be sure, I think that MC analysis is useful and it’s a nice supplemental tool to what I’ve been doing. And if I can “outsource” that work to a blogging buddy like Gasem, even better. Less work for me!

There isn’t one single simple MC method. There are many different ways of performing this MC analysis and the devil is often in the details. At the heart of MC analysis is – of course – drawing random numbers to be used in the Withdrawal simulations. And there are many different approaches. Here are a few:

  1. Resampling of existing asset returns, single years. Also called bootstrapping. The advantage is that your simulated returns will have the exact same statistical distribution as the actual observed data; mean returns, standard deviations, skewness and kurtosis. This is very useful when we want to replicate the “non-Normality” of asset returns, especially the negative skewness of equity returns. (for the stats geeks, negative skewness means that the large outliers tend to be big equity market declines). This is the setting that Gasem will use in his MC simulations.
  2. A variation of method 1: Resampling of existing asset returns, but using blocks of consecutive data. Also called block-bootstrapping. This method still keeps intact the non-normality of returns but also introduces a little bit of mean reversion in returns, so we can better replicate a strong equity market recovery after a strong equity bear market, for instance. 
  3. Specify return parameters ex-ante and then draw Normally-distributed returns with the target return parameters. The disadvantage is that now you are back to normally-distributed returns with zero skewness. The advantage is that we can now target specific expected returns to take into account, for example, today’s low bond yields and high equity CAPE ratio. But this approach still suffers from the Garbage-in-garbage-out problem: your MC simulations are only as good as the inputs you feed into the process.

MC Simulations in practice (back to Gasem)

Gasem Guest Post Fig1
Monte Carlo Simulation results. Source: PortfolioVisualizer

This chart above is generated by a Monte Carlo engine at Portfolio Visualizer a free to use financial tool kit.

[ERN: If you like to play around with your own MC models, here’s is a link to the first baseline model with the 50/50 portfolio over 30 years. Notice that your results may vary slightly from the ones posted here simply because the random number generator uses a new set of random draws. Even with a sample size of 10,000, there can be subtle differences! Don’t cry wolf if Gasem gets a median final net worth of $1,974,143 and you get $1,971,123. That’s still within the realm of expected statistical variation!]

The analyzer works like this. It creates a model from a given portfolio (in this case 50% US total stocks and 50% US total bonds) and then runs it through 10,000 sequences of historical returns. It mixes in inflation and a standard sequence of return risk, and spits out a plot of the 10,000 probable future return paths from most likely to least likely. The most likely is the mean and is the 50% line the least likely graphed probability is the 10% line and the 90% line. There are successes below 10% but at some point there are failures. the 10% line represents 30 years of overall poor returns, but when all is said and done you still have 561K in the bank at 30 years with poor returns.

Another calculator in the suite the efficient frontier calculator calculates the nominal rates of risk (as SD) and return for the 50/50 portfolio described above with data going back to 1987:

Gasem Guest Post Fig2
Efficient Frontier (Stocks vs. Bonds).

With a 50/50 you can expect on the average 8.56% return, 2.56% above your 6% limit. These are quantitatively calculated statistical values not just guesstimates, useful and more granular knowledge than guesstimates.

[ERN comment 1: I love this plot! Notice how even with the cushion of 2.56% excess return over the 6% return target (at which you’d maintained your purchasing power!!!) you not only drop below capital preservation, but you even exhaust your entire capital after 30 years. That’s all the impact of asset return volatility and Sequence Risk!

ERN comment 2: Over a 30-year retirement horizon, a high bond share like this is not a bad idea. True, you have a lower expected return, especially with today’s bond yields, but over a 30-year horizon you can rely a lot more on capital depletion, so the lower expected return isn’t that much of a problem. This calculus changes dramatically when using 50+ years of retirement, though! See part 2 of my SWR series!]

In the above example over 30 years, out of 10,000 simulations, 9838 succeeded to make 30 years and the rest failed before 30 years. When did the failures start?

Gasem Guest Post Fig3
First failures start in year 18. Source: PortfolioVisualizer

By year 18, 3 people had failed, year 17 nobody failed. Quite a bit of information on a simple 2 fund 50/50 portfolio. Useful information in planning your future, since this is a future looking calculator.

[ERN: Just for comparison, using my Google Sheet and historical returns would have implied a 4.9% failure rate. I believe that the high bond share together with the bad experience of sustained low bond returns during the 1970s is responsible for this higher probability when using historical data. In contrast, with bootstrapping/MC you sometimes draw a return pair from the 1970s and then from the 2000s in the subsequent year, so you’re less likely to experience the sustained bond nightmare of the 1970s in your MC simulations.]

What happens when we use 80% Stocks and 20% Bonds?

Gasem Guest Post Fig4
Monte Carlo Simulation of an 80/20 allocation. Source: PortfolioVisualizer

After 30 years, 9504/10,000 succeed the rest fail. Roughly a 5% failure probability.

[ERN: Using my Google Sheet, an 80/20 portfolio would have had a 1.4% failure probability after 30 years. That’s lower than the MC figure. I suspect that the mean-reversion feature of equity returns kicks in here. In the historical data, a bear market is usually followed by a strong rebound. This is especially pronounced with an 80% equity share.]

Gasem Guest Post Fig5
The first failure in year 11! Source: PortfolioVisualizer

The first failure occurs in year 11 out of a 30-year retirement. The 10% guy at 80/20 only has 396K left in his account compared to 561K for the 10% 50/50 guy.

[ERN: $396k is a lot for a traditional retiree at age 95 or 97. Not so much for an early retiree who retired at age 30 or 35 and finds him/herself with only 40% of the inflation-adjusted capital left. The following years you’d then have an effective withdrawal rate of 10%, which will deplete your capital pretty rapidly! Not enough for another 20 years as we will see below!]

What about bad Sequence of Return Risk? You can adjust the SORR by putting the bad SOR in the first years of the model. Just like if you retired in 1972 you had about 3 years of bad SOR plus very high inflation! Here is a nominal 3-year bad SOR scenario with an 80/20 asset allocation:

Gasem Guest Post Fig6
80/20 plus “bad luck” in years 1-3 imply dramatically higher failure probabilities! Source: PortfolioVisualizer

Only 6722/10,100 survive the first 30 years, so we have a failure rate of about 33%. Ouch!

[ERN: This “three years of bad luck scenario” doesn’t directly correspond to any particular outcome in my historical simulations. For example, if I condition the failure probability on an elevated CAPE ratio, I increase the 30-year failure probability from 1.4% (unconditional) to 5.5% conditional on equities being expensive. Still relatively low but that’s because there are too many instances where the CAPE is high but the stock market rally stays intact (think 2012-2019).]

Gasem Guest Post Fig7
And the first failures occur in year 9. Source: PortfolioVisualizer

The first failures are at year 9 and the 10% line is out of money at year 16 AND the 25% line is out of money at year 23. This is with a 30-year retirement. What about 50 years of 80/20 asset allocation with 3 bad years of SOR first?

Gasem Guest Post Fig8
Over longer horizons, more and more portfolios fail. Source: PortfolioVisualizer

Only 3508 survive and 10% 25% AND 50% are out of money before 50 years! A failure rate of 65% over 50 years!

[ERN: Just for comparison, the failure rates over 50 years were 11.6%, 31.6%, and 50.8% for unconditional, CAPE>20 and CAPE>30, respectively. So, with extremely high CAPE ratios and a good chance of some bad sequence risk around the corner, we get to roughly the same ball-park. But again, the historical simulations had slightly smaller failure probabilities, again for the same reason as above: there is still a good chance of a continued rally for a few years!]

Gasem Guest Post Fig9
The first failure is in Year 8! Source: PortfolioVisualizer

The first failure is year 8. So that’s what you’re messing with a leveraged future. Remember this is the standard 4% Rule, 25x retirement plan everybody quotes. Sobers you right up, doesn’t it?

ERN: Thanks, Gasem, for putting this together! I learned a lot from this approach! I’m certainly happy to see that the MC simulations don’t differ too wildly from my historical simulations. The results can’t be (shouldn’t be) identical, of course, and where they differ I have a good explanation.

I personally consider MC analysis as a supplemental tool for my historical simulations. And others (I presume including Gasem) prefer their MC analysis and they might consider my historial simulations supplemetal to their MC analysis. We can both live with that. That’s because both approaches come to very similar basic conclusions:

  1. Beware of the difference between a 30-year and 50+-year retirement horizon!
  2. Beware of the difference between unconditional and conditional probabilities. A lot of financially/mathematically/statistically illiterate people out there tout the success probabilities of the 4% Rule. But since the unattractive valuations of both stocks (historically high CAPE ratio) and bonds (historically low yields) raise the probability of bad returns in the near-term we should look at the failure probabilities conditional on elevated Sequence Risk!

We hope you enjoyed today’s guest post. Please share your comments and suggestions below!

Picture Credit: Pixabay.com


67 thoughts on “A Different Way to Plan Retirement – Guest Post on “Monte Carlo” Simulations by “Gasem”

  1. Kudos for a great post Big ERN and Gasem!

    You have highlighted rightly the problem of volatility in messing up the 4% rule. Specifically, recall in the continuous time model, the long run return on the portfolio is actually: (mean – vol^2/2). So when the portfolio volatility gets higher (as in the case when the equities allocation goes to 70%, the volatility of the equities portion starts eating into the expected return, resulting in a higher failure rate.

    This leaves us between a rock and a hard place – we need the higher equity allocation in order to beat inflation, but at the same time, the higher volatility gives more SORR and puts a drag on returns!

    My own simulation work uses a normally distributed Monte Carlo as I do not have a long enough run of history in Asian stock markets to do either a historical backtest, or bootstrapping, but because my simulations don’t have mean reversion, the impact of volatility on long run returns is more pronounced. I am glad to see that I am on the right track as the results I am getting are similar to what you are seeing here.

    Look forward to sharing and hearing more!

    1. Exactly. I also have this “between a rock and a heard place” feeling. I’ve always pointed out that the low expected returns today don’t mean that we should stay away from equities. Quite the opposite, in order to get to decent expected returns we’d need a *higher* equity share. And cross my fingers that SoRR doesn’t strike.
      In contrast, if bond yields were 6% and the CAPE at 12, I could afford to keep more bonds in the portfolio and buy myself some piece of mind. Tough times today!

      Thanks for stopping by!!!

      1. Hi, ERN, I actually just coincidentally sent you this question in an email, but thought I’d post it here too to let others see and chime in:

        Hi, Karsten, I was wondering if you might have an opinion, or might blog about, on using implied equity risk premia as opposed to CAPE ratio when modeling. I find the implied ERP approach solves the many major problem I have with the whole P/E approach – a) forward-looking vs. backward looking, b) cherry picking (there’s nothing special about CAPE-10, it just happens to correlate slightly better than other years, but I’m not sure there’s a theoretical reason this should persist over time), and c) accounting issues (the way we define earnings is very imperfect – and may change over time). It explains how the market has performed so well for so long this past decade in the face of a high CAPE; and if you buy into it, it suggests in the near term equities will perform better than a lot of big names are saying to expect (definitely better than the CAPE yield suggests). The big drawback, at least for your purposes, is the lack (or absence) of historical data to run simulations. Thoughts?

        1. And here my email reply in case anyone else is interested in the answer:

          Good question! You’re preaching to the choir here! That’s (part of) what I used to do at work: derive expected equity returns (and equity premia) from forward-looking data (dividends/earnings) and do this in a systematic way, every day, for every imaginable equity index (bottom-up through all the individual stock data), sub-index, and even all individual equities themselves. It’s the only possible way to do so for professional money managers because clients will laugh you out of the room if you say you’re using the CAPE-10.
          Three problems with this approach:
          1: it’s labor-intensive. I had one guy working for me doing almost only this one task, making sure all the daily inputs are OK, troubleshooting, patching data errors, etc.
          2: data subscriptions cost a fortune, six figures a year, I believe
          3: you still can’t take any of the expected return values at face value because earnings forecasts are only slowly updated around turning points. You need an additional layer of complexity to avoid “value traps” where the price drops in 2008/9 but the earnings are too slow to respond so you start buying equities way too early. I wrote all the models for this task.

          So, with all those limitations, I still like using the CAPE-10 as a quick-and-dirty number I can look up in 10 seconds. 🙂

  2. Thanks Gasem for the post, I appreciate the different perspectives on how to approach risk management in retirement. And ERN thanks for the helpful comments and comparisons that you added throughout, it was helpful to place the post in context to all your other research.

    I was a little thrown back by the intro by the statement “So if inflation is 2% you need to make 6% on your money to run this money machine. 6% is the leverage on your future, That’s the “math” behind the 4% projection.” If I understand the origins of SAFEMAX correctly, I do not believe this “math” has anything to do with how the 4% rule was derived. I’m pretty sure this is merely coincidence that 4% happens to be approximately the difference between inflation and return assumptions. For example, if you change the withdrawal period to 20 years and keep inflation/return assumptions the same (i.e. sampling from the same historical data) the SWR increases to around 5%.

    To use this math as a justification for monte carlo analysis by saying that you can’t rely on 6% returns I believe is not understanding SAFEMAX correctly. 4% withdrawals already accounts for SORR (i.e. less than 6% returns), and from my understanding monte carlo analysis just helps us to prepare for situations where future returns may deviate from anything we’ve seen historically.

    But please let me know if I’m understanding this incorrectly. Thanks!

    1. Got it, SAFEMAX is a term from Bengen’s 1994 study. It is just a number based on his analysis, it’s not a guarantee. SORR on your particular portfolio is unclear and that is my problem with the whole historical analysis, it can’t predict the future it only predicts success in the past. Big ERN has the horse power to stand that cognitive dissonance, I do not. I’m much more comfortable living a “probable” kind of life with tweaks adjusting my level of risk down so it’s a matter of philosophy. I found his calculations very interesting using Sharpe’s as a risk adjuster, in fact brilliant. I would like to incorporate Sharpe’s data into the Monte Carlo model. I did the analysis using FIREcalc between Monte Carlo and historical and the non Sharpe’s adjusted data is VERY different and much more scary IMHO, but again it’s just a means trying to divine tea leaves. IMHO if you think Bengen’s “SAFEMAX” is a real value, from my analysis you’d be right about 4/5 times so those are your odds. If you had those odds in Vegas and a big enough bank you’d soon enough own the casino, but if you had a one shot like a single retirement you’d loose 20% of the time. not enough safety for me.

      1. I slightly changed the language in that paragraph and added that the 6% was derived to target *capital preservation.*
        Of course, over short horizons, you could also add a little bit to account for capital depletion. Not very much over a 50-year horizon. That’s why I like this approach of gauging the needed expected return: over very long horizons (as for most FIRE folks), the aim has to be capital preservation at least initially. Thus, the calculation inflation +4%.

  3. Hi Matt, I used the 6% number because that is the number that kept withdrawal at a steady state given 2% inflation. It emulates the notion once you make your million you can yank out 40K/yr inflation adjusted forever. I’ve never heard the term SAFEMAX before so not quite sure what it means. The 6% case is the kind of number a Future Value Calculator would give you inflation adjusted to live forever on 1M and a 4% withdrawal. The problem is life is nothing like a FV calculator because of the excessive risk we all own. SORR is unknown and variable. If you retired in Dec 1999, the SOR was horrible and subsequent growth in the S&P required almost 7 years to get back to 1999 levels only to be followed by 2008 which took things down again. If you owned 100% S&P it took till mid 2013 to get even! That’s 13 years of a 30 year retirement you spent underwater. If you were pulling 40K/yr out it would have made things virtually impossible to recover from. As it is, its unclear the 1999 cohort will survive 30 years if there’s another big one, and they certainly won’t survive if inflation kicks up. Monte Carlo has a statistic it generates called perpetual WR. In the 50/50 AA case perpetual WR is calculated at 3.65% on a 50 year withdrawal at the 10% (bad returns) line, so it just depends on how risky you are. You should understand there is no actual “safe WR” when you choose WR you are making a bet, not signing a contract. It may or may not payoff. All of this calculator mumbo jumbo is about trying to understand the risk of that bet.

  4. I don’t really trust the 4% rule. It should work when you’re 55, but it might not if you’re 35.
    That’s why I’m still working a bit to bring in some income. A little active income is a huge cushion.
    I can put off withdrawal until I’m a bit older. Also, it’s way easier to work a bit when you’re young.
    Working will be a lot more difficult when you’re older. It’s harder to adapt as you get older.
    Lots of data, good post.

  5. Hi Guys,

    Nice article. I appreciate reading everything on this website. You are guys are definitely super duper into this.

    However, please find a way that will make it simple for common folks.

    Please kindly consider writing the following post: “If you do this, you should be fine in your retirement” and “If you want to make couple of more percent which will compound to a lot over time, read the rest.”

    1. Hi Karl Unfortunately at least from my perspective retirement and spending down a portfolio is a lot more complex than the 4 x 25 crowd lets on. I have a 4 part series on my website called Parsing Cash Flow in retirement that discusses how I optimized my retirement. I also have a post on how to construct a reliable budget called Financial Intermittent Fasting and another called How to Create a Budget Spreadsheet. In those articles I go through how I think about constructing tax efficient reliable retirement income and a Roth which serves as self insurance in case of medical disaster and end of life care for 2 people. I’m 67 fully retired with a wife, no side gigs, living off my money machine, and I NEED as reliable an analysis as I can muster. in order to not run out of money before we run out of breath. I would love to write the post you suggest but I try not to deal in fiction. If you read through this post you will start to become familiar with some of the concepts and that’s a basis on which to grow your knowledge.

      1. Hi Gasem,

        Thank you very much. I will start looking at your blog.

        Little about myself. I am 39 years old and roughly 1.5M in investments. In my humble opinion I am neither poor or rich. I am okay. This is after diligent in savings and investing for 23 years.

        I want to get myself on the right path. Our financial exchange system and the flow of electrons of assigned value that is used to exchange of goods or services is simply amazing. It is hard to call it real money after seen the same $80 in my wallet not being exchanged for a long time. Thus, getting the right formula in place is critical.

        I won’t retire just yet because I have no need to. I get tons of time off plus I still got lots of life left in me. I have been in lots of places.

        Lastly, what is amazing about the the blogosphere is that real people put in real numbers with real results and genuine opinions with real goals.

        In general, no more shady investments opportunities or shady investments funds that will squeeze everything of our your money and put you at a loss.

        These types of blogs make better life for everyone that wants to be better.

    2. Thanks!
      I wish we had a simple solution like this. It also depends on what’s your definition of “fine”
      But here are some ideas:
      1: Use the fail-safe WR that would have survived both the Great Depression and the 1960s-1980s. It’s hard to believe that what’s ahead can be much worse than those two events. Problem: you will likely withdraw way too little.
      2: Use a CAPE-based SWR (see part 18 of the SWR Series). Problem: your withdrawal amounts will fluctuate depending on how the market evolves.

  6. First, in Karl’s comment above, he would like you to write a post “If you do this, you should be fine in retirement”. I think the answer is “work”, huh? The fact is, saving is simple, but withdrawing is truly not. That’s why I really appreciate posts like this one and the vast number of posts from Big ERN. I believe the most important observations come from looking at the standard deviations. The fact that they are large is the big take away for me. It makes me happy that we did overshoot before quitting work and also happy that I just can’t help myself from finding new ways to make money.

    Also, it is great fun for me personally to read your post, having shared the microphone with you and being one of the lucky few who actually have seen you, albeit on the screen. A memorable experience!

    1. Hi Susan,

      Your response “work” is very cute but not what I was looking for. Let me clarify.

      There has to be a middle ground somewhere where I won’t have to get a Ph.D. in “effective withdraw rate” in my retirement but also enjoy the tons of money that I have saved up for many years as my reward.

      I love to read this blog and absorb all of the very valuable information presented but not everything needs to be a thesis paper of thousands of words.

      Obviously, the 4% is not the way to go pretty much in any real scenario, so now ~3%+ a little might be the way and in the significant market pullback times 0% withdraw rate is probably the best. That said 0% withdraw rate I am not enjoy the fruits of my labor.

      Or, may be there is another way. For example: Today Mr. Market is flying high and expected to fly for little while more until all of us will think that it will not and here comes lovely correction that and a real opportunity to get wealthy appears on the horizon.

      May be Big Ern analysis could reveal that we should take out 4 years of your expected spending put it bonds and let it all ride in equities. I honestly don’t know but would like to find out the answer.

      I am asking our community to come up with a rather simple plan that works and it is relatively good enough. I would love to have 20M in my 80’s after living off initial 1M after 30 years but that is not realistic. I think, the true success the same amount in the account adjusted for inflation while enjoying it for a long time.

      1. Hi Karl,

        My apologies for being cute, but the reality is that there is not a “rather simple plan”. I credit Big ERN for pointing out that while saving for retirement can be shockingly simple math, creating a plan for withdrawals is shockingly unsimple. Hence the 31 and counting posts on SWR. As a reader here, I have found that in spite of PhD type of analysis, Big ERN is able to then explain in much more simple ways the various conclusions he makes from the data. From this, you can find different points that will assist you in figuring out your own retirement asset allocation and withdrawal rate plan. The truth is that SWR analysis is very complex and I consider Big ERN to be a gift to our community in doing the really difficult lifting that will help us all make better choices.

      2. I agree with Susan in that Big Ern’s value to the community is his depth of analysis. The simple-ish answer can probably be found in his glide path articles where he recommends 60/40 -> 90/10 during the first 5-years of retirement. That reduces the SOR risk scenario played out here. This article is a very deep dive into the complexities of modelling. It’s a great article b/c every other analysis out there (Trinity, Kitsch, etc.) and every planning/simulator tool uses MC and not historic returns. It’s like modeling the “100-Year Flood” vs. modeling an actual historic storm. Do you design a dam for the 100-Year Flood or an actual storm that happened in the past? It is a very nuanced question. I believe Big Ern’s conclusion was that it doesn’t particularly matter since the results convey the same two issues: watch out for SOR in the beginning years and 2) 4% is still a bit optimistic for 30-60 yrs horizons.

      3. A simple plan is to have 2 portfolios. The main portfolio is risked at a moderate risk (say 10%) and contains the bulk of your wealth. The second portfolio is what I call the fuse portfolio. It consists of about 2.5 years of WR risked at the Tangent portfolio which is about 85% total bonds and 15% total stocks. It’s risk is MUCH lower about 4% so if stocks drop in half the stock part of this portfolio goes from 15% to 7.5% hardly noticeable. Your fuse portfolio is still 93% solvent, and after a few years of growth is probably 100% solvent. Also own some GLD maybe 5% that you can sell when necessary. In a crash GLD and stocks tend to be negatively correlated.

        I looked at the market and it crashes around 20% of the time meaning it makes money 80% of the time. SOR is only dominant over the first half of retirement , so in a 30 year retirement from 5 years before to about 10 years after. In a 60 year it’s active for about 30 years. The worst case is the initial 4-5 years. When the portfolio is making money use the portfolio to buy your hamburgers. When the portfolio crashes use the tangent portfolio to buy your hamburgers. This closes off the main portfolio from SORR. You should probably tighten your belt as well. If you carry 10% risk you should live on 90% of your WR, and that 90% WR then comes from the fuse. Use all or part of the fuse portfolio, and if still needed sell the GLD. In a downturn GLD tends to soar so you have something to sell high when stocks are low. Every year re-balance everything including the tangent according to mechanical re-balancing techniques DO NOT SECOND GUESS THE SYSTEM. My analysis showed you only need burn the fuse once to save the main portfolio from SORR so it’s not a bucket system which is a drag on return, it a sacrificial system that sacrifices the fuse to save the main. If you make it to the last half of retirement, the chances are there is nothing you can do (within reason) that will run you out of money before you die. You can glide path or dance a jig or whatever. So those are 3 simple techniques own a fuse, own GLD and do mechanical re-balancing that can aid your portfolios longevity. In addition don’t retire too early, don’t over risk with too high of a AA, keep your portfolio on the efficient frontier which is a line that promises most return for least risk. Understand what you are doing

        1. >Also own some GLD maybe 5% that you can sell when necessary. In a crash GLD and stocks tend to be negatively correlated… In a downturn GLD tends to soar so you have something to sell high when stocks are low.

          Why GLD over treasury bonds? Treasury bonds (including TIPS) have positive expected return and historically have an even more negative correlation with US stock market than GLD does (according to PortfolioVisualizer’s Asset Class Correlation page).

          1. I own treasuries too, but treasuries serve the purpose as a bank for increasing stock value on the way up. If you re-balance a little extra goes into bonds. Come a crash that extra value is returned to stocks just in time to explode to the up side. Stocks are not money. Stocks are property. The goal is to buy as much property as you can when it’s on sale. When the market crashes the worst thing is to have to liquidate. Stocks are the growth in money machine bonds are the risk management. If you start selling pieces of your money machine (beside the WR) eventually it will quit working. SELLING your money machine in a crash IS the definition of SORR. Home don’t play that

            If you look at a yahoo chart of S&P 500 and add GLD and scroll back to 2009 you will see what I am talking about. The volatility of GLD jumped up the price as much or more than the vol of stocks drove them into the dirt. The rule is buy low sell high. I bought my GLD low. Yes it just sits there. So? It does just what I want it to do, hedge my bet, and it does it on the cheap, it just sits there. If I owned the VIX it would cost me an arm and 2 legs. It gets big and fat and gives me something to sell in a down turn. Portfolio viz looks at correlation over a long period and you are correct over a 30 year average but I have a specific plan over the 3-5 year course of a market crash

            I’m going to really blow your mind I also own BTC which I bought at $275. After it went to 10K I sold a tiny part and got my principal back and bought BRK.B with that dough and left the profit ride as a free trade, so I’m into BTC @ zero dollar basis and that basis money is in BRK.B. If BTC goes to zero I’m out nothing. If it goes to the moon I go too. There are other ways to create value besides owning low cost index funds.

          2. Gold had the tendency to hedge risk during all of the major down markets. Treasuries got soaked in the 70s/80s. But use it sparingly, otherwise you water down the expected return during the non-crisis periods! 🙂

      4. Also, keep in mind that because everyone’s situation is different, there can never be a universal answer. You’d still have to get your hands a little bit dirty and enter your personal parameters (retirement horizon, additional cash flows from pensions/SocSec, etc.) in the SWR Google Sheet (part 28) if you like to see the historical fail-safe.

    2. Thanks Susan! Great to hear from you!
      You’re completely right, there is no easy answer for the “if you do this then you should be fine” issue (though I tried to give two suggestions). Withdrawals are much harder than saving for retirement! 🙂

  7. When I run portfoliovisualizer for: retirement starts now at age 63, duration 35 years to age 98, monte carlo statistical returns, SORR worst 5 years first, a conservative initial annual dollar withdrawal of 3.25% of initial portfolio value, increased annually for inflation, custom percentiles of 1, 2, 5, 10, 25, 50, I get the best success rates and ending portfolio values for U.S. 10% equity / 90% bond and 20% equity / 80% bond vs. higher equity portfolios like 60 / 40 or 80 / 20. Interesting! So for a 35-year retirement starting now, with a current high CAPE / high SORR, and an initial low withdrawal (3.25%) well below the “4% rule of thumb,” maybe it’s not necessary to take on the additional market and volatility risk of a higher equity portfolio. More to think about……

    1. Kind of my conclusion as well. During accumulation you are interested in increasing return, but in retirement you are interested in lowering risk. During accumulation you let the job be your risk management. bad times? Work another year or two. In retirement you don’t want that pile of risk you owned during accumulation so you jettison some risk for more stability as long as the return is adequate to cover the WR and inflation plus a little

    2. I’m not surprised. Historically, bond yields were much higher. But with today’s yield (10-year at a little over 2%) you will not be able to repeat that success rate. So, I’d be cautious about using the MC analysis for optimizing portfolio shares…

      1. Thanks ERN. Regarding historically higher bond yields, is this nominal or real? When I look at multpl.com their calculator shows basically no real 10-year bond return or stock return for that matter between 1966 and 1982. So at today’s 2% inflation rate and 2% 10-year treasury yield isn’t it a similar regime?

  8. I see high CAPE frequently thrown around as a boogeyman. Maybe in hindsight we might just realize that CAPE is no longer the right metric to value stocks in a world where the effective lower bound is not zero; but in fact negative for interest rates.

  9. Your web site as well as the retirement cafe and more recently Gasem have done a much better job than other bloggers I have found of discussing the risks of retirement planning, SORR and inflation risk. What is the downside of an alternative strategy for dealing with these issues where one retires at 62, funds a TIPS ladder with 1/3 of his portfolio to completely cover anticipated expenses from 70-95 and leaving the bulk of one’s portfolio to grow in a mix of Roth and post tax accounts? Social security taken at 70 would essentially double the amount of income needed to cover the expected expenses serving as a second hedge against inflation and takes SORR out of the picture for the later decades of one’s life. 62-70 can be funded with 3-3.25% of the remaining portfolio. I recognize I am essentially building my own annuity but with greater flexibility, lower costs and retention of retained capital at the end of life. I have seen this strategy mentioned but always very cryptically. What downsides am I missing?

    1. Why don’t you just buy a regular annuity? There are plenty available and it would be cheaper.

      1. I have thought about annuities a great deal. I have rejected them because the fees are very high and the industry is not very transparent, not to mention most are not inflation adjusted. An analogy I use is the difference between paying cash for a house and getting a mortgage. A mortgage is ‘cheaper’ in that it is less money upfront but the fees have never been less than 5000$ in my experience as well as months of submitting documents over and over again (banks have had a tendency to claim they ‘couldn’t find’ documents submitted). The retained money can plummet in value depending on market returns. Last year I paid cash for a house for the first time. Total closing cost was $800. Closing took 11 minutes and only that long as the attorney was required to read part of the agreement and they talk slowly in the south. Documents were a screen shot of a bank account and then telling my banker to wire the money to an escrow account. It took a few minutes of time total. The money came out of the stock market and avoids sequence risk as it is sitting in a house which tends also to be an inflation hedge. I can access it any time via a HELOC. I see the TIPS ladder the same way. I have ‘won’ in a sense so removing money from risk and guaranteeing my living expenses in today’s dollars seems the best course.

      2. Too expensive, especially for a 44-year old. And the annuity is then only nominal, i.e., eroded away by CPI inflation.
        But I can see that for 60+ year old might want to pay out a portion of his/her net worth through an annuity to provide a consumption floor.

    2. Read my series on Parsing Cash Flow in retirement. It’s pretty much what you describe except I optimized the tax burden and analyzed specifically a precise predicted cost of a 20 year retirement and built a reliable budgeting tool to track actual expenses. Real hard data like a reliable budget is useful in planning. My twist is I left 500K in a TIRA risked at 15% stocks 85% bonds and let it go to RMD. This throws off a reliable slowly growing income with quasi inflation adjustment because of the progressive nature of RMD, gives me a place to store my bonds and when mixed with SS keeps me in the 12% bracket for 15-20 years with the 0% cap gains advantage. The rest of the budget is provided by brokerage mixed with 0% or Tax Loss Harvest so the brokerage is effectively like a Roth. My actual Roth is self insurance to fund end of life or medical disaster or high inflation, big ticket stuff. It can also cough up a new car once in a while or a trip to EU

    3. Thanks!
      I think your strategy works just fine. The “downside” is that a conservative, 100% safe strategy like that would probably require much more capital than the good’ol 4% Rule. But if you already got the money, you’re doing the correct thing!
      Might not be exactly replicable for the average super-FIRE retireee in their early 30s, though! 🙂

  10. The FIRE community tends to look at retirement as a problem of investment returns. This is why they strongly focus on high stock allocations. My view is that retirement planning is really a question of risk management. With that in mind the TIPS approach seems to achieve the primary goal and allow for growth in the rest of your portfolio.

    1. Rather than indite the FIRE community I think peeps are well versed in building a money machine, while their risk is being covered by a W2 but less clear about what to do once the W2 is gone and spending commences. Running the money machine is no the same as building the money machine. I fully agree de-risking while maintaining your lifestyle is necessary

      1. I am not indicting them. While working 100% stocks is reasonable. I am referring to the 40 year olds who are retired with 1 million dollars and advocate the same portfolio. They are struggling to find a way to cope with inflation risk as well as SORR when they really don’t have enough money and write about retirement as though the only concern is portfolio failure. My real point is they don’t seem to understand how risky what they have done is and they should consider ‘insuring’ their portfolios in other ways including working longer. Going broke in retirement is as likely to be due to unplanned spending shocks as it is to SORR and portfolio failure and with 1 million dollars and a 4% withdrawal they have no protection against either over a very long period of time. You have written about this in a different way on your site. The whole idea of pursuing financial independence is great. I fear that some of the young writers don’t fully appreciate the risk. Work such as yours and ERN help underscore the risk in different ways and are most welcome additions to the discussion.

        1. Why do you think everybody has a side gig? Nobody trusts the numbers. Nothing better than a job to cover your risk. Of course if the gig goes away you’re kinda hosed. I hope my work does offer a means to better inform about risk and methods on how to beat it. It’s been a total gas figuring all this stuff out.

        2. Thanks!
          Fully agree: While working 100% stocks seems OK. In retirement, SoRR calls for a a more measured approach. Another reason to be more conservative with both asset allocation and SWR: the unpredictable spending shocks you mentioned. Good point!

    2. Agree. All the talk back in the 1990s (Bengen, Trinity) was all moot because in the late 1990s you could have generated a 30-year TIPS ladder with a 5% SWR.
      Unfortunately, today’s bond yields are so low that even a 30-year retiree doesn’t get to 4% SWR with that approach. Much less a 60-year retiree.
      So, you’d have to save much, much more than 25x, even more than 33x (which would have beem the fail-safe in 1929) with the bond ladder approach.

      1. I was thinking about this and low bond yields may actually be somewhat protective for the levered up portfolio. Bond yields are not free money because bonds are contracts issued by the government and someone has to pay that say 5% to the bond holder as opposed to 2%. The debt would balloon and the market would tank with an immediate reversion to or below the mean (as we started to see last December) and FIRE tycoons would start jumping out windows or queuing up for the one job opening at Lowes.

        A 50/50 portfolio has a certain amount of risk much lower than a 100/0 or a 90/10 portfolio. The Bengen study was based on a 50/50 with a certain historic bond yield much different than today’s. If the Bengen study at a 50/50 AA therefore could be invalidated because of today’s low bond yields, the Monte Carlo suffers from the same systematic error because it’s model is based on a 32 year average of bond yields which included at least some of the high yield years of the 90’s. Based on this analysis, I’m not sure whether MC or Historical is “more accurate” as a future predictor.

        1. Good point. At double-digit rates for Treasury bonds we’d be finished. But I think 4-5% yields would be the the sweet spot. Affordable for the government and enough yield for investors and enough room for bond yields to drop to serve as a diversifier in the next recession. 🙂

  11. >ERN comment 1: I love this plot! Notice how even with the cushion of 2.56% excess return over the 6% return target (at which you’d maintained your purchasing power!!!) you not only drop below capital preservation, but you even exhaust your entire capital after 30 years. That’s all the impact of asset return volatility and Sequence Risk!

    What hypothetical person/situation (“you”) is ERN referring to? The plot shows the 8.56% CAGR of a 50/50 portfolio over the time frame of 1987-2019. ERN’s SWR Toolbox spreadsheet shows that a 50/50 portfolio for a 30-year retirement starting in 1987-Jan can support a 7.69% SWR for capital depletion, 6.39% SWR for capital preservation, and would end up with 2.83 times the initial value if a 4% WR was used.

    1. That’s one single SWR simulation with volatile returns. The calculation here was a “back-of-the-envelope” calculation. A 6% fixed return with 2% fixed inflation can support a 4% SWR with inflation adjustments.
      It’s merely a side-issue, so I’ll leave it at that.

  12. Looks like the comment stream has dwindled to a trickle, so I would like to thank Dr Big ERN for the opportunity he afforded me. I consider it an honor. Karsten is one of a few to whom I pay attention. Other’s are Kitces and some of the seeking alpha crowd who pose interesting perspectives from which to learn. This article was a contrast in data analysis and simulation techniques to try and reach a more accurate understanding of the likely future.

    I think one of Karsten’s lasting contributions is adding a Sharpe’s dimension to the analysis of risk. It would be good to add that to the Monte Carlo model. Another is his view on the economy, and a third is his AA which includes an options play, a very different kettle of fish than buy VSTAX, hold forever and fret about how many bp you pay to own it. It’s proof there are other ways to make money outside of index funds and real estate. I day traded options for a decade back in the 90’s, made some good money but it requires dead bang risk management to not loose your shirt. I would create a “mini mutual fund” of 4 or 5 different option trades either short or long and let that diversity improve my chances.

    1. Thanks, Dr. Gasem! Nice post and great summary.
      Yes, beyond the SWR analysis I also do a few other things differently, including the options strategy, currently 35% of our financial portfolio. I should probably try to write a post on how the option selling strategy works in a SWR context and how it may alleviate SoRR. Lots of things to do! 🙂

  13. I use bootstrapping monte carlo; but I also combine with ERN’s approach: first 15 years are the historical assumption based on CAPE. Then, after that, results are bootstrapped from historical returns.

  14. BTW, you can also do as I do with Portfolio Visualizer, and do your monte carloe with ERN’s monthly Sp500 and 10yB data set. The same reasons that apply to ERN using monthly for his method apply to MC as well.

  15. “we should look at the failure probabilities conditional on elevated Sequence Risk!”

    Exactly !! … my own simulation work is not based on historic data but on what-if, ie if the annual performance is x, y or z and so on. In a way a harsh stress-test. A 1 in 10 chance of running out (for example) misses the essential point that we cannot afford to run out

  16. Great post. There’s one thing I don’t understand about the Portfolio Visualizer Monte Carlo simulation results. The simulated portfolio time plots are always smooth whereas I understand a true Monte Carlo Simulation would draw random return samples from the historical data thus resulting in a “jagged” path. Does anyone know why ? Makes me wonder is this is a tru Monte Carlo or some idealized growth based on a projected average return.

      1. Thanks Ern! That makes sense. I’m writing my own simulation script (in R) and this difference was bothering me:) . I’m also finding that running Monte Carlo Simulations vs Historical data results in more conservative results for safe withdrawal rates. That is to say, Monte Carlo tends to draw sequences that are even worst than the historical record. I’ve read that you are not a big fan of Monte Carlo – even when drawing from the data rather than assuming a normal distribution with a projected growth/sd rate. Is there any place for Monte Carlo in your opinion (given these shortcomings?

        1. I wouldn’t discard MC completely. For example if someone assumes that we’re now hopelessly overvalued and after the next bear market will merely recover at average growth rate and we’ll never get back today’s CAPE ratios, then sure, MC would be a good model. Much more cautious than historical simulations where you always saw a strong recovery after every bear market.

          1. Hi ERN, what steps / parameters would you recommend using your Google sheet and / or portfolio visualizer in order to model the scenario you outlined above? Thanks.


            1. Well, there’s no MC analysis in the Google Sheet. But I think that both the 1929 and 1965/66 starting points are enough of a worst-case scenario for an equity market that takes a long time to recover.

  17. I have used both Monte Carlo and Historical methods to check my retirement plan. Usually the Monte Carlo method gives more conservative results. Lately many of the financial blogs have been recommending that analysis be done on an on-going basis, rerunning Monte Carlo analyses after retirement as well. However no article I have seen has given any indication of exactly how to do this. For example, my analyses have been based on the 25 year average market and bond returns and standard deviations assuming a 25 year life-span. Of course, things have not exactly gone according to plan with regard to both income and expenses. Now that I have been retired 7 years so now I have a better idea of how things will go from now on. If I rerun the Monte Carlo starting with today’s balances and with these new income/expense numbers should I be basing it on 18 year average returns now? A shortened life-time would probably lead to more variability (sigma) and an even more conservative result.

    1. Yes, Monte Carlo doesn’t easily produce a swift recovery like in 2009/10. So, a big stock market drop will seem too permanent in an MC simulation.
      That’s why I don’t recommend MC simulations.
      The other weakness with MC is the exact problem you raise: how to pick expected returns and the COV matrix. I don’t think 25 rolling window historical returns are long enough. 18 years is certainly too short.

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