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:
- 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.
- 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.
- 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)
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:
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?
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?
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.]
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:
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).]
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?
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!]
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:
- Beware of the difference between a 30-year and 50+-year retirement horizon!
- 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