Your Complete Guide to Index Investing with Dan Bortolotti

Planning to Drive a Monte Carlo

2013-01-31T08:04:22+00:00January 31st, 2013|Categories: Indexing Basics, Research|27 Comments

One of the lessons I’ve tried to stress is that investing is not about choosing the right products. ETFs changed the game by giving the little guy sophisticated and low-cost investment tools—no doubt about that. But the fact is, whether you choose this fund from iShares or that one from Vanguard will likely have zero impact on your overall success.

That’s why I was pleased to read Chapter 4 of Larry Swedroe’s new book, Think, Act, and Invest Like Warren Buffett. The chapter is called “The Need to Plan: It’s Not Only About Investments,” and it explains why we need to look at the bigger picture.

“There is evidence showing the biggest drivers are your spending rate, your savings rate, and how long you work,” Swedroe told me in a recent interview. “They influence the outcome far more than an extra 1% return you might get if you are a brilliant investor—and we know active investors would kill for 1% or 2% of alpha. When you run a Monte Carlo you can see how much more important these factors are.”

What’s a Monte Carlo?

Running a Monte Carlo doesn’t mean driving a classic Chevy coupe. Swedroe is referring to software used by financial planners to estimate the probability of meeting one’s goals. “I don’t know how you make any investment decisions without running Monte Carlos,” says Swedroe, “because otherwise you’re just pulling numbers out of your behind and guessing at the right asset allocation.”

Let’s say you want to know if a $500,000 portfolio will last for 30 years after you retire. A host of factors will have an influence, including how much you spend, the inflation rate, and the volatility and expected returns of your investments. Remember, even if you’re confident stocks will deliver 7% to 8% annualized over 30 years, it won’t be a smooth ride, and the sequence of returns matters a lot. If a devastating bear market comes near the end of your life, you’ll probably be fine. But if it comes shortly after you retire, you might never recover from the losses, and you risk outliving your money.

Monte Carlo software can take all of these variables and run thousands of simulations on your $500,000 portfolio over 30 years. It will estimate the odds your nest egg will endure if it is invested in, for example, 50% stocks and 50% bonds and you withdraw 4% a year, adjusted for 2% inflation. If you don’t like your odds—most investors won’t tolerate anything less than 90% or 95%—then you need to make adjustments. And since you can’t control inflation or investment returns, that means spending less, saving more, or adjusting the amount of risk in your portfolio. “If you do it properly you can ask questions like, if I cut my spending by 5%, or if I shift my equity allocation, what would that do to the probability?” Swedroe explains.

The details matter

There are a number of online Monte Carlo tools, including this retirement nest egg calculator from Vanguard. These are fine for rough guidelines, but beware of planning your financial future on the back of an envelope. As the saying goes: garbage in, garbage out. “We won’t let anyone but a small team in our company run a Monte Carlo because it is too easy to make a minor error that changes everything,” Swedroe warns.

The Monte Carlo software used by financial planners can often factor in employer pensions, Canada Pension Plan and Old Age Security, income taxes and other important factors—all of which will have a greater effect on your retirement than your choice of ETFs.


  1. Chris January 31, 2013 at 8:16 am

    BTW, “Monte Carlo” is an adjective, not a noun, in this case. It’s more correct to refer to a “Monte Carlo simulation”.

    Swedroe’s statement: “We won’t let anyone but a small team in our company run a Monte Carlo because it is too easy to make a minor error that changes everything” makes me think of this YouTube video:

  2. Danno January 31, 2013 at 8:58 am

    Is there a place where we could learn more about the more advanced tools the financial planners use? I get all of this and I am behind it in theory. I am an engineer by training, so I have at least some modest understanding of statistical methods, and the number of variables that can influence outcomes, so I completely understand why a Monte Carlo simulation is necessary to properly gauge their interactions.

    What I have always struggled with on this is that, despite comprehending all these variables (asset returns/probabilities, inflation, etc.) the whole thing seems to be to still be a very heavy function of your “need” (ie yearly withdrawal rate). And that, it seems to me, is really nothing but a semi-educated guess for younger people.

    Take my case. I am 32 today. I know how much I earn today and what my expenses are/could be today, if I were to retire today. But I can’t do that. I likely won’t retire until I’m 60 – 30 years away – and SO much can change in that time which, at least to my imagination, even a great Monte Carlo simulation has no hope of capturing.

    So it strikes me that while a tool like this (I played w/ the Vanguard one linked, neat) might be really useful if I was say 60, considering retiring today, and wanted to know the probability that my accumulated nest-egg could last me X years at Y withdrawal rate. But at my age today, I feel like the best I could hope for might be a RANGE of estimates of what I may need in retirement, and that narrowing down to a single dollar value is likely not really reliable. Ie I might say, for example, I need between 50k and 80k inflation-adjusted dollars. But to try to claim that I know today that, when I retire in 2043, I will need precisely 65k inflation adjusted dollars frankly seems like as much of a guess as anything else, no? Will I be living in the same place? Will my family be close or far? What will the world be like? And as you aptly suggest, garbage in = garbage out … so wouldn’t a Monte Carlo just tell me that I have a 95% probability of meeting a value that I guesstimated I might need?

  3. Canadian Couch Potato January 31, 2013 at 9:42 am

    @Danno: You raise an excellent point. The short answer (which I’ve learned from working with Justin Bender) is that Monte Carlos are really only useful when you’re within shouting distance of retirement. If you’re in your 50s, you need to start thinking about whether you need to ramp up your savings, plan on working longer, plan to spend less, etc. If you need to make adjustments, they will have a meaningful impact. But if you’re 32, there are so many unknowns that the simulation becomes really dubious, and probably useless.

    I’m putting together an example based on a real client, which I’ll post next week so you can see it action.

  4. Andrew F January 31, 2013 at 10:37 am

    I know all about Monte Carlo simulations–I wrote a program to perform them in school… My concern is that relying on such simulations may be flawed as well. Typically they assume random variables are normally distributed. We know that many asset class returns are not actually normally distributed. They typically exhibit ‘fat tails’. Thus I am concerned about the illusion of precision in using these models. They can give a rough estimate of the risk, but I expect the estimates are not that accurate.

    This is the same trouble that caused so many problems in the Long Term Capital Management blowup, mis-pricing risk in CDSs, etc. people forget that models are only as good as their assumptions, and to the extent the assumptions include a normal distribution for RV, they do not hold in practice.

  5. Canadian Couch Potato January 31, 2013 at 10:46 am

    @Andrew F: There’s no question you need to be aware of the “illusion of precision.” You always have to recognize the limitations in a model like this, but they can help you make more informed decisions. Obviously no model can predict the unpredictable, but you can get a decent estimate of your probability by making conservative assumptions about expected returns and using historical values for volatility.

    The best a Monte Carlo can do is say, “In the past, had you followed this plan you would have run out of money X% of the time.” If you can get that number to 95% or even 100%, you can be reasonably confident of success, even if you can never be guaranteed.

    The real question is, if you’re not going to use a Monte Carlo, how are you going to make these decisions?

  6. Andrew F January 31, 2013 at 10:56 am

    I agree that a simulation can be better than nothing, just cautioning about being overconfident in the estimates it produces. It’s definitely worth revisiting every few years to determine whether any course adjustments are required in terms of savings, how long you should continue to work, etc.

  7. Mike Elliot January 31, 2013 at 11:47 am

    Part of the appeal of your Couch Potato approach is that it’s DIY. I’m 62 and retiring shortly and wonder if there are any DIY Monte Carlo sims out there? I really want to avoid a financial advisor (no offence intended but my experience has been very poor with them).

  8. Canadian Couch Potato January 31, 2013 at 12:16 pm

    @Mike: The Monte Carlo tools available free online are pretty unsophisticated. As I say in the post, they’re fine for very rough calculations, but I can’t imagine making a significant financial decision using one of them. The ones used by financial planners incorporate Canadian tax information, too, which makes a huge difference.

  9. Mike Elliot January 31, 2013 at 12:27 pm

    Thanks for your reply… I enjoy your blog and find your advice very helpful.

    OK. Compliments out of the way. I’ve seen two broker advisors, two advisors who are fee only and a couple of bank types in the early days. In all cases, I come away feeling that these folks have at least some conflict of interest. Even the fee-only guys expect to execute the transactions to match their recommendations which no doubt generates a second income source. I never have felt comfortable in the knowledge level of the advisor and I object to having to decide on their motives when considering recommendations.

    So I’m looking for software that I can use myself that takes into account taxes on RRIF/RRSP withdrawals, OAS clawbacks, and the like, so I can test my retirement plan and modify it if necessary. I know advisors can get access to this type of software but is there anything out there for DIY people?

  10. Canadian Couch Potato January 31, 2013 at 12:45 pm

    @Mike: There is some professional financial planning software you can buy, such as:

    My concern echoes Larry Swedroe’s comments above. Without proper training I think you can get into a lot of trouble using these products incorrectly.

  11. Trevor January 31, 2013 at 3:10 pm

    Andrew F,

    Your point about gaussian error structure is a good one but I think you are about 10 years out of date. I use MCMC all the time and I frequently use lognormal, beta and gamme distributions to better approximate how the data are distributed. Further, accuracy and precision are very different things and I think you are using them backwards.

    Understanding uncertainty and bias through simulation is a very important tool – CC touches in this a little in his book where he describes how you can risk a lot to make a little more but that risk also allows for the probability of losing a lot. This is how I describe buying houses in the west coast of Canada. Currently I believe there is a small probability that housing may go slightly higher but a much higher probability that prices will go down. Conclusion: sell if it you’ve got it.

    The greatest advantage of using MCMC is not that it’s mcmc at all but that a formal modelling approach is taken towards planning your finances. In this, you are forced to address your assumptions and really consider whether they are valid or not.

  12. Canadian Couch Potato January 31, 2013 at 3:25 pm

    @Andrew F and Trevor: “Your point about gaussian error structure is a good one but I think you are about 10 years out of date.” Alright, boys, keep it cool. There’s room for a range of opinions about Gaussian error structure. :)

  13. Trevor January 31, 2013 at 3:33 pm

    Why would you buy this software anyway? Some of the most powerful statistical software out there is open-source.


    Yes, you’ll be forced to learn how to code some but if you can’t handle that you probably shouldn’t be trying to predict the stock market anyway.

  14. Canadian Couch Potato January 31, 2013 at 3:43 pm

    @Trevor: Monte Carlo simulations have nothing to do with predicting the stock market. And I think it’s fair to say that the number of DIY investors who could successfully write code and adapt software like this can be rounded to 0%.

  15. Trevor January 31, 2013 at 3:56 pm

    @CC: You are incorrect about mcs – I’m not trying to be flippent but MCS is simply a generic method and can and is used in stock market prediction

    I do, however, realize that it’s not really how you describe it’s use here where you describe how it can be used to understand asset value under a given scenario.

    As for the average DIY investor not being able to write code – and implement a statistical MC model, I think you are unfortunately correct. :)

    Sorry for the tangent.

  16. Que January 31, 2013 at 5:31 pm

    @Dan & Mike Elliot: Dan, maybe Justin, Shannon, and yourself can reconsider your ideal client (being “in the accumulation stage of life—that is, building wealth rather than drawing it down in retirement”) and help out people like Mike Elliot and maybe please all those “upset yield-hungry” folks with an alternative. By the way, I’m looking forward to your post to followup on that topic.

  17. Mike Elliot January 31, 2013 at 5:45 pm

    It’s not about coding. I mean, really, do you think the average financial advisor knows how to code? So if my alternative is turning a generic risk management program into something that I can predict my retirement plan, I’m out. But if I can get access to the (non-coding) financial advisor’s software, I’m in.

    Let’s not be snobbish about this. I can understand dividends, tax rates, TFSAs and RRIFs without having to understand coding!!

  18. Noel January 31, 2013 at 5:52 pm

    @Trevor – Had to pipe in here. Being a DIY investor, average or not, does not (and should not) require one to be able to write code and implement statistical MC models. It is, quite frankly, ridiculous to claim this.

  19. Trevor January 31, 2013 at 5:53 pm

    Sorry, I wasn’t trying to be snobbish. I was just going along with Andrews points of software that assumes normally distributed data where the data actually have fatter tailes (which really isn’t a huge issue, you cam just use a t-distribution instead).

    It then snowballed.

    Anyway, most of these MC are only that in the most simplest sense – many wouldn’t even use any distributional assumptions at all.

    As I said originally. Just sitting down and putting together a forward projection spreadsheet where you are forced to confront your assumptions (i.e is 7% after inflation REALLY reasonable??? ) gets you 90% of the way there.

    You can do a psuedo mc if you just play around with the parameter values. Easy peasy.

  20. Oldie January 31, 2013 at 6:31 pm

    @CC: I understand your and Andrew F’s cautions about not taking these projections absolutely literally because of the compounding imprecision of assumptions and the difficulty of predicting the future. This is all new to me, and the MC simulator seems to me a welcome new tool, even if you warn that it is somewhat coarse. I’m sure that the statistically challenged investors like me don’t have to fret the fine details to try to make the modelling more precise — I think I can live with the given imprecision.

    Suppose I were to test drive the MCS to estimate to likelihood of the worse case scenario (i.e. that my portfolio won’t last the 30 years I project I will live for, under the worst economic scenarios that the 5000 simulations of the Vanguard simulator, for instance, can crank out). If I make some conservative assumptions and end up with a “95% likelihood ok” prediction, my usual obsessive compulsive mindset would normally worry away at that 5% doomsday possibility; but in real life, because I started with a generous assumed annual drawdown, if, while living out this plan, we get 5 years of the worst economic downturn in a row, I can always reduce my drawdown to the point of recapturing my goal of not depleting my assets, can’t I? So, real life flexibility helps to make tools like the MCS, asset allocation rules of thumb, and the whole general principles of Couch Potato Investing “Good Enough”, which is all that we need, am I not correct?

  21. Canadian Couch Potato January 31, 2013 at 6:40 pm

    @Oldie: Yes, I think you’re correct. You can always adjust your lifestyle if things change dramatically five or 10 years into the process. The idea here is to create a reasonable flight plan and then make some course corrections along the way if necessary.

  22. Dan Hallett January 31, 2013 at 9:13 pm

    The more mathematically-inclined might want to read an older article by Moshe Milevsky on answering the same questions with a much simpler approach than MC but without the complexity.

    If you poke around the web, you’ll also find a spreadsheet that Milevsky created and placed in the public domain that allows any user to define simple inputs and do a reasonably good MC-type of estimate.

    Also have a look at things like RRIFmetic (which, I’m told, has a full T1 calculation and MC ‘engine’) and Jim Otar’s Retirement Optimizer (which is not MC but based on long-term U.S. market data)

  23. Canadian Couch Potato January 31, 2013 at 9:17 pm

    Thanks for the tools, Dan!

  24. Greg February 1, 2013 at 8:35 pm

    Moshe Milevsky’s calculators and spreadsheets:

  25. Flagen February 2, 2013 at 5:57 pm

    A couple of years ago, I bought RetireWare (retirement planning software capable of running a MC simulation – download or CD). At that point it came with free annual updates.

    I just visited their website and things have changed. But it looks like you can still buy this, but now it’s web based and requires an annual subscription fee. I haven’t used it to its full capacity as I need time to get back to retirement planning, but it seems pretty good so far. It’s not outrageously expensive and another option to consider:

  26. Canadian Couch Potato February 2, 2013 at 6:07 pm

    @Flagen: Thanks for the suggestion—I wasn’t familiar with this software, but it looks like a good choice for the DIYer.

    RetireWare: sounds like a store that sells clothing for seniors.

  27. J A H February 4, 2013 at 9:44 am

    Just checked out RetireWare. You can get access to the software for free if you join a Leader’s Group led by a qualified professional, but they will not make this feature live until the end of March 2013.

    It isn’t clear what relationship is expected between free subscribers and Leaders. I’d like to see what comes of it. As a DIYer, I wouldn’t want to be exposed to constant sales pitches.

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