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Welcome to personal finance for
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long-term investors, where we believe
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Benjamin Franklin's advice that an
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investment in knowledge pays the best
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interest both in finances and in your
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life. Every episode teaches you personal
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finance and long-term investing in
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simple terms. Now, here's your host,
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Jesse Kramer. Welcome to Personal
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Finance for Long-Term Investors, episode
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134. My name is Jesse Kramer. By day, I
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work at a fiduciary wealth management
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firm helping clients nationwide. You can
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learn more at
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bestinterinterest.blog/work.
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The link is in the show notes. By night,
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I write the bestinterest blog. I host
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this podcast. I also put out a weekly
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email newsletter, all for free. And all
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of these different projects help busy
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professionals and retirees avoid
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mistakes and grow their wealth by
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hopefully simplifying their taxes, their
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investing, and their retirement
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planning. Today, we're going to do a
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deep dive episode all about Monte Carlo
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analysis. I've been working on this one
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for a little while. I've gotten some
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good questions over the years from
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listeners like you about kind of wanting
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to go into the into the details under
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the hood of Monte Carlo analysis. You're
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going to hear me say Monte Carlo
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analysis a lot today, just FYI. But
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before we dive into the details, we'll
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do our usual thing. We will do a review
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of the week. This one is from App Trail
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1 who left a five-star review and said,
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"Gold Medal Podcast. This podcast checks
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all the boxes. Accurate, accessible,
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honest, and unbiased. All sprinkled with
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a little bit of dry wit." Well, Apptrail
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1, thank you very much for those kind
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words. You can shoot me an email to
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and I'll get you hooked up with a
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supersoft podcast t-shirt. Now, on to
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the main course today, the big show.
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We're talking about Monte Carlo
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analysis. What it is, what it isn't, how
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to use it, all those kind of things. If
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you haven't heard of it before, of
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course, we'll introduce it. But, you
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know, this very quick preamble, I want
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you to think today that that Monte Carlo
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analysis, the thing I'm about to talk
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about, it's not a crystal ball, but it
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is a a stress testing tool. It is a very
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excellent conversation starter. It's not
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necessarily predictive though, right?
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It's not a predictive machine. It's not
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a crystal ball. The outputs from Monte
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Carlo analysis, things like a success
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percentage, for example, can be a
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double-edged sword. It does provide
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important data on whether you're
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thinking about retirement in the right
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way. But it can also hide different
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faulty assumptions. It can mask
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overconervatism. It can mislead you
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emotionally. So today, we're going to
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dive into all those kind of things. and
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and hopefully you leave today
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understanding why I begin with that
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preamble. Today we're going to cover
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specifics like why we need to do
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in-depth analysis like Monte Carlo
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analysis. What's going on under the hood
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of a Monte Carlo analysis? How does it
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actually work? Especially how does it
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work in financial planning? I mean,
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that's why we're here. Where can Monte
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Carlo analysis go wrong? How do you
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cautiously but accurately or or at least
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helpfully interpret the results of a
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Monte Carlo analysis? And how do you
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make sure your Monte Carlo analysis of
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course isn't misleading you, right? How
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do we get led down the right path with
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these results instead of one of the many
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different wrong paths? So, let's start
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with why do we need to do in-depth
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analysis in the first place? I would
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argue that most of us have big hopes,
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but also maybe some big fears. We have
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big questions certainly about
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retirement. How do we answer those
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questions? Some questions can only be
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answered via conversation and and
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looking within. Some questions are
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certainly subjective in nature. But
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plenty of questions, plenty of these
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retirement questions at least are
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objective, right? They're fact-based.
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They're based on numbers, plain and
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simple. But retirement has a bunch of
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different moving pieces and a lot of
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different numbers. And there are a lot
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of different ways that someone can begin
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to analyze their retirement plan. And
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when I say analyze, I mean use some form
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of numerical methods to determine if you
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can retire, how successful your
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retirement might be, how much you can
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spend, etc., etc. There are plenty of
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free, widely available online retirement
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calculators that usually provide
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something like a retirement score or a
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probability of success based on average
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static assumptions. And I think the key
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word there is static. And you'll hear me
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today use the word static and dynamic a
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few different times. So when I say a
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static assumption, these type of free
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online calculators, they often assume
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static unchanging earnings, static
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unchanging savings rates, static
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investment returns, 7% per year, 9% per
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year. It's just a a static
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one-sizefits-all constant return. And
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that's fine. It's fine to use that type
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of tool as a general readiness check for
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retirement. But it's about as loose a
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rule of thumb as as you could muster.
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You know, if that type of static
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calculator suggests that you should, and
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I'm using air quotes, that you should
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have four times your income saved, but
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you only have three times your income
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saved, well, I still wouldn't know
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enough to know if you're truly behind or
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not because the tool itself is too
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coarse to come up with that kind of
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conclusion. But then if that calculator
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suggests that you should have four times
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your income saved and here you only have
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one times your income saved, well then I
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might wager that you need to dig into
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the details a little bit deeper because
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there's a good chance you're actually
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behind on your retirement savings. My
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point there is that these coarse static
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online calculators, they're just that
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they're coarse. It's hard to walk away
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with really good really good outputs and
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really good direction when you're using
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such a course tool. Now, if we dial up
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the complexity a little bit more, we
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might focus on something like a, you
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know, quote unquote deterministic cash
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flow modeling. So, this type of tool
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allows for much more detail, such as
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specific retirement spending, maybe
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part-time work in retirement, big
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one-time expenses like your daughter's
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wedding or buying that vacation home. It
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helps you project future income, project
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future expenses, your net worth. It
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helps you project your net worth on a
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year-by-year basis. You can model in
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social security income, pension income,
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basic tax calculations in a way that is
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certainly more detailed than the
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previous course analysis, but also
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personalized to you, specific to your
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timeline. And that is all great. That is
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something we're looking for. We're
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moving in the right direction here. The
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problem though is is that exercise, this
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deterministic cash flow model. It
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typically assumes a static investment
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return. The focus is on cash flow and
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the dynamic cash flow. It's not
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necessarily on dynamic investment
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returns. We know though that investment
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returns are a really vital component of
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retirement planning and of course that
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investment returns are dynamic in
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nature. So that's where if we go one
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step further in terms of kind of the
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complexity of analysis types, that's
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usually where Monte Carlo analysis comes
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into play. Monte Carlo analysis is a a
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more sophisticated analysis type that
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tests your financial plan, your
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retirement plan against thousands of
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different possible market scenarios
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rather than testing it against only one
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average static market return. So Monte
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Carlo might simulate uh market
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volatility to determine the probability
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of success. You know, as in there's an
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85% chance of success that your money
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will last you to age 95. Success is
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another one of these big words that we
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will come back to multiple times today.
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We need to talk about exactly what
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success means in this context and and
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like I said, we'll come back to that.
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So, done well, a Monte Carlo analysis
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takes your unique projected cash flow
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that we just kind of talked about a
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minute ago. So, your unique retirement
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cash flow and then it layers that cash
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flow on top of a wide range of possible
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investment returns. And then it asks
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which types of investment returns, which
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series and sequence of investment
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returns could lead to bad retirement
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outcomes could lead to really good
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retirement outcomes. I mean what is the
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range of of possibilities in your
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retirement future? So for example, we
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could walk away from a from a Monte
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Carlo analysis and look at it and say
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well in this analysis we ran most kind
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of standard typical investment return
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series actually caused our retirement
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plan to fail. Oh, that doesn't really
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sound good. Or maybe we walk away and
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say, listen, only the worst of the worst
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investment series actually cause this
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retirement plan to fail. And that
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certainly sounds much better. Or maybe
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if we go even a step further, we'd see
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that our retirement cash flow actually
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survives even the very worst possible
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investment series that this Monte Carlo
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analysis could muster. And then we
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should ask ourselves, well, maybe we're
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being too conservative then, right? If
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our retirement fails, even the the worst
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scenario possible, are we just
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underspending our retirement? But before
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diving further into the specifics of
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financial planning, Monte Carlos,
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because we will get into those
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specifics, I want to take a quick step
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backward. Maybe it's the little engineer
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in me. So, how do Monte Carlos work in
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general? I think that's actually a
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really important place to start. And
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heck, why do we even call them Monte
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Carlos in the first place? So, let's
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talk about that. Let's talk about how
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Monte Carlo analysis works in general.
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When you hear Monte Carlo simulation,
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Monteol analysis, Monte Carlo, anything,
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you should think lots and lots of random
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trials. That's what I want you to think.
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Lots and lots of random trials. For
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example, one might ask themselves, well,
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how often in poker Texas Holdem does a
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player get dealt two aces. Now, a true
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statistician would be able to use actual
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statistical equations to answer that
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question, like probability equations.
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It's not that hard of a question to
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answer if you understand how many cards
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are in a deck and how statistics
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probability works. But you could also
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use Monte Carlo analysis to answer that
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question. You could teach a computer,
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you could program a computer to randomly
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deal out a twocard hand and then have it
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repeat that random dealing another
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billion times, which for a computer,
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it's pretty fast to do a billion kind of
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those simulations. And over those
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billion random trials, a really accurate
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probability of a two ace hand will
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become apparent. So cards and dice and
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darts and I suppose other games of
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chance are easy targets for Monte Carlo
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simulations, but Monte Carlo can also be
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used on on much more complex stuff like
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weather predictions. For example, when
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you see one of those um spaghetti plots
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that a hurricane weather forecaster
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might use to show all the various paths
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that a hurricane might take, that's
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often a product of a Monte Carlo
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simulation. So these meteorological
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models use fluid dynamics. And fluid
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dynamics, one of my former courses as an
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engineer, fluid dynamics is famously
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unpredictable. And that unpredictability
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can be somewhat tamed or at least
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understood by using Monte Carlo methods.
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So if you're unsure if the winds are
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going to shift faster or slower, well,
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you simulate both those outcomes a
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million times. If you're unsure whether
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the wind is going to shift east or west,
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you simulate both a million times. Is
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the hurricane going to move over warmer
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waters or colder waters? You know, a
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hurricane's path might depend on a
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million different variables. And a Monte
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Carlo simulation allows you to take
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those million inputs, vary them a few
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different ways, and then output a huge
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range of results. And one set of inputs
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might say that Miami is going to get
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crushed by this hurricane, but another
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set predicts that the hurricane won't
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even make landfall. And over millions of
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simulations, a probability distribution
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emerges. And you might say, you know,
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Miami is is only going to get hit by
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this hurricane in 1/100th of a percent
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of the results. And that's a probability
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that you can probably live with. Now,
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Monte Carlo, I'm learning now kind of
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after the fact, was the name of a famous
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casino in Monaco, which is that what
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French like citystate, very wealthy
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citystate. And uh two mathematicians,
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including the very famous John Vanoyman,
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developed the Monte Carlo method. And
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they named it after the gambling house,
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kind of thinking to themselves that they
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could use this method to look at darts
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and dice and and cards. But the original
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purpose for Monte Carlo analysis was not
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fun and games. It was working on nuclear
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weapons at Los Alamos. I suppose if
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you're unsure how a high energy neutron
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will penetrate into fisionable uranium,
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you might simulate that neutron's path a
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billion times and see what the results
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look like. We still use Monte Carlo
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analysis for a lot of different purposes
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today. We used it at my old job where we
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were designing and analyzing and
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building and testing satellite telescope
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systems. In fact, Monte Carlo analysis
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exists in lots of places in engineering.
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Here's an example. You know what
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turbulence feels like in a plane. Many
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of you have probably flown in a plane.
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Some flights are very smooth. Some
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flights have a couple bumps and some
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flights cause you to kind of yell out in
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terror and feel sick to your stomach.
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That's turbulence. Well, an orbital
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rocket flies about 30 times faster than
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a commercial jet. So, you better believe
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there's some serious turbulence, you
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know, atmospherical turbulence when your
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telescope is getting a rocket ride out
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in space. But due to the again the
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chaotic nature of fluid dynamics, just
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like in the hurricane example, how do
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you model out that turbulence
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accurately? And more importantly, how do
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you model out the turbulence as it
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combines with some of the other
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uncertainties in your engineering
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design? Well, one way of doing it is by
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brute force of lots and lots of random
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trials. Monte Carlo analysis comes to
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the rescue in that situation. But in any
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numerical analysis, including Monte
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Carlo analysis, one of the the biggest
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takeaways is that garbage in equals
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garbage out. And I suppose what I mean
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there is that, you know, the accuracy of
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your inputs determines the accuracy of
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your outputs. If I'm trying to simulate,
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you know, the odds of a particular poker
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outcome, but I accidentally model the
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deck of cards of having 50 cards instead
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of having 52 cards, I'm going to get the
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wrong answer. Everything else about my
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model could be correct and elegant and
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and programmed uh efficiently, but if I
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made a major poor assumption like the
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wrong number of cards in a deck, it's
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going to mess up my entire analysis. So,
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that's an important lesson as we pivot
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towards specifically discussing Monte
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Carlo analysis for retirement planning.
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So, let's start thinking about how your
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one unique retirement might play out.
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So, you're sitting there at 50 or 55 or
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60 or 65 years old. And you probably
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know some of the following. You probably
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know what your current asset base looks
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like. You know how much you have in the
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bank, how much you have in retirement
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accounts and a taxable brokerage. You
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know how much your your house is worth,
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all those kind of things. Hopefully, you
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understand your cash flow. You have good
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data on what you could spend.
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Importantly, you have a reasonable
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understanding about how your spending
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will change over time. You might not be
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totally precise there. After all, you
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know, our crystal balls are foggy, but
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you know, if you have, again, a big
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wedding to pay for, you know, if you
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have ACA premiums, uh, when you're early
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retired or something like that, you you
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understand roughly what your future
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spending looks like. Hopefully, you
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know, at least some of the details of
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your withdrawal strategy. You're aware
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of which accounts you'll be withdrawing
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assets from over time. If you're unsure,
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I recommend checking out episode 121 of
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this very podcast for some detail on the
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the generally accepted retirement
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withdrawal framework. What you don't
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know though, among other things, you
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certainly don't know how capital markets
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will behave over your 20 or 30 or 40 or
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more years of retirement. How will
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stocks and bonds and other assets
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perform? Will you be subjected to a a
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generous or a harsh sequence of returns?
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That's something you don't know. And the
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first blush reaction is to simply assume
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some fixed rate of return. Maybe be a
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little conservative with your fixed rate
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of return and do that for the full 30 or
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40 years of your retirement. And if all
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you have is a simple pocket calculator,
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that's probably the best you can do. And
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that's not a bad place to start. And
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that's one of those methods we talked
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about before is try to get really
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accurate with your cash flow and then
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assume some constant rate of returns and
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see how your retirement plan performs.
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But thanks to better and better
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computing over recent decades, we can do
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a Monte Carlo analysis here. Remember,
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Monte Carlo analysis simply means lots
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and lots of random trials. So instead of
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assuming one stream of investment
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returns and a constant stream of
00:14:51
investment returns at that, we can
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assume many different streams of
00:14:55
investment returns with some
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randomization in there. We can assume
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thousands of different variations on how
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the market could perform. And each one
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of these trials, each one of these
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thousand trials is really a a full
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financial life story in and of itself. A
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single simulation projects year-by-year
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portfolio returns, cash flows, taxes,
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withdrawals from today through the end
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of the planning horizon. Whatever you
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know you define what the end of your
00:15:20
planning horizon is. So here the
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sequence of returns is really a feature
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of the analysis. It's not some sort of
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bug that we're trying to avoid. We want
00:15:28
to see sequence of returns risk here. We
00:15:29
want to see how impactful it is. And by
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by shuffling the order of returns across
00:15:34
these hundreds, if not thousands of
00:15:36
different trials, the Monte Carlo
00:15:38
analysis will explicitly capture that
00:15:40
sequence of returns risk. And that's
00:15:42
something that these deterministic
00:15:44
projections that we talked about before,
00:15:45
they completely ignore sequence of
00:15:47
returns risk. We're going to spend more
00:15:49
time in a few minutes talking about the
00:15:51
specific inputs that go into a Monte
00:15:54
Carlo analysis. But first, I actually
00:15:56
want to dive into the output before we
00:15:58
dive further into the inputs. We want to
00:15:59
talk about the outputs. The output of a
00:16:01
Monte Carlo run is a distribution of
00:16:04
outcomes. It's not one single answer.
00:16:06
It's a distribution of answers. So
00:16:08
instead of one final portfolio value,
00:16:11
you get a wide spread of final portfolio
00:16:13
values. Some are terrific looking, some
00:16:16
are mediocre, and some are catastrophic.
00:16:18
Some show that you run out of money. But
00:16:19
that's the entire point of of doing the
00:16:21
analysis in the first place. One thing
00:16:23
that you see as an output is the
00:16:24
so-called success rate. It's probably
00:16:26
the headline output, the most viewed,
00:16:27
the most cited output of a Monte Carlo
00:16:30
run. In short, the success rate says out
00:16:32
of these thousand different trials or
00:16:34
however many you run, out of these
00:16:36
thousand different trials, how many of
00:16:37
those trials ended as a success? And
00:16:39
typically, by default, success means
00:16:41
that you die with at least $1 of
00:16:43
positive net worth. But it's very easy
00:16:45
to tweak success if you want to to be
00:16:47
like, I want to die and gift $100,000 to
00:16:50
each of my five grandkids. So now you
00:16:52
need to die with 500 grand and that's a
00:16:54
success. or something like that. The
00:16:56
most common result again is the
00:16:58
percentage of trials that are
00:16:59
successful. So by getting a 82% success
00:17:02
rate, it means that 82% of the trials
00:17:05
met your success criteria but 18% failed
00:17:09
your success criteria. And that's useful
00:17:11
to know. But that simple number, 82%
00:17:14
success, that simple number ignores the
00:17:16
wide range of possible successes. It
00:17:19
also ignores the wide range of possible
00:17:21
failures. It ignores the scenarios where
00:17:23
you you almost ran out of money and you
00:17:25
probably would have been really really
00:17:26
anxious about running out of money, but
00:17:28
technically it was a success. It also
00:17:30
ignores the scenarios where you barely
00:17:32
ran out of money and you were really
00:17:34
okay except for bouncing the the final
00:17:36
check of your life and it calls that a
00:17:38
failure. The point is that success rate
00:17:41
and those distributions of outcomes,
00:17:43
it's a pretty blunt way of viewing the
00:17:45
output of a Monte Carlo analysis.
00:17:47
Another common output from Monte Carlo
00:17:50
is the average net worth at death.
00:17:52
That's another common output. If you
00:17:53
look at the thousand scenarios that you
00:17:55
run, it'll just say, let's take an
00:17:57
average of what the net worth is in all
00:17:59
thousand scenarios and report that back
00:18:01
to the user. This too is is useful, but
00:18:04
a very blunt metric. It can be helpful
00:18:06
to see how much your average net worth
00:18:08
has changed over time in all the
00:18:09
scenarios. But this one average kind of
00:18:12
papers over all of the important
00:18:14
details. I think I actually use this
00:18:16
either in writing or in a previous
00:18:17
episode. Imagine we have one scenario
00:18:20
where you die with $10 million and then
00:18:22
we average that with four scenarios
00:18:24
where you die with zero. You actually
00:18:25
run out of money. The average of those
00:18:27
five scenarios, 10 and then four zeros,
00:18:30
the average is $2 million, which sounds
00:18:32
great. If I told you, yeah, your average
00:18:34
retirement, you will die with $2
00:18:35
million. A lot of you will say, well,
00:18:37
that sounds good to me. That's kind of
00:18:38
what I'm looking for. But what you might
00:18:40
not realize is that the real important
00:18:41
outcome from the data I just quoted you
00:18:43
is that 80% of those five trials
00:18:46
actually fail, right? Four of the five
00:18:48
are just abject failures. So again, the
00:18:50
the average net worth at death, there's
00:18:52
some usefulness in that output. It masks
00:18:55
over some important details. But okay,
00:18:57
let me pause there cuz I'm going to come
00:18:59
back in a little bit and I'm going to
00:19:00
talk about better ways, at least in my
00:19:02
opinion, to to examine Monte Carlo
00:19:04
outputs and results. Here's a quick ad
00:19:07
and then we'll get back to the show. I
00:19:09
love getting your questions and some of
00:19:10
you ask me questions about the wealth
00:19:12
management firm I work for in Rochester,
00:19:14
New York. Others ask about the Best
00:19:15
Interest blog and this podcast, Personal
00:19:17
Finance for Long-Term Investors, which
00:19:19
operate without advertising, without
00:19:20
pushy sales, and with no payw walls. How
00:19:22
can the blog and podcast stay afloat
00:19:24
without me dumping my own money into it?
00:19:26
Well, to answer both those questions, I
00:19:28
want to point you to episode 78 of
00:19:29
Personal Finance for Long-Term
00:19:31
Investors. I intentionally recorded
00:19:33
episode 78 to shine light on those
00:19:34
topics and inform you how you are
00:19:36
actually helping and can continue
00:19:38
helping these projects carry forward. So
00:19:40
if you've ever been curious about the
00:19:41
business of my blog and podcast or if
00:19:43
you're curious about my day job in
00:19:45
wealth management, please check out
00:19:46
episode 78 and let me know what you
00:19:48
think. But let's pivot now. Let's talk a
00:19:50
little bit more in depth under the hood
00:19:52
about how Monte Carlo simulations work
00:19:54
and and therefore once we establish that
00:19:56
we can start to understand more about
00:19:57
how Monte Carlos might go wrong, how to
00:20:00
interpret the results that we get from
00:20:02
one of these analyses, how to make sure
00:20:04
that your Monte Carlo analysis isn't
00:20:06
misleading you in some way. And and
00:20:08
usually the the first place, the most
00:20:09
common place where a Monte Carlo
00:20:11
simulation or any kind of simulation or
00:20:13
analysis can go wrong, it's just like in
00:20:15
engineering, there's an aspect of
00:20:17
garbage in, garbage out. And what that
00:20:19
really means is that if the inputs into
00:20:21
your mathematical model are bad, if
00:20:24
that's the garbage in, then you just
00:20:26
know that the outputs are going to be
00:20:27
bad too. That's the garbage out. So it's
00:20:29
really important that we try to provide
00:20:31
really accurate inputs and that we try
00:20:33
to understand how the the inputs that we
00:20:36
choose actually affect the outputs that
00:20:38
we end up getting. So anyway, that's why
00:20:40
it's it is imperative that we understand
00:20:42
the inputs here such that they play such
00:20:45
a vital role in determining our outputs.
00:20:47
It's almost like the Play-Doh machines,
00:20:48
right? Where you you stuff some Play-Doh
00:20:50
in and you turn the crank and it shapes
00:20:52
the Play-Doh in a certain way and then
00:20:54
you get your output. It can be really
00:20:56
important to understand what's going on
00:20:57
when you turn that crank. And in the
00:21:00
Monte Carlo world, there really three
00:21:01
unique ways that the math is is kind of
00:21:04
done underneath the hood when you're
00:21:05
turning the crank. And I just want to
00:21:07
talk on those three different ways
00:21:08
really quick. The first method is called
00:21:10
the independent identically distributed
00:21:13
method or independent identically
00:21:14
distributed returns because really we're
00:21:16
talking about investment returns here.
00:21:18
The second method is is newer but very
00:21:19
interesting. It's called the block
00:21:20
bootstrap approach. And then the third
00:21:22
and the most common one is the
00:21:24
statistical distribution approach.
00:21:26
They're all very similar but they have
00:21:28
some pretty important nuance
00:21:29
differences. To explain them simply, I
00:21:31
want you to imagine that you're maybe
00:21:32
creating a video game. It's kind of like
00:21:34
Sim City or The Sims. you're building
00:21:36
some sort of society in your game and
00:21:38
for whatever reason it's important in
00:21:40
this game that you you model out the
00:21:41
heights and the weights of the
00:21:43
individual little digital people in the
00:21:45
game. If you were given that problem,
00:21:47
there are probably a few different ways
00:21:48
that you could do that. The first idea
00:21:50
that you think of is you could look up
00:21:52
some health study that has actual height
00:21:54
and weight data from, you know, a
00:21:56
100,000 different people. You upload all
00:21:58
these heights and weights into your game
00:21:59
and then whenever you need to assign the
00:22:01
height and weight to someone, some
00:22:03
little digital person in your game, you
00:22:05
could pull some of the actual real data
00:22:07
that you've already uploaded, some of
00:22:09
the real data from from actual humans.
00:22:11
The second idea is that you could kind
00:22:13
of do the same thing except maybe you
00:22:15
could upload it in blocks because what
00:22:17
you'd say is, well, if I have a family,
00:22:19
let's say I'm trying to determine the
00:22:21
the height and weight of one of my
00:22:22
digital families, like their height and
00:22:24
weights are probably all going to be
00:22:26
correlated in some way. At least for the
00:22:28
kids, they are, right? Because if you
00:22:30
have the same genetics, if you have the
00:22:31
same parents, your height and your
00:22:33
weight is probably correlated to your
00:22:35
siblings in some way. That's a second
00:22:36
method you could use. But then the third
00:22:38
method is is much more statistical in
00:22:40
nature. You could just upload the
00:22:42
average height for all people, the
00:22:44
average weight for all people, and then
00:22:45
some information about how those data
00:22:47
are distributed. For example, you might
00:22:49
describe them as, you know, two bell
00:22:50
curves with some standard deviation of 3
00:22:53
in in height and 20 lb in weight or
00:22:56
something like that. And then when you
00:22:57
need to create a person in the game with
00:22:59
a height and a weight, you simply use
00:23:01
some sort of random number generator to
00:23:03
say, "Hey, take my averages, see where
00:23:05
my random number falls in a bell curve,
00:23:07
and assign that height and assign that
00:23:09
weight to my digital person." So the
00:23:11
first method is using only real data
00:23:13
points. The second method is also using
00:23:16
only real data points, but it recognizes
00:23:18
that often these data points can be
00:23:19
correlated to one another. They can be
00:23:21
kind of grouped together. And then the
00:23:23
third method is using real data
00:23:25
originally to create a statistical
00:23:28
model, but then technically it's it's
00:23:30
really making up new data points that
00:23:32
just so happen to fit within that that
00:23:34
same model. And these are the three ways
00:23:36
that retirement Monte Carlo simulations
00:23:38
are are basically done. The first way
00:23:40
it's the independent identically
00:23:42
distributed return. In this method, we
00:23:44
are only using real data. We are not
00:23:46
creating some sort of investment return
00:23:48
or series of returns out of thin air. We
00:23:50
are not saying that 10% is the average.
00:23:52
So please create some sort of random
00:23:54
number between minus30 and plus 50% and
00:23:56
make that my return this year. That's
00:23:58
not what we're doing. Instead, we are
00:24:00
taking historical returns, real returns.
00:24:03
Sure, we're selecting them at random and
00:24:05
then we are kind of laying them in
00:24:07
series with one another. So if we need
00:24:09
say 50 years worth of returns to
00:24:11
simulate our retirement, we would select
00:24:13
600 cuz that's 50 years 600 months. We
00:24:16
would select 600 random monthly returns
00:24:19
from the existing historical return set
00:24:22
to create a random time series and we'd
00:24:24
string those 600 months together. And
00:24:26
this detail I'm about to say is
00:24:28
important in order to preserve the
00:24:30
correlations between assets in each
00:24:32
month. each asset would receive its, you
00:24:34
know, appropriate return from the same
00:24:37
original month. So, what I mean is that
00:24:39
we aren't selecting a stock return from
00:24:41
October of 1982 and pairing that up with
00:24:44
a bond return from January of 1960,
00:24:47
putting them in the same month in our
00:24:48
simulation. You know, the stock returns
00:24:50
and the bond returns for month one are
00:24:53
both going to be from October of 1924.
00:24:56
And then the stock returns and the bond
00:24:57
returns for month two are both going to
00:24:59
be from January 1991. We're going to
00:25:01
rinse and repeat that process month by
00:25:03
month until we've filled up our entire
00:25:05
simulation. And that's just one
00:25:08
retirement run, right? So again, if we
00:25:09
go back to the 50 years or the 600
00:25:11
months, we put together a series of 600
00:25:14
monthly returns. And that's simulation
00:25:16
one. But then we do it again, again, all
00:25:19
random. We do it again for simulation
00:25:21
two and then again for simulation three
00:25:23
over again and over again and over again
00:25:24
another thousand times. So in that way
00:25:27
we built our Monte Carlos simulation
00:25:29
with all these random returns. They are
00:25:31
real data right from the real uh data
00:25:33
set. We just kind of randomized the
00:25:35
order in which those returns occur. Now
00:25:38
this next method is a variation of that
00:25:40
independent identically distributed
00:25:42
return. This one's called the block
00:25:43
bootstrap method. And the idea here is
00:25:45
that we shouldn't take one month from
00:25:47
1928 and then follow it up with a month
00:25:49
from 1961 and then a month from 1949 and
00:25:52
1997 etc. So that's what the independent
00:25:55
identically distributed return method
00:25:57
does. But the reason that the block
00:25:59
bootstrap method does something
00:26:01
different is that we've kind of realized
00:26:03
that whatever happened in that one month
00:26:04
in 1928 is connected in some way to the
00:26:07
month before it and the month after it
00:26:09
and the month before that and the month
00:26:10
after that. These economic cycles and
00:26:12
bull markets and bare markets can take a
00:26:14
long time to play out. So it doesn't
00:26:16
make sense to pull one random month at a
00:26:18
time. It might not even make sense to
00:26:19
pull one random year at a time. Instead,
00:26:22
the block bootstrap method suggests we
00:26:24
take much longer blocks of returns. The
00:26:27
most common length being 10 years, 10
00:26:29
years of returns at a time. So, to
00:26:31
create a a 30-year retirement
00:26:33
simulation, we would grab three
00:26:35
different 10-year blocks of returns and
00:26:37
use those to simulate one full 30-year
00:26:40
retirement. Each of those 10-year blocks
00:26:42
would have some true long-term economic
00:26:45
patterns within it. And then we do it
00:26:47
again with three different 10-year
00:26:49
blocks. And then again with three
00:26:50
different 10-year blocks from that. And
00:26:52
every time we're randomly selecting the
00:26:55
start date for these different 10-year
00:26:56
blocks. We do that over and over again
00:26:59
hundreds if not thousands of times.
00:27:01
Again, now we have a a true Monte Carlo
00:27:03
simulation with thousands of individual
00:27:05
trials all randomly selected. But rather
00:27:07
than having 30 or 40 or 50 years worth
00:27:10
of totally random monthly returns, the
00:27:13
block bootstrap method carries some some
00:27:15
real economic oomph with it because the
00:27:18
blocks have some sort of underlying
00:27:20
patterns that more closely resemble
00:27:22
reality. But that brings us to the third
00:27:24
approach which I think is the most
00:27:26
common approach. It's certainly the one
00:27:27
that I've seen most frequently. It's the
00:27:29
statistical distribution approach. So
00:27:31
this is the method that requires you to
00:27:33
input an average rate of return based on
00:27:35
the performance history of your specific
00:27:37
assets or the performance history of
00:27:39
your specific portfolio allocation. You
00:27:42
input the average return. You also input
00:27:45
information about the distribution of
00:27:46
returns. For example, bell curves or
00:27:49
normal distributions or Gaussian
00:27:51
distributions. These all mean the same
00:27:53
thing. A bell curve is a normal
00:27:55
distribution is a Gaussian distribution.
00:27:57
It's probably the most common type of
00:27:58
statistical distribution that people are
00:28:00
used to. even if they might not be aware
00:28:02
that they're used to it. You know,
00:28:03
you're used to the fact that 95% of
00:28:06
American men are somewhere between 5
00:28:08
foot five and six foot five. And that
00:28:10
it's much more rare, but not unheard of
00:28:12
to see someone who's 6'8. And it's much
00:28:14
rarer still to see someone who's 7 foot
00:28:16
tall, you know, etc., etc. That's
00:28:18
because height data matches a bell
00:28:21
curve. It matches a normal distribution.
00:28:23
This is the the mathematical
00:28:24
distributions that just so happens to
00:28:26
accurately describe the way that height
00:28:28
data is is distributed amongst a large
00:28:31
population. And whenever you're trying
00:28:33
to describe the way a bell curve looks,
00:28:36
it's important that you define the
00:28:37
average of that curve, it's also very
00:28:39
important that you define the standard
00:28:41
deviation or a measure of how quickly
00:28:43
the bell as it were kind of dissipates
00:28:46
down as you move away from the average.
00:28:48
But there are other types of
00:28:49
distributions too. There's lognormal
00:28:52
distributions and power law
00:28:53
distributions and posson distributions
00:28:55
that all actually do have a place in
00:28:57
financial modeling of some sort. But the
00:29:00
big problem, the really big problem with
00:29:02
using a statistical distribution to
00:29:04
model out investment returns is that no
00:29:07
single statistical distribution seems to
00:29:09
model investment returns that
00:29:11
accurately. So I'll say that again.
00:29:13
There's no statistical distribution that
00:29:16
models investment returns as accurately
00:29:18
as we would want them to be modeled. For
00:29:20
example, the normal distribution, the
00:29:22
classic bell curve. This is the
00:29:24
distribution that many Monte Carlo
00:29:25
simulations actually use. You know, if
00:29:28
your Monte Carlo software of choice is
00:29:30
using an average return plus a standard
00:29:32
deviation, I'd wager under the hood,
00:29:34
it's using the standard bell curve, the
00:29:36
normal distribution, the Gaussian
00:29:37
distribution. But the problem is that
00:29:39
the stock market, investment markets,
00:29:41
they have these crazy days and crazy
00:29:43
weeks and crazy months, maybe even crazy
00:29:45
years that we've heard of before. We're
00:29:47
used to the idea that yeah, once in a
00:29:49
while, like April of 2025, the market
00:29:52
did happen to drop was it 9% in one day
00:29:55
and then the next day it was back up 9%
00:29:57
again. The problem is that if we if we
00:29:59
use the way a standard distribution
00:30:02
really works and if we look at how
00:30:04
infrequent those really rare events are
00:30:06
supposed to happen, you know, a standard
00:30:07
distribution says that something might
00:30:10
be a 1 in 1,000-year event. And if we're
00:30:13
talking about the height of a human and
00:30:15
we say, well, you know, if we're going
00:30:17
to get a human who's 9 ft tall, odds are
00:30:19
one is going to be born every 500 years,
00:30:22
well, there aren't many 9 foot tall
00:30:24
people walking around. And and the bell
00:30:25
curve's way of describing the frequency
00:30:27
of 9 foot tall men actually plays out in
00:30:30
reality. But when we use a a bell curve,
00:30:32
a normal distribution to describe the
00:30:34
stock market, we have these events that
00:30:36
should be one in every 1,00 years. But
00:30:39
we see those events occurring way too
00:30:41
frequently in real life because the
00:30:43
normal distribution has very thin tails.
00:30:45
The normal distribution says that, you
00:30:47
know, the market dropping 8% in one day
00:30:50
ought to occur once in a million trading
00:30:52
days except it's occurred eight
00:30:54
different times in the last 10,000
00:30:56
trading days. It's just not a accurate a
00:30:58
way of describing market behavior. The
00:31:00
good news though, the good news it
00:31:02
seems, is that the normal distribution
00:31:05
does become more and more acceptable at
00:31:07
longer time frames. Meaning, if we
00:31:09
needed to model daily market returns,
00:31:12
the normal distribution would be a very
00:31:14
bad choice of doing that. Totally
00:31:15
inappropriate. There are just too many
00:31:17
crazy days up or down in the market for
00:31:19
the normal distribution to to accurately
00:31:21
model it. But if I'm modeling one-year
00:31:23
returns, then suddenly the bell curve
00:31:26
becomes not perfect per se, but
00:31:28
certainly better, much better. It turns
00:31:29
out that the most accurate way to create
00:31:32
real world market returns is just to use
00:31:34
an actual data set of real world market
00:31:37
returns and not to let a statistical
00:31:39
distribution kind of create those market
00:31:41
returns for you out of thin air. But
00:31:43
many commercially available Monte Carlos
00:31:45
software packages do use a bell curve, a
00:31:48
simple bell curve, a normal distribution
00:31:51
to distribute and randomize their
00:31:53
returns. Balden, for example, Balden is
00:31:55
a a very popular DIY financial planning
00:31:58
software which includes a Monte Carlo
00:31:59
package and a lot of again a lot of DIY
00:32:02
financial planners out there use it. It
00:32:04
has a a Monte Carlo simulation based on
00:32:06
a normal distribution curve, a bell
00:32:08
curve, and it uses the average rate of
00:32:10
return and the reasonable standard
00:32:11
deviation that you input into the
00:32:13
software to create your Monte Carlo
00:32:15
output. Now, if you're really curious,
00:32:17
it it seems like the uh lelass
00:32:20
distribution is at least better at
00:32:21
capturing the the fat tail nature of the
00:32:24
stock market. And I can throw a link
00:32:25
into the show notes that kind of has an
00:32:27
overlay of a bell curve and a lelass
00:32:28
curve if you want to see them on top of
00:32:30
each other. But I don't have a
00:32:32
statistics degree and most of you don't
00:32:33
either. And the good news is that we
00:32:35
don't really need a statistics degree to
00:32:37
be able to run a Monte Carlo analysis,
00:32:38
right? We're all going to be okay. I
00:32:40
think it's just worth understanding that
00:32:41
there are different ways to do any sort
00:32:44
of numerical method underneath the hood.
00:32:46
And it's just important to know that the
00:32:47
method that you choose has a bearing on
00:32:49
the output. It might not impact the
00:32:51
output a ton. And that's where if you if
00:32:54
you understand what's going on under the
00:32:55
hood, then you can make that kind of
00:32:57
value judgment for yourself. Am I
00:32:58
willing to accept any sort of error
00:33:00
that's going to occur because of the the
00:33:03
numerical method that I'm picking here?
00:33:04
I think that's why they say there's a
00:33:06
very common phrase in the world of
00:33:07
numerical modeling that all models are
00:33:10
wrong, but some are useful. Like like if
00:33:12
you're doing some sort of statistical
00:33:14
method like the ones we've been
00:33:15
describing, you know that your answers
00:33:17
are going to be wrong. Like no answer
00:33:19
that you get from any Monte Carlo is
00:33:21
going to perfectly match the one unique
00:33:24
pathway that lies ahead of you for the
00:33:26
next 30 years. Of course, that's not
00:33:28
going to happen, right? We know that.
00:33:30
But we also know that these models can
00:33:31
be really useful in explaining the range
00:33:33
of possible outcomes that we might live
00:33:35
through. As long as you understand what
00:33:36
kind of errors you're introducing into
00:33:37
your range, you're going to be okay. But
00:33:39
next, whether we're using a a normal
00:33:41
distribution or some other distribution,
00:33:43
the important inputs of a Monte Carlo
00:33:46
actually aren't quite done yet. Because
00:33:47
with any distribution, we need to define
00:33:49
the parameters of that distribution. We
00:33:52
need to define what average actually
00:33:53
means and we need to define the you know
00:33:56
how quickly the curve flattens out how
00:33:58
the data is dispersed within the
00:34:00
distribution and whether we're talking
00:34:02
about a normal distribution or a lelass
00:34:04
distribution or for many statistical
00:34:05
distributions that term is called the
00:34:07
standard deviation or the variance and
00:34:10
in investment lingo we might use the
00:34:12
word volatility instead. We're trying to
00:34:14
define how volatile these assets are. So
00:34:16
in Monte Carlo software, you'll often be
00:34:18
asked to define the average return and
00:34:20
the standard deviation of that return.
00:34:22
Maybe you'll be asked about your
00:34:23
portfolio as a whole or maybe you'll be
00:34:25
asked to define those data points for
00:34:27
specific asset classes. So perhaps the
00:34:30
software will already have those numbers
00:34:32
programmed in so that you don't have to
00:34:33
put them in. If you're inputting
00:34:35
specific asset classes, so you know,
00:34:37
data for stocks, data for bonds, data
00:34:39
for real estate, etc., Then you'll also
00:34:41
probably have to input the correlation
00:34:43
for those assets. Stocks and bonds and
00:34:45
real estate and all other capital
00:34:46
assets. They don't behave independently
00:34:49
in a vacuum. They behave in a dynamic
00:34:51
world where they influence one another.
00:34:53
So the return profiles of different
00:34:54
assets are correlated to one another to
00:34:57
varying degrees and a proper Monte Carlo
00:35:00
analysis will account for that. And
00:35:01
maybe this goes without saying, but the
00:35:03
more inaccurate your return assumptions
00:35:05
are, the more error will end up in your
00:35:07
results. So if you decide to be extra
00:35:09
conservative with your return
00:35:10
assumptions, then you have to accept
00:35:11
that your failure rate is going to be
00:35:13
skewed higher than it otherwise would
00:35:15
be. If you underestimate the standard
00:35:17
deviation in your portfolio, which yes,
00:35:19
we can call volatility. If you
00:35:20
underestimate the volatility in your
00:35:22
portfolio, then your investment ride
00:35:24
will be far smoother inside the Monte
00:35:26
Carlo than in real life. And you'll
00:35:28
probably end up underestimating just how
00:35:31
the sequence of returns risk might
00:35:32
negatively affect you. So typically,
00:35:34
this is where we go consult history. We
00:35:37
look at historical market data. We ask
00:35:39
ourselves questions like how has this
00:35:40
asset or this portfolio performed over
00:35:42
time? What's been the average return?
00:35:44
How volatile has it been? And that
00:35:46
becomes your input or at least it should
00:35:48
heavily heavily guide your inputs. And
00:35:50
then you let the Monte Carlo run. Okay.
00:35:52
So, what's going on uh when we let the
00:35:54
Monte Carlo run? Again, the the main
00:35:56
inputs into a Monte Carlo simulation are
00:35:57
typically your unique future cash flows,
00:36:00
namely how much withdrawal out of the
00:36:02
portfolio you're expecting on an annual
00:36:04
basis. And then your portfolio return
00:36:06
profile, both the average and the
00:36:08
average return and the expected
00:36:10
volatility. And one thing you you might
00:36:11
have noticed by now is that since the
00:36:13
return and the volatility and even the
00:36:14
correlation between assets are single
00:36:16
entries, you're usually assuming that
00:36:19
you will have one portfolio allocation
00:36:21
throughout retirement in a Monte Carlo
00:36:23
run. So that's the way that most Monte
00:36:25
Carlo programs operate. Even if we know
00:36:27
that a real retirement might look
00:36:29
different. So even in something as
00:36:31
dynamic as a Monte Carlo simulation, it
00:36:33
requires even more dynamism to say,
00:36:35
well, is this retiree going to be
00:36:37
changing their investment allocation
00:36:39
over time? Are they going to retire at
00:36:40
6040 and then eventually go down to
00:36:42
50/50 only then to realize they have too
00:36:45
much money and they're saving it for
00:36:46
charity and their heirs and they go back
00:36:48
up to 7030? Like most of these software
00:36:50
packages can't handle that level of
00:36:53
dynamic complexity. So they just assume
00:36:55
you have one single static allocation
00:36:57
throughout your retirement. Even if we
00:36:59
know that might not be the way that your
00:37:01
specific retirement will go. But the
00:37:03
program takes your portfolio return,
00:37:04
your expected volatility, and some form
00:37:06
of a random number generator to create a
00:37:09
decadesl long sequence of returns that
00:37:11
your portfolio will endure. And those
00:37:13
returns combined with your future
00:37:15
outflows. That's all you need to see how
00:37:17
your portfolio will fare in retirement.
00:37:19
And then the program does it again using
00:37:21
the same average return and the same
00:37:23
volatility, but now a different set of
00:37:24
random numbers to create a different
00:37:26
decadesl long sequence of returns. Now
00:37:29
that's you have a a second version of
00:37:30
how your portfolio fares. You can do
00:37:32
that 10 times. You can do it a thousand
00:37:33
times. You could do it a million times
00:37:35
if you had enough time to do it. But
00:37:37
either way, you now have many many many
00:37:39
hypothetical retirement paths to
00:37:41
examine. How do we interpret those
00:37:43
results? How do we make sure your Monte
00:37:45
Carlo isn't really misleading you in
00:37:47
some way? As I alluded to earlier in the
00:37:49
episode, the the surface level results
00:37:51
from Monte Carlo runs can leave out a
00:37:54
little too much detail, and I think we
00:37:55
need to go deeper. So, first, I think we
00:37:58
need to discuss what failure means in
00:38:00
the context of retirement planning or or
00:38:02
Monte Carlo analysis. Typically, Monte
00:38:04
Carlo programs define failure as not
00:38:06
meeting your end goal. And most of the
00:38:08
time, that end goal is not running out
00:38:10
of money at death. So to have at least
00:38:12
$1 is deemed a success and having
00:38:15
anything less than $0 is deemed a
00:38:17
failure. The second most common end goal
00:38:20
though usually involves leaving assets
00:38:22
to heirs or to charity at death. So
00:38:24
again, if you want to leave five kids
00:38:26
each $100,000, then in that case,
00:38:28
anything less than $500,000 at death
00:38:30
would be deemed a failure because you've
00:38:32
said that's your end goal. That's pretty
00:38:34
black and white. But imagine this. You
00:38:36
retire at 55, things go well for a
00:38:38
couple years, and then the market throws
00:38:39
you some rough curve balls. You hit a
00:38:42
pretty bad sequence of returns in your
00:38:43
first decade, and you know that some of
00:38:45
the smart ideas we discuss here, you
00:38:47
decide to pair back your spending a
00:38:49
little bit. You do what you can to
00:38:51
mitigate sequence of returns risk as
00:38:52
best you can. And because you take this
00:38:54
evasive action, your retirement gets
00:38:56
back on track, so to speak, and you live
00:38:57
happily ever after. That is something
00:38:59
that all of us have the power to do in
00:39:01
our retirements. But a Monte Carlo
00:39:04
analysis, at least the commercially
00:39:05
available ones, do not model that for us
00:39:07
in the least. Now, why not? Because what
00:39:10
I just described there was dynamic.
00:39:12
Based on the bad sequence of returns
00:39:14
that we lived through in my
00:39:15
hypothetical, we dynamically decided to
00:39:17
decrease our spending. And then when
00:39:19
things turned around, we dynamically
00:39:21
decided to increase our spending. Again,
00:39:23
Monte Carlo programs don't do that. Or
00:39:25
again, it's not that they can't. It's
00:39:27
just that such many different degrees of
00:39:30
dynamic modeling. That's a challenge.
00:39:31
It's a difficult challenge to program
00:39:33
and to be fair, it becomes a challenge
00:39:35
for end users like us to implement that
00:39:38
in a clear way. You know, if you're
00:39:39
looking at some sort of online software
00:39:41
program where you have to input a
00:39:43
hundred different numbers in order to
00:39:45
quote unquote model your retirement, it
00:39:47
might prevent you from taking that next
00:39:49
step and actually modeling it in the
00:39:50
first place. It's too intimidating. It's
00:39:51
too difficult. So in order to keep Monte
00:39:54
Carlos simulations kind of on the
00:39:55
simpler side, there are some dynamic
00:39:57
things that we would normally do in real
00:39:59
life that just are not part of
00:40:01
standardly available software packages.
00:40:03
But what it really means is that the
00:40:06
failure percentage from Monte Carlo
00:40:07
analysis is misleading. What failure
00:40:10
percentage what it really should be
00:40:11
thought of is the likelihood that you
00:40:14
might need to be dynamic in your
00:40:16
retirement decisions. When your Monte
00:40:17
Carlo run gets a 80% pass rate, it means
00:40:20
that in 80% of realistic market
00:40:22
conditions, you could literally go on
00:40:24
autopilot and not run out of money. But
00:40:26
in the other 20% that are deemed
00:40:28
failures, but in those 20% of simulated
00:40:31
market conditions, you would have to
00:40:33
make a dynamic decision in order to
00:40:35
achieve retirement success. It doesn't
00:40:37
mean that you outright failed. It means
00:40:39
that you would have failed if you were
00:40:40
just on spending autopilot and
00:40:42
withdrawal autopilot. But if you decided
00:40:44
to be dynamic, you might have succeeded.
00:40:46
Here's a quick ad, and then we'll get
00:40:48
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for free at bestinterest.blog.
00:41:37
And that brings us to another um kind of
00:41:39
challenge when it comes to interpreting
00:41:40
Monte Carlo outputs. Imagine you run a
00:41:43
Monte Carlo simulation with a thousand
00:41:44
different trials. And somewhere in those
00:41:46
thousand trials, you're going to find
00:41:49
two of those thousand that just so
00:41:51
happen to be on either side of the
00:41:53
failure line. You know, one of them
00:41:54
happens to terminate with $129 in
00:41:57
positive net worth and that's
00:41:59
technically a success and the other one
00:42:01
terminates with negative $400 in net
00:42:04
worth and that's technically a failure.
00:42:06
So you could have started retirement
00:42:07
with a couple million dollars and and
00:42:08
gone through decades of spending and
00:42:10
investing and at the end of it all a
00:42:12
measly you know $561 ends up being the
00:42:16
difference between these two trials
00:42:18
between success and failure. Yeah, that
00:42:20
is how the simulation works. It's not a
00:42:22
bug. It's not a problem. But it is
00:42:24
important that you understand these
00:42:25
inner workings because Monte Carlo
00:42:27
analysis can be presented to you as
00:42:29
black and white as successes and
00:42:31
failures. But those two scenarios I just
00:42:33
described where after 30 years, $560
00:42:37
determine the difference between success
00:42:39
and failure, those two scenarios are
00:42:41
almost exactly the same shade of gray.
00:42:44
It's just that we we draw a little
00:42:45
dotted line somewhere in that gray area
00:42:47
and that dotted line happens to divide
00:42:50
positives from negatives. If we're not
00:42:52
careful, we'll falsely believe that the
00:42:54
the dotted line actually separates black
00:42:55
from white. It doesn't. It separates
00:42:57
gray from gray. Gray from slightly
00:43:00
darker gray. I guess I reached out to uh
00:43:02
Carsten Yesi. If you don't know Carsten,
00:43:04
he goes sometimes by the nickname Big E
00:43:06
N. Big E R N as in early retirement now.
00:43:09
Ern, Big N. He's the author of the
00:43:11
highly acclaimed financial independence
00:43:13
blog, Early Retirement Now. And Ern,
00:43:16
I'll call him Ern even though his first
00:43:17
name is Carson. He's definitely one of
00:43:19
the biggest kind of foremost thinkers
00:43:21
when it comes to safe withdrawal rate
00:43:23
research such as the 4% rule. And I was
00:43:26
noodling on the problem I just described
00:43:28
or or part of the problem of Monte Carlo
00:43:30
analysis. So I wrote to him and I said,
00:43:31
you know, hey Ern, my understanding is
00:43:33
that retirement withdrawals can be a
00:43:35
slippery slope. If when your retirement
00:43:36
nest egg drops below a certain
00:43:38
threshold, your risk of running out of
00:43:40
money increases dramatically. Or perhaps
00:43:43
set another way, as your retirement
00:43:45
accounts drop, there is an exponential,
00:43:47
not linear, there is an exponential
00:43:49
increase in the probability that you
00:43:50
eventually run out of money. The
00:43:52
sequence of returns risk is a terrific
00:43:54
example of this fact. So to that end, it
00:43:56
begs the question, why do we pass fail
00:44:00
safe withdrawal rates based on 0 left in
00:44:02
the account? We start retirement at 100%
00:44:05
funded. We withdraw 4% or some other
00:44:07
percentage per year adjusted for
00:44:09
inflation. And usually markets have
00:44:11
increased our nest egg to 200% or 300%
00:44:13
or more by the time of death. And we
00:44:16
define 0% as a failure when really I'm
00:44:19
not interested in the point when we hit
00:44:20
0%. By that time it's too late to change
00:44:23
my future. I'm much more interested in
00:44:26
when should I be worried? When do I need
00:44:28
to take evasive action? Is it when my
00:44:30
accounts hit 80% of where they started?
00:44:33
Is it when they hit 50% of where they
00:44:35
started? Is it something else? Is there
00:44:37
an inflection point where you believe it
00:44:38
makes sense for a retiree to seriously
00:44:40
consider a change in course as their
00:44:42
probability of failure has just become
00:44:44
too high? So, that was what I wrote to
00:44:47
Ern, and he got back to me with
00:44:48
something that he called a conditional
00:44:49
success rate. I'll link to this article
00:44:51
in the show notes. This conditional
00:44:53
success rate helps retirees contemplate,
00:44:55
you know, it's been Years since I
00:44:58
retired and my portfolio is currently
00:45:00
down X%. How does that compare to
00:45:02
history? How worried should I be
00:45:04
compared to other time periods? I know
00:45:06
my retirement hasn't failed yet, but
00:45:08
surely I'm in a worse position now than
00:45:09
other historic periods. Surely because
00:45:11
my portfolio is down, I ought to
00:45:13
consider tightening the belt and
00:45:14
spending less. You know, we can compare
00:45:16
that to other probabilistic games. We
00:45:18
can compare it to poker. You know, hey,
00:45:20
I'm playing poker now that a king has
00:45:22
come out in the flop. What's the
00:45:24
conditional success of my pocket pair of
00:45:26
queens in in Beijian terminology, right?
00:45:29
This is adjusting your priors. Your
00:45:31
future probabilities change or I guess I
00:45:33
should say your current probabilities
00:45:34
change based on this new information.
00:45:37
So, you have to adjust your prior
00:45:39
assumptions. And part of my question
00:45:41
essentially is how should retirees
00:45:43
adjust their priors as they move
00:45:45
throughout retirement? More applicable
00:45:47
to to real life, how and when should
00:45:48
retirees adjust their spending
00:45:50
throughout retirement? This is a
00:45:52
question of course that many people are
00:45:53
attempting to answer in in many
00:45:54
interesting ways, but it's always good
00:45:56
to have some analytical rigor behind
00:45:57
whatever your your answers are going to
00:45:59
be. So, here's a cool tidbit from Big
00:46:01
Earns Research to kind of fill you in on
00:46:03
my thought process. Imagine our retiree
00:46:06
retires with $1 billion and they have a
00:46:08
30-year retirement goal ahead of them.
00:46:10
They're invested in 75% stocks and 25%
00:46:13
bonds. They're following the 4%
00:46:14
withdrawal rule and adjusting for
00:46:16
inflation. And we're going to use real
00:46:18
historical market data here. It turns
00:46:20
out that this retiree, their plan, their
00:46:23
rigid plan, right, which isn't dynamic
00:46:24
at all. It's the 4% rule. It's going to
00:46:26
fail in about 1.8% of all historical
00:46:29
scenarios. But let's take that tidbit.
00:46:32
It fails 1.8% 8% of the time. Let's now
00:46:35
fast forward 10 years into this person's
00:46:37
retirement. Can we look at that 10-year
00:46:39
mark and can we start to see if they're
00:46:41
on the road to long-term success or the
00:46:43
road to long-term failure? In other
00:46:44
words, for some of the trials, by year
00:46:46
10, their accounts will have gone down.
00:46:48
Sometimes they'll they'll have less than
00:46:50
$750,000.
00:46:52
Sometimes they'll have less than
00:46:53
$500,000. They started with a million,
00:46:55
but then for other trials, their
00:46:57
accounts will have gone up. They'll have
00:46:58
more than 1.25 million after 10 years,
00:47:01
even with all their spending. And if we
00:47:02
had to guess, I would wager that we'll
00:47:04
see far fewer failures from the second
00:47:06
group, I guess maybe from the third
00:47:08
group. We'll have far fewer failures
00:47:09
from the people who accounts where their
00:47:11
accounts have gone up and we'll see more
00:47:13
failures from the people who 10 years in
00:47:15
their accounts have gone down. That just
00:47:17
seems to be the way that the sequence of
00:47:18
return risk works. And this is called
00:47:21
conditional probability. We ask how does
00:47:24
the probability change once we add a
00:47:26
specific condition. Perhaps the
00:47:28
condition is you made it to year 10 and
00:47:29
you're already down to $750,000.
00:47:32
Or the condition is you made it to year
00:47:34
10 and you're already up to $1.25
00:47:36
million. And what big earns analysis
00:47:39
shows is that if at year 10, if a
00:47:41
retirees portfolio was already down
00:47:43
below $500,000, then they have a 13%
00:47:46
chance of outright retirement failure
00:47:48
and they only have a 33% chance of dying
00:47:51
with more than the 500k in their
00:47:53
portfolio at that time. So there's a
00:47:55
twothirds chance that their portfolio is
00:47:57
going to continue going down from there.
00:47:58
And that's a scary thought if you're
00:48:00
only 10 years into retirement. But if at
00:48:02
year 10 your portfolio had already grown
00:48:05
to 1.25 million or more, there wasn't a
00:48:08
single outcome where you died with less
00:48:11
than $500,000. Not one. So in the first
00:48:14
bad scenario we just outlined, you had a
00:48:16
twothirds chance of dying with less than
00:48:18
500,000. But in the good scenario, you
00:48:20
have zero chance of dying with less than
00:48:22
500,000. In fact, in the good scenario,
00:48:24
you have a 75% chance of dying with more
00:48:27
than $2 million. The takeaway again is
00:48:30
that the early years of retirement
00:48:32
absolutely set your path. Your end
00:48:34
results are conditional upon the way
00:48:36
your early years unfold. And therefore,
00:48:38
if you can make smart, dynamic decisions
00:48:41
in your early years, you will be
00:48:43
shifting the conditional probabilities
00:48:44
in your favor. A Monte Carlo simulation
00:48:47
for all its power does not do this. It's
00:48:50
on you to understand that fact. For me,
00:48:52
one of the keys of understanding a Monte
00:48:54
Carlo output also lies in percentiles.
00:48:56
You've probably heard percentiles
00:48:58
before. Wow, that baby is so fat. Yeah,
00:49:00
he's in the 98th percentile for weight.
00:49:03
Okay, that means that baby is heavier
00:49:05
than 98% of his peers. So, the 75th
00:49:08
percentile shows us the result that is
00:49:10
better than 75% of the other simulations
00:49:12
and worse than 25% of the simulations.
00:49:15
The 10th percentile shows us one of the
00:49:17
worst outcomes. In fact, the 10th
00:49:19
percentile is worse than 90% of the
00:49:22
outcomes in the simulation. And by
00:49:24
comparing different percentiles in a
00:49:25
Monte Carlo run, we begin to understand
00:49:28
our range of reality. Financial planning
00:49:30
is very much about understanding your
00:49:32
range of potential outcomes. Imagine I
00:49:34
compare the 10th percentile to the 90th
00:49:36
percentile. In doing so, I now
00:49:38
understand 80% of my total range of
00:49:41
outcomes. Then I can start to ask, well,
00:49:43
just how disperate is that 80% range? If
00:49:46
it's all over the map, say I retire at
00:49:48
age 55 with $3 million and the Monte
00:49:50
Carlo simulations range from abject
00:49:53
failure at the 10th percentile up to $15
00:49:56
million in terminal wealth at the 90th
00:49:58
percentile. If it's that wide of a
00:50:00
range, it tells me some interesting
00:50:01
things. Specifically, it might tell me
00:50:03
that the volatility in my portfolio
00:50:05
subjects me to some significant sequence
00:50:08
risks. Now, the good sequences are 5xing
00:50:11
my money before I die, but the bad
00:50:12
sequences are leading to retirement
00:50:15
failure. So, hm, I might want to play
00:50:17
around with that result. I might want to
00:50:19
adjust my allocation, my volatility
00:50:21
accordingly. If I'm comparing the 99th
00:50:23
percentile though to the first
00:50:25
percentile, well, I expect that range of
00:50:27
outcomes to be pretty big no matter what
00:50:29
because it contains almost all of the
00:50:30
simulations, including the ones that
00:50:32
have some really crazy sequences built
00:50:34
into them. you might as well just be
00:50:36
looking at the the maximum and the
00:50:37
minimum, the total range. But by cutting
00:50:40
5% or 10% or even 20% of the data on
00:50:42
either end, that still leaves you with
00:50:44
this big majority chunk of data in the
00:50:46
middle that captures most of the
00:50:48
possible outcomes and defines your
00:50:50
likely range that you could have to deal
00:50:52
with. If you're feeling particularly
00:50:54
statistical, I guess you might have to
00:50:56
know that 34% on either side of the mean
00:50:59
average of a normal distribution, that
00:51:01
34% captures one standard deviation. So
00:51:05
by measuring between the the 16th
00:51:07
percentile, that's 50 minus 34 in one
00:51:10
direction. Between the 16th percentile
00:51:12
and the 84th percentile, which is 50 +
00:51:14
34. So between the 16th and the 84th
00:51:17
percentiles, you're capturing 68% of the
00:51:20
results that occur within one standard
00:51:22
deviation. either direction of the
00:51:23
average. It's just a handy way of making
00:51:25
use of Monte Carlo outputs without
00:51:28
focusing so much on the worst of the
00:51:29
worst outcomes or the best of the best
00:51:31
outcomes. And then you can ask yourself,
00:51:33
you know, how many scenarios in that
00:51:35
range that I've just described, how many
00:51:36
of those scenarios end up starting to
00:51:38
slip down that slippery slope toward
00:51:40
running out of money? And I mean, how
00:51:42
many of those scenarios end up on the
00:51:43
other side where you're compounding
00:51:45
faster than you can spend such that you
00:51:47
die with three times or five times or 10
00:51:49
times what you started retirement with?
00:51:51
So, I think that's one really good way
00:51:52
to to look at Monte Carlo results. But
00:51:54
then I also really recommend you
00:51:56
understand a middle-of the road failure
00:51:59
scenario. So, yes, a failure scenario.
00:52:01
So, let's say for example, your initial
00:52:03
Monte Carlo run has an 80% chance of
00:52:06
success. That's great. I recommend you
00:52:08
grab a couple of the outputs, a couple
00:52:10
of the trials from the middle of the 20%
00:52:13
of failure scenarios and really dig into
00:52:16
those couple of outputs. Try to
00:52:17
understand at what point in this failure
00:52:20
trial did things start going off the
00:52:22
track. What could you have done
00:52:23
differently? Again, if you were allowed
00:52:25
to be dynamic, if it's if you're living
00:52:27
your life, what could you have done
00:52:28
differently in that trial specifically
00:52:30
in terms of spending less? How many
00:52:32
years of lowered spending and what
00:52:34
magnitude of lowered spending could have
00:52:36
turned that particular failure into a
00:52:39
success? I think that will really help
00:52:41
you understand again that that's a
00:52:42
really good way of going beyond the
00:52:44
surface level results of a Monte Carlo
00:52:46
and really digging into the detailed
00:52:48
results. The very last thing I'll I'll
00:52:50
go over in this episode. What are some
00:52:51
other common Monte Carlo mistakes? A
00:52:53
really easy one to avoid and this can be
00:52:55
very consequential is understanding how
00:52:57
your particular Monte Carlo software
00:53:00
handles inflation. For example, do you
00:53:02
need to account for inflation when you
00:53:04
input your spending numbers or does the
00:53:06
program ask you for a particular rate of
00:53:08
inflation and then it automatically
00:53:10
inflates your spending numbers for you?
00:53:12
Do you need to account for inflation in
00:53:14
the portfolio return assumptions or not?
00:53:16
You know, nominal returns or real
00:53:17
returns. Considering long-term inflation
00:53:20
averages out to like 2 to 3% per year,
00:53:22
you need to get inflation right. You
00:53:25
need to make sure you model it
00:53:26
accurately. Double counting inflation,
00:53:28
thus reducing your real return by an
00:53:31
extra 2 to 3% per year, creates way more
00:53:34
failure than reality ought to, but then
00:53:36
not counting your inflation at all, thus
00:53:38
increasing your real return by an extra
00:53:40
2 to 3% return. Well, that's going to
00:53:42
create way more success than reality
00:53:45
otherwise would. So, you've got to get
00:53:46
inflation right. Overall, these Monte
00:53:48
Carlo programs, they're great tools to
00:53:50
to examine where you're at and to
00:53:52
understand the range of possibilities
00:53:53
that your future might go through. But
00:53:56
importantly, your unique future, it only
00:53:58
partially exists in that range of
00:54:00
possibilities that a Monte Carlo is
00:54:02
going to create for you. There are a lot
00:54:03
of dynamic aspects in retirement
00:54:05
planning. And a Monte Carlo analysis
00:54:06
captures some of that dynamism amazingly
00:54:09
well, but it does not capture all of it.
00:54:11
Other parts of retirement the Monte
00:54:13
Carlo has to assume are static and then
00:54:15
you, the user, you have to infer from
00:54:17
there. So, if I didn't answer any
00:54:20
specific questions you have about a
00:54:21
Monte Carlo analysis, by all means, feel
00:54:23
free to email me to jessebinest.blog.
00:54:25
blog. I know this was a wonky one. I
00:54:27
don't expect any of us to be out there
00:54:29
writing our own Monte Carlo software or
00:54:32
uh getting statistics PhDs to understand
00:54:34
what's really going on under the hood.
00:54:36
It's just one of those things where a
00:54:37
Monte Carlo, like many things in this
00:54:39
world, it's got a bit of that
00:54:40
double-edged sword to it. And as long as
00:54:42
you understand how to use that sharpness
00:54:44
for your benefit and not to get injured
00:54:46
by it, I think you'll be in a good
00:54:47
place. So, thank you as always for
00:54:49
listening.
00:54:49
>> Thanks for tuning in to this episode of
00:54:51
Personal Finance for Long-Term
00:54:53
Investors. If you have a question for
00:54:55
Jesse to answer on a future episode,
00:54:57
send him an email over at his blog, The
00:54:59
Bestin Interest. His email address is
00:55:01
00:55:04
Again, that's jessevestinterest.blog.
00:55:08
Did you enjoy the show? Subscribe, rate,
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00:55:16
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00:55:18
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00:55:20
for Long-Term Investors. Personal
00:55:23
Finance for Long-Term Investors is a
00:55:25
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00:55:27
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00:55:29
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00:55:31
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00:55:32
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