# Financial Geekery

Monte Carlo simulations are one of the cornerstones of what I call "adaptive financial planning". The idea is to keep you on track -- not to die rich, nor to die poor, but to live richly. By using Monte Carlo to project potential outcomes decades into the future, we can make small course corrections now to effect large changes over time. (Contrast this with waiting until the iceberg is right in front of you, when it's generally too late!)

If you're not familiar with Monte Carlo sims, don't blame yourself! It's not often discussed, because most financial advisors feel they're "too complicated" for most people to understand. They're not, really, so -- let's talk about them.

What exactly is a Monte Carlo simulation?

In the broadest sense, a Monte Carlo simulation is simply a simulation that takes random input and uses it to create a statistical output. They're often used in physics for systems that have so many degrees of freedom that it's infeasible to model them otherwise.

Where financial planning is concerned, Monte Carlo simulations use a randomly-generated sequence of market returns to project how a portfolio might behave over time. (If you must know: the model is a Gaussian bell curve, which is imperfect given the market's kurtosis and skewness, but works remarkably well.)

In other words: as you know, the market doesn't go up in a straight line. Rather, it goes up, then down, then way up, then waaaaay down, etc. Monte Carlo randomizes the order of that up-and-down movement and shows you the range of possible outcomes. And this "sequence of returns" matters, quite a bit.

Now, the mathematically inclined among you may say, "wait a minute. Why does the sequence of returns matter? I learned the commutative property way back in elementary school: if the market goes up 10% and then down 10%, that's 1.1 * 0.9, which is the same as 0.9 * 1.1. Sequence of returns shouldn't matter at all!"

Congratulations! You get a gold star. (No, seriously, that's a good question.) It turns out that sequence of returns does matter, for this simple reason: your portfolio doesn't exist in a vacuum. You're contributing to it in your early years, and withdrawing from it in later years. These inflows and outflows have a (perhaps surprisingly) large effect on the outcome!

An intuitive way of thinking about it is this: a market downturn during your first year of retirement is considered to be among the worst-case scenarios. Why? In that case, you end up withdrawing a larger percentage of your portfolio, which takes a bite out of your returns for the rest of your retirement!

Monte Carlo: the practical part

So that's what Monte Carlo is; what does it look like, and what does it do? Where does the theory actually come into practice?

Here's the "basic" output of a Monte Carlo simulation:

This is a representation of each of 1,000 runs, which the lighter shades indicating the more common (read: more probable) results, and the blue line indicating the median. (Again: sequence of returns matters a lot.)

Interesting, but not necessarily useful, right? This might be more helpful.

The right hand side shows 3 of the 1,000 simulations: the 25th best, the 25th worst, and the median. It gives you an idea of the feasible range of outcomes, without the brain dump of the earlier graph.

On the left hand side, you see the "probability of success". This is the percentage of Monte Carlo simulations that projected the portfolio staying above $0. Note: this does NOT mean a 12% chance of running out of money! The simulation assumes that you see the iceberg coming and don't do anything about it. In the real world, you'd run Monte Carlo simulations every year, see the success rate trending downward, and make small course corrections to bring it back up.

So...what's a good success rate, then? That's a good question, and you really need to come up with that answer yourself. For my clients, I often target a range of 75-90%. 90% is pretty high, but it adds an important element of conservatism; while ideally I want my clients to live richly, dying poor is a much worse alternative than dying rich! If we stay in the 91-100% range for a few years, I encourage my clients to consider ways to live more richly -- retiring earlier, working less, travelling more, giving money away! Below 75%, and we start making course corrections.

Not just for retirement planning

You can see how Monte Carlo is pretty much essential for retirement planning, but it's a cornerstone for financial planning in general. Any financial strategy we consider should go through the Monte Carlo analysis. For example:

Asset allocation: This is one of the most important applications of Monte Carlo sims. If your asset allocation is too conservative, Monte Carlo will show a low success rate due to the low average returns. If it's too aggressive, sims will show a low success rate due to excessive volatility -- too many runs where a downturn at the wrong time torpedoed your plan. Monte Carlo sims can help determine an optimal asset allocation for your particular situation. It's an essential part of determining your risk capacity.

Social Security analysis: Conventional wisdom is to delay taking Social Security for as long as possible. But conventional wisdom doesn't take Monte Carlo into account! Delaying Social Security means living off of more of your investments during those fragile early years of retirement. Therefore, despite the excellent ROI of delaying Social Security, the Monte Carlo sims for doing so may project a lower success rate!

Mortgages and other debt: Should you pay off your mortgage sooner, or later? Should you take a reverse mortgage in retirement? It's hard to make an apples-to-apples comparison of paying off low- to mid-interest debt versus investing in the market. Why? Because while the market returns may be higher, the market is also volatile. Monte Carlo sims help you analyze that tradeoff, by combining volatility and expected returns into a single output. (Of course, any debt with a higher interest rate than your portfolio's expected returns should be eliminated with extreme prejudice!)

Garbage in, garbage out

I want to be clear, here: Monte Carlo sims aren't magic, and they're only as good as their inputs.

For one thing, in order to create that Gaussian curve I mentioned, you need your portfolio's expected returns and standard deviation. We can estimate those with surprising accuracy, but an error of even 1% in expected returns can make a huge difference in the Monte Carlo outcome.

Moreover, your income and expenses will almost never match up perfectly with the assumptions you make. Your job may change. Your family situation may change. Tax law may change. These will have a large impact on your simulations, as well.

Does this mean Monte Carlo is useless? No! However, that's one of the reasons why I insist on re-running these simulations twice a year, and set my threshold for course corrections at a pretty high success rate. This way, we catch the issue the moment the success rate dips below 75%, and can make a small course correction to adjust.

In other words: "plans are nothing, but planning is everything."

Where do I go from here?

So you're sold and want to start running Monte Carlo sims as part of your financial planning process. Where does one get these marvelous things? There are a few options out there that I like:

**Vanguard's Retirement Nest Egg Calculator **is a great place to get your feet wet, and it's free! It's only got a few knobs that you can turn, so there's more "garbage in" than otherwise, but it's pretty solid, has an intuitive interface, and gives you an idea of what Monte Carlo is all about.

Want something with serious horsepower? Flexible Retirement Calculator is a cool project that lets you play with all sorts of variables, from taxes to your spending plan in retirement. You can evaluate it for free, and if you decide you want to use it, you can purchase a license for whatever you feel it's worth. (They suggest $20.)

Of course, there's always hiring a financial advisor. "But wait!" you say. "I don't want comprehensive financial planning, or investment management, or any of that stuff. I just want a Monte Carlo sim!" And that's fine; an increasing number of advisors are happy to do one-off projects for an hourly rate! (Seaborn is one of those, and you can find other advisors who only do hourly work at Garrett Planning Network.) The advantage here is that you not only get access to the tools, but you get the expertise of someone who can help you minimize that whole "garbage in" phenomenon I mentioned above. (Yes, I'm biased, but seriously -- of all the investments I can think of making, financial planning is the one with the most obvious payout!)

Monte Carlo's a technical topic, but a tremendously important one, and I hope this article helped. Have more questions? Feel free to drop a comment, or send me an e-mail! (I'm serious -- if there's something you don't get or you disagree with, let's talk about it!)

Britton is an engineer-turned-financial-planner in Austin, Texas. As such, he shies away from suits and commissions, and instead tends towards blue jeans, data-driven analysis, and a fee-only approach to financial planning.

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