Planning for personal finance issues, such as saving for retirement or college, is a problem that most of us have thought about at some point. It also happens to be an excellent use case for Ancho, my in-development Monte Carlo tool. In this post I'll try to explain why.

Most life-event planning calculators start with a few variables that are taken as given: your current income, your age, perhaps the age of your spouse and children. They require you to choose an age at which you'll need the money, which would be either the age at which your child turns 18 or the age at which you expect to retire. Typically they also require you to assume an annual rate of return, which is assumed to be constant, and they solve for the required level of savings to meet the goal.

Fancy ones might also account for a couple of other variables. Maybe you aren't sure what the rate of inflation will be; there are different rates depending on whether you're talking about consumer prices, medical inflation or higher ed inflation. Maybe it gives you different outcomes depending on whether your average return is 6% or 7% or 8%, and shows you some pretty charts and graphs.

If you have kids or a 401(k) account, you've probably seen something like this at least once. Most people, I think, intuitively realize that this kind of planning is somehow insufficient. Still, they can't put their finger on why that is so, and the whole question of how much to save seems overwhelming. They just pick a number that seems like the level of savings they can afford, and hope for the best. As events unfold, they adjust their plans accordingly.

The problem with these planning methods, at least *one* of the problems, is that they don't account for the variability and complexity of how things might develop over time. You have no idea exactly how your investments will perform over time. If there's one thing you *can* be certain of, it's that you won't make a steady 6% annually for the next 20 years. Even if the annual returns did turn out to *average* 6%, the variability and the exact sequence of those returns makes a huge difference. People in the neighborhood of 60-65 years old are keenly aware of this, having seen their retirement portfolios grow and then shrink unexpectedly in recent years. Now their assumptions about when (or even whether) they'll retire are in question.

As you might expect -- or I wouldn't have brought up the topic -- Monte Carlo simulations provide a very useful way to think about these issues. As I've said before, planning based on point estimates is not very useful, because you can be relatively assured they'll be wrong, and the variability in exactly how they're wrong is significant. Note that I'm not saying that these things are *entirely unpredictable*. You have historical data about each factor's variability that allows you to estimate the probable range of future outcomes.

For instance, you could estimate your rate of return by looking at the U.S. stock market over the last 100 years. Take a random sampling of one-year stretches and determine the year-over-year return for that period. Look at the distribution. What you'll see is probably a bell curve with tails on either side. That distribution curve -- not a single number -- is your "estimate."

You could do similar things to estimate things like consumer price inflation, real estate appreciation, tuition and medical cost increases. You can lay your own odds on whether you think Social Security will still be there by the time you might need it, or whether your child will get a scholarship, or whether your child will even go to college. You can take into account the very real possibility that you or your spouse will encounter some kind of long-term disability before you reach retirement age that will interrupt your savings. My point is not to exhaustively list all these factors, but to illustrate the range of things that you could take into account. It just depends on how much effort you want to put into the model.

Once you've estimated all the "input" factors as probability distributions, and created your model accordingly, the computer can do the number crunching. The result will be another set of probability distributions. Instead of a planning tool that says "you need to save $525 per month for the next 26.5 years," that relies on overly simplistic assumptions, your answer is going to be more like "in 90% of modeled scenarios, $550 in monthly savings will be sufficient for your needs."

Further analysis may also yield insights beyond the answer you were originally looking for, such as "in the 10% of modeled scenarios where $500 per month is not sufficient, the reason is not because your returns were too low, but because you developed a disability during your peak earning years that prevented you from saving." So maybe you'd be better off saving a little less and buying a long-term disability policy. Your model is not going to make specific suggestions like that, of course, but you would be able to inspect the results and see what happened in situations where you outlived your savings.

This is probably a good time to point out the limitations of a Monte Carlo analysis. Using this method requires you to actually *understand* the problem you're trying to model. Monte Carlo is not a substitute for thinking, but instead a tool to aid and guide your thinking. There's always going to be something you haven't thought of. But the tools you're probably using now aren't even accounting for the things that you *have* thought of, so it's still a big win.

I can think of three general classes of error for a Monte Carlo model:

**Failure to estimate probabilities correctly.**For instance, if you were sitting in the year 2000 and only looked at the 10 most recent years of stock market data to estimate future returns, you would have looked at a time when market returns were higher than usual, and your savings would be woefully insufficient.**Ignoring a key variable.**Imagine, for instance, that you were planning your retirement in 1980. If you assumed that your longevity would be like that of your parents, you might have underestimated by 5 or 10 years because you didn't take into account the long-term trend that people are living longer.**Misjudging the relationship between some variables.**For instance, you might have assumed that the mortgage interest deduction would always be there. You modeled your income tax estimates accordingly. If that deduction goes away due to some post-fiscal-cliff tax reform deal, and you didn't account for that possibility, you're suddenly paying taxes on an extra $10,000 a year that you hadn't planned for, and your retirement savings plan blows up as a result.

I have one more use case to write about after this, but describing Ancho's usefulness in my chosen field -- risk management -- is turning out to be hairier than I thought. I've already discussed enough use cases to start talking about features, so that will be coming next. Sometime before 2013 rolls around, though, I hope to get back to the risk management topic.