Monte Carlo or Bust

I have been looking at some Monte Carlo simulations this week. For those unfamiliar with them, they allow you to take your portfolio and input factors such as withdrawal rates, inflation and portfolio make up. The software then runs something like 10,000 scenarios and gives you an idea as to whether your portfolio will run out before you do.

You can then rerun as many times as you like by tweaking your parameters and say withdrawing slightly less or assuming a larger rate of inflation. Typically you want to adjust these to such a point that your money doesn’t run out in the vast majority of cases. Obviously your level of acceptance of risk determines whether this number is say 75%, 100% or somewhere in between.

Most investment house websites as well as independent websites will have versions of these all with differing amounts of visibility as to what is going on under the hood. Typically the more things you can see, the likelihood is the better it will be so there is greater visibility on the assumptions taken.

For those of us who have retired early then we want to run these over a period of something like 50 years, however when you do that you obviously get a massive variation in the possible outcomes. When run on our own portfolio, the P90 was a small increase in our initial portfolio over 50 years (i.e. there was a less than 10% chance we would lose money over 50 years) and the P10 was somewhere close to $250 million dollars! If someone offered me a 10% chance to win a quarter of a billion dollars in a lottery I think I would take those odds.

The mid point, which seems a sensible benchmark, shows a $60 million dollar portfolio after 50 years.

So immediately the thought of a $250 million nest egg rings some alarm bells! Intellectually I know that is not going to happen, so where has the simulation fallen down?

The simple answer is in how a lot of these simulators calculate the portfolio returns for the upcoming 50 years. A lot of them use historical returns, which means they are using the returns seen over the previous 100 years or so to drive the next 50. There are several issues with that, firstly the past is never a predictor of the future you simply can’t use a market’s gain from say last year to determine what it will do this year. There is simply no correlation. The second is these algorithms will often not handle long term trends. In the real world it is possible to have multiple year recessions where the markets maybe down for several straight years. These software packages usually don’t have this level of sophistication built in.

The net result of this is that often Monte Carlos are run with an assumption of up to 10% net return every year. If that’s the case then of course at the extreme end you will end up with portfolios of several hundred million dollars!

So if you do use one of these tools be very aware as to what rate of return it is using, if you can override these assumptions then you should as I don’t think that 10% per year is a reasonable assumption to use.

If I rerun the predictions above with a more conservative but possibly realistic assumption of 5% market gain then the P10 drops to somewhere around $30 million (still a lot!) and the midpoint at P50 shows a small portfolio gain (not adjusted for inflation) after 50 years.  This seems intuitively more reasonable.

I also note that this simulation suggests that there is about a 25% chance we will run out of money sometime around the 40th year. Again this seems reasonable, if we are drawing down around 2.5% each year and inflation runs at an average of 2.5-3% then the 5% increase just barely covers it. But this particular model didn’t take into account any additional income such as pensions or social security which will offset this. Some models will do this though, especially those that are for sale

One other way of looking at this type of prediction (but without the Monte Carlo element) which is quite nice is to present your portfolio against a 50 year profile based on the last century. So what would happen if you had invested your portfolio in 1901, how would it look in 1951. What would happen from 1902-1952, 1903-1953 etc. and then displaying all the results on a graph. This provides a nice picture of possible scenarios.

Although this approach puts the real world element in which is very nice and a great way of looking at investments for visual learners, it still assumes that the past has any bearing on the future.

At the moment though I don’t know of any better ways of analyzing your portfolio than using statistical tools driven by past performance, but just be aware of the limitations.

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PETER WANG Recent comment authors
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Great idea!