One way you can see some possible outcomes of your retirement plan is to use a retirement simulator similar to one available from Vanguard. These simulators use Monte Carlo methods to run several thousand possible patterns of investment returns to see how your portfolio holds up through retirement. Behind the impressive scientific-looking tools are some problems. Here I show the problems in pictures.
To understand these problems, we need to look at the fairly simple way these simulators work. To generate a possible outcome for your portfolio, many of these simulators begin with some actual historical investment returns from a range of years. They build your simulated results one year at a time by choosing one of the historical years randomly and applying that year’s returns to your portfolio.
Before getting into why this method has some issues, let’s go to a couple of charts. I grabbed some annual TSX investment returns for the past 47 years. Then I made a chart of portfolio growth for all 28 overlapping 20-year periods. Here are the 28 results for a starting portfolio of $20,000:
It’s hard to learn too much from this mess, but bear with me. What matters is the range of outcomes. The next thing I did was to put the 47 years of TSX returns into a random order and draw the same chart again. I used all the same return percentages, but in a different order. Here is the result:
The main thing to notice is how much more spread out the 20-year returns were in the random order case. Both charts have exactly the same log-scale. The portfolios for the TSX returns in actual order had an ending portfolio value range of $82k to $251k. For the randomized return order, the range was $46k to $339k. This is a substantial difference. Once the return order is randomized, the portfolio outcomes become much wilder.
What’s the explanation for the change? It turns out that the stock market has a tendency to revert to the mean faster than random chance would suggest. A string of years with poor returns are somewhat more likely to be followed by good returns than more poor returns, and vice-versa. When we randomize the order of the annual returns, we eliminate this effect.
So, many retirement simulators give results that are wilder than you can really expect in real life. If you choose a spending level and run the simulations, the simulator might overstate the likelihood of running out of money. On the other hand, if average annual stock returns are lower in the future than they were in the past, the simulator may be understating the likelihood of running out of money. We might hope that these effects would cancel, but it’s likely that one will dominate the other, and it’s hard to say which.
This doesn’t mean that using Monte Carlo simulations to get a sense of the range of possible outcomes is a bad idea. It’s just important not to be too impressed with the science and math. These simulations have two important limitations: they remove return correlations across time, and they assume that future average returns will match past average returns. Buyer beware.