Monaco hot spots
If there’s one thing that those in the media love to do when it comes to investing, it’s attempting to predict the future. Turn on any channel that focuses on the stock market and you’re guaranteed to hear pundits making forecasts of the future with almost near certainty. The statements are made with such confidence and bravado it’s almost as if they know exactly what’s going to happen and when. Of course, this can’t be the case because they’d all be billionaires several times over if it were. Educated guesses can be made, but no one has ever consistently predicted what the market is going to do ahead of time, no one.
There’s no shortage of forecasting tools used by market analysts. From technical analysis of the stock’s price to macro trends associated with debt cycles, investment experts employ all sorts of methods to try and get a leg up on the market. Sometimes it works and attracts much fanfare, sometimes it flops with much humiliation. And rarely do investors recheck the tape to see how their favorite gurus’ predictions stacked up against what actually happened.
One of the more conservative forecasting methods is named after a gambling hot spot in Monaco, which probably doesn’t do the model any favors. Monte Carlo (MC) simulations were first developed by Stanislaw Ulam, a mathematician who worked on the Manhattan Project.1 Basically, these models are used to display the probability of various outcomes with several random variables. Monte Carlo simulations assume perfectly efficient markets, essentially disregarding elements that are not built into the price movement of the stock. In other words, if there’s a change in management or if TV pundits are touting an increase in stock price of a particular company, MC simulations will ignore these variables and plot the results as if they never occurred. It’s not a perfect forecasting tool, but no method of predicting the future is.
Figure 1 is a statistical exercise taken from the Bogle Financial Markets Research Center. It’s designed to estimate the odds that an actively managed equity fund will outperform a passively managed index fund over various time periods. For example, over one year, about 29% of active funds would be expected to beat the index; over 10 years, only 9% would be expected to outperform their benchmark index. Over a lifetime of investing (in this case, 50 years), only 2% would be expected to beat the market. If investors are looking to play the odds of receiving outsized returns year in and year out, models like this will provide an estimate of what it will take to realize that goal.2
Figure 1. Monte Carlo simulation, probability of active funds outperforming passive funds
This simulation is merely a forecast, and like any other forecast, it shouldn’t be used as a tool to allocate your capital in anticipation of it actually being realized as predicted. It can, however, serve as a guide to analyze risk and return over various time periods.
One tool of many
We should caution readers that potential pitfalls of Monte Carlo simulations do exist. The primary drawback is that it can give investors a false perception that their particular financial situation is reflected in the model. It would be impossible to forecast all inflows and outflows of cash, the timing of those transactions, and the relative market trends of those contributions and distributions. In essence, MC simulations are incapable of accurately depicting dollar-weighted returns, which account for how investors add to and subtract from their investments. However, when a fixed dollar amount is used—without any inflows or outflows—these simulations can provide a clearer picture of what the probability of a certain goal may look like.
Although Monte Carlo simulations can provide some insight into how certain investments will perform, like all other forecasting techniques, it shouldn’t be taken as gospel, but rather used as one of many methods to maximize risk-adjusted returns.
2. Notes: The simulation makes assumptions about the volatility of equity fund returns and the extent to which they deviate from the stock market as a whole. Assumptions regarding the all-in costs of equity investing (e.g. expense ratios, transactions costs, turnover costs, and market impact costs) are also considered and total 0.25 percent per year for index funds and 2 percent per year for active funds, on average. Source: Bogle Financial Markets Research Center