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Portfolio > ETFs > Broad Market

The Truth About Monte Carlo

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One of the hottest tools in the investment industry is Monte Carlo simulation or, if you would like the $20 term, stochastic modeling. Why has this esoteric modeling methodology garnered so much attention so quickly? How is it different than what we have done in the past? What is the best way to use it, and how can we avoid misusing it?

In an uncertain world, there is comfort in having confidence. The bear market has shaken the confidence not only of investors, but also of their financial advisors, and rightly so. What investors and advisors have always desired was some certainty in what they were doing. Of course, our industry is founded and regulated on the premise that there are no guarantees. We may have price targets for thoroughly analyzed stocks and track records that supposedly demonstrate investing skill, but in reality we all know that despite these efforts and information, things do not always go as planned.

So you see the apparent irony in Monte Carlo simulation. This methodology allows one to see the likelihood that things may actually end up far worse than anyone would normally plan, often with very scary results. But it ends up being a tool exploited to provide comfort and a sense of confidence.

If you have been living under a rock or hiding under your desk, you may still be unfamiliar with how Monte Carlo simulation works. For math and statistics geeks, the concept is brilliantly elegant and simple. For the rest of us, when we try to start to understand it a step at a time, it is a little like entering the Black Forest; each step takes us further into the darkness.

Simply put, the concept of Monte Carlo in investment planning is the ability to stress test a package of financial goals along with an investment strategy to measure the odds of achieving those goals. The odds exposed by Monte Carlo can provide confidence and, therefore, comfort. In contrast to what we have done in the past, these odds–this confidence and resulting comfort–have been, historically, completely avoided and ignored.

Traditionally, we made an assumption about investment returns. By merely disclosing to clients that all we did was make assumptions, we left him in the dark. We disclosed that past performance was no indication of future results, and that we had no idea of whether things would work out as planned. But, if the assumptions by luck happened to be similar to what we projected, things would be all right. Of course, we couldn’t tell clients the odds of things going the way we assumed.

With Monte Carlo, if used correctly, instead of taking that uncertainty and simply leaving the client in the dark about it, we can actually exploit that uncertainty to know how confident and comfortable the client can be about achieving his goals.

Our traditional uncertain projections are normally based on a fixed average return assumption, which conceptually gives us 50/50 odds. Most clients would not be comfortable basing their entire financial future on the flip of a coin, and clearly they wouldn’t pay for advice with those odds. Maybe this is why we have not historically exposed the odds. Fortunately, financial advisors are trained to be conservative and in a study we at Financeware Inc. did of over 13,000 clients of financial advisors, the average investor had nearly a 60% chance of things working out as planned.

This statistic is really not what is important, however. Monte Carlo is important because prior to it, the odds were completely unknown. Now we can harness the technology to calculate these odds and produce the comfort that goes with that knowledge.

A nuance that is often the focus of Monte Carlo corrects for another mistake in our prior projections. While historically we identified investor risk tolerance and thoroughly analyzed asset allocation for risk and return efficiency, the projections we have made assumed that regardless of how much risk the investor was taking, it would disappear when it came to projecting the financial future.

Think about this for just a moment and you will start to see the forest. What is the standard deviation, the maximum drawdown, or investment risk modeled in a planning projection that assumes the same return each year? It is zero. While historically we identified risk tolerance and analyzed asset allocation efficiency, and while we know portfolios with less volatility are more efficient, instead of planning on this volatility we assumed that it disappears when it comes to projecting the client’s financial future. Just as a portfolio with equity-like returns and no volatility would look fabulous on our risk/return efficient frontier, so do the results of a wealth management plan that makes the same assumption. Table 1 demonstrates this effect.

Results for an investor with $100,000, spending approximately $11,600 a year for 10 years with three different portfolios, all with the same compound return: In Table 1 we see that our projection using the same return each year could have overstated the results by nearly forty-fold (if we started with a bear market) or understated the results by 60% (if we started with a bull market). You may notice that the returns for the bull and bear markets are the same. They just happened in the opposite order. Many advisors mistakenly assume the extra money produced in the “bull market first” example, or the shortfall in the “bear market first” is due to the compounding effect of the results in early years. This really is not completely the case, as it is dependent on the client’s unique plan and the opposite relationship can easily be see in a different client scenario as shown in Table 2.

Early bull market returns compound the impact of later bear markets; three scenarios for a client investing $10,000/year for 10 years. In Table 2, we see that those fabulous early returns were indeed compounded, but not as we normally think of as producing benefits for us. Instead, those early bull market returns compounded the impact of the later bear market. This left the investor with 25% less money than if we assumed the same return each year and nearly half as much as if the investor got the bear market out of the way early and enjoyed the bull market later on.

Clearly the assumption of the same return each year, even when compared to other series of returns with identical compound returns, is erroneous.

The sole impact modeled in Tables 1 and 2 is timing risk. The impact of this should be familiar to us since AIMR standards long ago required track records of money managers to be based on time-weighted returns, which by definition remove the actions or goals of a particular client. AIMR requires this because dollar-weighted returns are determined more by the action of the investor, rather than the skill of the manager.

Dollar-weighted returns are what is important to the client. But if we evaluated managers on a dollar-weighted return basis, we would be measuring the decisions of the client, and not of the manager. Did clients put more money in just before a bear market (which would artificially understate manager results for a different client) or add money right before a bull market (which would artificially overstate the manager results)? While we recognized this impact to manager records long ago, we have completely ignored the impact in our traditional planning projections.

We have taken one step into the Black Forest and learned that when you get return can be far more important than how much you average in return. Of course, no one knows what the market will do in any one year. This is uncertain and Monte Carlo enables us to measure the uncertainty of how different patterns of returns may occur. If the market only produced 10 different returns that we knew would occur and the only uncertainty was when each return would occur, there are 100 potential results. Of course, these examples all assumed we knew what the compound return would be over time and considered only the uncertainty associated with the timing of returns. But, just as we do not know when different returns will occur, we also do not know what the returns will be over long periods of time. Table 3 (below, left), which shows the rolling 30-year average and compound return for large-cap stocks based on monthly data going back to 1926, shows that even over long periods of time, a few months or a year can dramatically impact return. This exposes another uncertainty Monte Carlo can help us model. Not only is the timing of returns uncertain, but so is the long-term return.

A Confidence Measure

If we have the right inputs, Monte Carlo enables us to measure the odds, or confidence, and resulting comfort of both the potential timing and level of investment returns as it would impact a particular client’s wealth management plan. Correcting our past mistakes, exploiting risk rather than ignoring it, and measuring the odds, along with the resulting confidence and comfort, is why Monte Carlo has spread like an airborne virus. Unfortunately, like viruses, certain people are at greater risk if exposed.This has been the case with Monte Carlo, as more often than not we see it being misused.

The biggest mistakes we see in applying Monte Carlo are not the arguments debated in journals. These theoretically interesting but practically meaningless debates–like whether 1,000 or 100,000 simulations are sufficient or the merits of normal versus log-normal distribution–obscure far more important points.

Far more practical mistakes are being made. Monte Carlo still requires thoughtful analysis of the inputs because the math engine powering the analysis stupidly calculates whatever it is told. We often see simulations, advertised as “stress testing,” based on the historical nature of the market, with results that simulate half of the trials producing better results than the market ever has. Likewise, we see simulations based on “conservative” inputs designed for planning tools that ignore risk, crammed into the Monte Carlo model that exploits risk, resulting in projections that model a quarter of all future markets being worse than the Great Depression.

For some this is not a problem because they view their job as getting the client to the highest probability of meeting his goals, which based on our past ignorance of the odds sounds enticing. In the world of Monte Carlo, though, the price of eliminating any uncertainty is doing nothing other than making it absolutely certain that the client will be sacrificing the only life he has. Higher probability is good up to a point. There is no useful information in learning the odds if all we are doing is positioning the client’s saving, spending, and investing decisions to give him a 95%-99% chance of dying with a larger estate than he desired. This is particularly true if the client values taking a vacation or traveling in retirement more than leaving the largest possible estate.

Each of these abuses alone is worthy of further discussion, as many of them shake the very foundation of basic premises our profession considers best practices. Monte Carlo simulation can correct many mistakes we have made in the past. It can provide certainty and comfort. It can help us help our clients reach their financial goals. But it cannot achieve these benefits without a skilled operator.

So, before you swing the Monte Carlo hammer, make sure you know a nail is your target, what you are driving the nail into, and why you are striking it in the first place. Otherwise, you may end up as one of the victims of the Monte Carlo virus.


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