From the February 2007 issue of Wealth Manager Web • Subscribe!

A Sure Bet?

Monte Carlo analysis isn't a commodity service in finance, but it's getting there.

A decade ago, virtually no one used Monte Carlo for evaluating client portfolios. Technology, of course, was one obstacle. Simulating an array of possible portfolio results demanded more computing power than the average PC could deliver in the mid-1990s. No matter, since few wealth managers at the time understood the finer points of Monte Carlo and how it could enhance portfolio risk analysis.

Today, stochastic modeling software is abundant, easy to use, affordable and, in the minds of many financial consultants, essential for assessing the odds that a given investment strategy will deliver as promised. There's also a variety of educational resources available, starting with the Web. Typing "Monte Carlo analysis" on Google, for example, yields a small library of reference material. No wonder that Monte Carlo claims a relatively large and growing fan base in the financial industry.

Even on the regulatory front, the statistical technique is winning over new friends. In early 2005, for instance, the NASD lifted a ban on member firms' using Monte Carlo simulation tools. And why not? Monte Carlo, if used properly, is less about forecasting than calculating the various futures that statistically lie in wait.

The harnessing of random numbers (rolls of the dice, if you will) inspired the label "Monte Carlo"--a reference to the international gambling mecca. But it's an unfortunate moniker, since financial applications drawn from Monte Carlo analysis are aimed at managing risk and minimizing the unexpected--the antithesis of gambling.

"Probably the majority of sophisticated financial planners are using some sort of Monte Carlo simulation in their planning software," says Glenn Kautt, CFP and president of The Monitor Group, a wealth advisory firm in McLean, Va. Kautt speaks from experience, as he runs educational seminars on the modeling technique. He and his partner, the late Lynn Hopewell, were early proponents of Monte Carlo in the second half of the 1990s, and they wrote a series of influential articles on its value in financial planning.

In the years since, Monte Carlo software and its financial applications have come a long way. But no matter how refined or popular the software, debate will always shadow the statistical tool on at least two fronts: designing a model and interpreting the results.

Indeed, not all Monte Carlo software is the same. "The problem with a lot of this off-the-shelf software--particularly some of this stuff on the Internet--is that you can't see what the assumptions are," warns Steve Doucette, a CFP at Proctor Financial in Wellesley, Mass. "It's nothing more than a model, and any model is driven by the inputs. You need to have a good understanding of what the drivers are."

Although something approaching consensus exists in financial planning about Monte Carlo's value for stress-testing portfolio assumptions, there's an ongoing discussion about what constitutes superior data inputs. Meanwhile, there are any number of opinions on deciphering the numbers a model spits out. In other words, there's more than one way to run Monte Carlo analysis and summarize the results.

Subjectivity inhabits the world of Monte Carlo analysis, advises Brian O'Toole, a CFP and CEO at AssetMark Investment Services, a fee-based investment advisory service that recently launched a Monte Carlo package for planners who use its platform. "We're trying to give advisors confidence that they've chosen the right strategy," he says of the California-based firm's Monte Carlo tool. But gaining confidence requires more than simply firing up the software.

As an example, O'Toole compares two hypothetical 50-year-old male clients with similar levels of net worth and comparable financial planning needs and lifestyle expectations. On paper, in other words, the two are virtually identical. Assume that after running a Monte Carlo analysis for each of their (also identical) investment portfolios, the software estimates a 70 percent confidence level that the current strategy will fund a 20-year retirement beginning 15 years hence. Does 70 percent suffice? Or should the asset allocation change in order to raise the confidence level? It depends, says O'Toole.

The 70 percent may be appropriate for an investor who's married and lives in a town where his adult children and extended-family members reside, O'Toole reasons. On the other hand, a higher confidence may be prudent for a client who's unmarried, lives alone and has no immediate family.

Monte Carlo tests a range of potential outcomes, but the software doesn't know anything about clients as people. And that is no trivial limitation for managing wealth.

Habits on money matters, for example, are crucial factors driving success or failure in an investing strategy, says Kautt. "Client spending behavior is the biggest determinant of the outcome for any Monte Carlo model," he says. "It overwhelms everything else." (As a quick digression, it's worth noting that Milton Friedman, the Nobel Prize-winning economist who died last November, observed in his permanent-income hypothesis that consumption behavior tends to be influenced by income expectations for the long term.)

In a perfect world, advisors could customize statistical analysis for personal behavioral traits, such as spending habits and how those habits change under different economic and financial scenarios. Alas, adding behavioral feedback loops to Monte Carlo software is easier said than done. The underlying research that would inform the design of such a model adjustment remains spare, for starters. Regardless, adding that kind of nuance to models would probably overwhelm the computational abilities of most desktop computers at the moment, says Kautt.

Then again, there are still plenty of gray areas to resolve for designing even a basic stochastic model. One of the more commonly debated issues: The returns distribution curve used in Monte Carlo analysis. The easy choice is a normal distribution curve, otherwise known as a standard bell curve of outcomes. But as any student of market history knows, returns in the capital markets are not normally distributed. Extraordinary, unexpected events intrude from time to time, skewing the curve away from anything resembling a conventional bell curve. In particular, a so-called fat tails distribution (i.e., a reflection of low frequency but high volatility returns) offers a closer approximation of reality.

"Extreme events are slightly more likely in the real world than they are in a normal distribution," says Ned Notzon, chairman of the asset allocation committee at T. Rowe Price, which uses Monte Carlo for its in-house advisory service.

Sophisticated users of Monte Carlo know that there are alternatives to normal distribution curves. In fact, there are many alternatives--perhaps too many. Knowing that a fat-tails distribution is a better representation of what occurs in the markets is one thing. Unfortunately, it's not obvious what kind of fat-tails distribution works best.

No matter, as some advisors say that in the long run, equity returns, for instance, are close enough to normal distribution to assume the same going forward. Yes, another crash could be lurking just around the corner, but it's unclear that quantitatively integrating that possibility into a model enhances the design of a portfolio that must endure for the next 20 years. "Because you don't know when an adverse event is going to occur, how can you use anything other than a normal distribution?" questions Martin Resnick, principal at Resnick Investment Advisors in Westport, Conn.

Nonetheless, there are a number of substitutes for a normal distribution. The newly launched Retirement Income Strategist, a Web-based tool from Morningstar, uses a log normal distribution for its Monte Carlo applications. Designed by Ibbotson Associates, a Morningstar division, the software's log normal distribution puts a constraint on the potential for losses when crunching the numbers. With a normal distribution, it's possible to lose more money than originally invested in some scenarios; log normal eliminates that potential. The reasoning is that leverage isn't often used in long-term investing for individuals, and so a log normal adjustment is said to offer a more realistic range of potential outcomes.

Another issue for designing a Monte Carlo model centers on the choice of historical data--namely, how much to use. Clearly, the last 20 years of history will give different results compared to the previous 20, and both will diverge from the past 100 years. Generally, longer is better, but with caveats. For instance, the further back in time one reaches for data, the less relevance the historical has for the future, thanks to ongoing evolution in capital markets and the global economy.

Whatever the choice of data history, there is more than one way to crunch the numbers. One could use a so-called Latin hypercube approach, a technique that separates data into subgroups for enhancing simulation estimates by discounting statistically irrelevant samples. Then there's the bootstrapping method of analysis. This approach crunches the performance history in an array of random sequences instead of limiting calculations to the actual chronological order of returns. This methodology effectively considers a fuller range of outcomes than delivered by the single sample that is history. "That's a way of getting more information out of the historical data," says Richard Michaud, a mathematics Ph.D. and president of New Frontier Advisors, a Boston investment consultancy that designed AssetMark's Monte Carlo service.

Frank Sortino, professor emeritus at San Francisco State and chief investment officer of Sortino Investment Advisors, says that bootstrapping offers "a more robust way of doing Monte Carlo [because it produces] more reliable estimates of what uncertainty looks like."

For Financial Engines, a pioneer in bringing Monte Carlo-based financial analysis to the masses, nothing less than a customized model informed by economic theory will do. The proprietary system used by the firm evolved from the pension consulting work of Nobel Prize-winning economist Bill Sharpe, who founded the Palo Alto, Calif. company in 1996.

The distribution curve used in Financial Engine's Monte Carlo system is neither normal nor log normal. Rather, it's a "non-analytical" distribution, says Christopher Jones, chief investment officer of the investment advisory firm. "It's a simulated distribution that reflects the mixing and interactions of different economic variables."

But no matter how a Monte Carlo simulation is run, the basic, timeless challenge remains: the future is unknowable. A stochastic model can estimate the range of possible outcomes, Kautt says, but it can't tell you when events will happen.

In other words, the classic distinction between risk and uncertainty, as outlined in 1921 by economist Frank Knight, is still intact in the tech-laden 21st century. Randomness can be measured precisely for estimating "risk," but rolls of the dice associated with "uncertainty" yield to no model, formula or equation. Stuff happens, as they say, and always will.

The next best thing is having a reliable estimate of the range of potential outcomes that can be measured. On that score, Monte Carlo works wonders. Assuming, of course, the model is designed prudently, the data inputs are sound, the analysis is informed and the advisor wisely applies the quantitative results on a client-by-client basis. Otherwise, it's a piece of cake.

James Picerno ( is senior writer at Wealth Manager.

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