Wealth Manager

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-yearold
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 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-byclient
basis. Otherwise, it’s a piece of cake.