‘Monte Carlo’ Simulations to Enhance Planning Recommendations
Rolling the Dice
SEPTEMBER 2007 - Consider
the following hypothetical situation: A 40-year-old individual with
$500,000 in fully liquid money market funds asks a personal financial
planner for help. This individual is saving $28,000 annually in
401(k) withholdings, employer matching funds, and miscellaneous
savings accounts. He wants to retire at age 65 and live on annual
withdrawals of $80,000. In addition, he wants to be assured that
he’ll have at least $2 million in investments at age 101 to
live on (if he remains alive) or to leave to his children (if he
financial planner runs some numbers in a spreadsheet (see Exhibit
1) and tells him that, assuming a 3% inflation rate, he’ll
need to average a 4% return on his investments in order to achieve
this $2 million goal. The planner assures him that a 4% return
(after fees and taxes) can be achieved with a relatively conservative
mix of investment funds. After warning him that nothing is guaranteed,
the planner invests the individual’s assets in such vehicles.
Has the planner
given all the advice this individual needs to feel secure about
his future and be confident in the planner’s ability to
provide him with all necessary information? Some investment advisors
believe not, and warn personal financial planners to think probabilistically
rather than deterministically when advising their clients.
Fallacy of Deterministic Thinking
individual is eager to invest $1 million in an industry sector
fund that averages 10% in returns annually. In fact, the fund
averages roughly 20% returns in nine out of every 10 years. However,
the fund has been known to crash and lose 80% of its value once
each decade or so.
2, if this individual intends to cash out his investment in
18 years, it might be worth over $4.4 million if the first decade’s
anticipated crash occurs in the ninth year and the second crash
doesn’t occur before the 18th-year cash-out. But it might
be worth less than $800,000 if the second crash occurs in the
17th year, one year before the client cashes out.
How can the
planner possibly know if, or when, the second crash will occur?
Indeed, no one can foretell the future. But many investments run
in historically measurable “boom and bust” cycles,
and with the appropriate data, personal financial planners can
“back test” investment plans against these historical
financial planner looks back at every 18-year period over the
past half-century. Also assume that the planner learns that in
only 10% of those periods, the “once a decade” crashes
do indeed occur within 18 years of each other, and in 90% of those
periods they do not. What should the planner tell a prospective
to Gregory Coghlan, a financial advisor at Merrill Lynch in Stamford,
Conn.: “In this situation, personal financial planners should
not tell their clients that, given an average expected
return on investment of 10%, the average expected investment value
in the 18th year is over $5.5 million [see Exhibit 2]. Instead,
they should tell their clients that, according to historical trends,
there is a 90% probability that the investment will be worth over
$4.4 million at that time, and a 10% probability that it will
be worth less than $800,000.”
words, Coghlan believes that the $5.5 million amount is mathematically
accurate but terribly misleading because it represents a deterministic
“average” statistic that will likely never occur.
In all likelihood, the investment will either grow to more than
$4.4 million or shrink to less than $800,000, and the individual’s
risk appetite must determine whether the investment is appropriate.
Monte Carlo Simulation Software
opportunities in the real world do not follow tidy patterns such
as the “positive 20%/negative 80%” returns noted above.
But such patterns, albeit in more complicated states, do exist,
and certain financial advisors make extensive use of them. Coghlan
and his partner, Michael Christie, are two such advisors. Christie
Monte Carlo simulation software to ‘back test’ every
relevant period and compute ranges of possible valuations. We
would never actually come up with point estimates like $4.4
million and $800,000, but we would divide up the potential 18th-year
valuations into ranges like: a) $0 to $1.5 million, b) $1.5
million to $3.0 million, and c) $3.0 million and over. We would
assign each range a probability percentage, and we would compare
the lowest possible outcomes to our client’s minimum living
needs. Our goal is always to encourage each client to adopt
a level of risk that is sufficiently high to be consistent with
his risk appetite, and yet sufficiently low to avoid jeopardizing
his financial future.
some personal financial planners spend their time and resources
purchasing their own complex simulation software and learning
how to program data and generate probabilistic information, another
option is to collaborate with advisors such as Coghlan and Christie.
Coghlan says, “We make our money by serving as fiduciaries
and earning fees on our clients’ invested assets; in a sense,
we run our software and provide this probabilistic information
for free.” Adds Christie, “Fiduciaries cannot provide
the full set of advisory services offered by personal financial
planning practices, and planners cannot provide the full spectrum
of investment management services offered by our firm. We’d
rather work as a team … a coordinated approach to client
service is always the preferred one.”
a financial planner tell the individual described at the beginning
of this article? Christie and Coghlan could run numbers under
two scenarios, one representing the “present investment
plan” and the other representing the “proposed investment
plan.” As noted in Exhibit
3, they would incorporate other data as well, such as tax
rates, Social Security income, and inflation growth.
and Coghlan present their recommendations in a distinct style.
First they use Monte Carlo simulation software to generate a set
of all possible outcomes. Then they select and refer to the outcomes
at the 98th percentile, 50th percentile, and 2nd percentile as
the best-case, expected-case, and worst-case scenarios, respectively.
Finally, they compute the probabilities that an individual’s
assets will last (i.e., the investor will not go bankrupt) at
different age levels in the future.
4 contains these probabilistic statistics for this potential
investor. According to Christie and Coghlan, this prospective
client should be told the following:
- If you
remain in fully liquid money markets, there is a 69% chance
that you will still own retirement assets in 31 years (i.e.,
age 71). But the best-case scenario is that you will own only
$460,000 in assets at that time, and the expected-case scenario
is that you will own a meager $70,000. Furthermore, there is
virtually no chance that you will still own retirement assets
if you survive to age 86.
- If you
move to a relatively conservative mix of investment funds (defined
by Christie and Coghlan as 60% in large cap, small cap, and
international stock funds, and 40% in high-yield bonds, long-term
government treasuries, and municipal securities), the probabilities
look much better. There is virtually no chance that you will
be bankrupt at age 71, although there is a 35% chance that you
will be bankrupt at age 86 (when the best-case scenario is a
portfolio worth nearly $47 million and the expected scenario
is a portfolio worth more than $6 million). Furthermore, there
is a 67% chance that you will be bankrupt at age 101.
an Informed Decision
If the potential
investor is comfortable with the odds that result from either
of these strategies, then he should be advised to “roll
the dice” and implement his preferred approach (see Exhibit
4.) If he finds these odds to be too low or too high, however,
then an alternative strategy—one that incorporates a different
future annual savings pattern or a different mix of investment
assets—would be appropriate.
line is that a deterministic approach to financial planning is
simply not sufficient to ensure that clients have confidence in
a planner’s ability to help chart their financial future.
A probabilistic approach, featuring Monte Carlo simulations based
on back-tested historical data, can provide individuals with the
necessary information to feel secure about their financial prospects.
Kraten, PhD, CPA, is founder and president of Enterprise
Management Corporation, Milford, Conn., and an assistant professor
at Suffolk University, Boston, Mass.