Using ‘Monte Carlo’ Simulations to Enhance Planning Recommendations
Rolling the Dice

By Michael Kraten

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 passes away).

The 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.

The Fallacy of Deterministic Thinking

Assume an 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.

Thus, according to Exhibit 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 trends.

Assume a 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 investor?

According 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.”

In other 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.

Using Monte Carlo Simulation Software

Most investment 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 says:

We use 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.

Although 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.”

Generating Possible Scenarios

What could 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.

Christie 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.

Exhibit 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.

Making 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.

The bottom 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.

Michael Kraten, PhD, CPA, is founder and president of Enterprise Management Corporation, Milford, Conn., and an assistant professor at Suffolk University, Boston, Mass.

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