Monte Carlo Simulation: are your client's boots in the water? (2003 Technology & Business Resource Guide).

Monte Carlo simulation is the latest statistical technique that financial planners are using to show clients the impact of an uncertain future on reaching their financial goals. Used correctly, the technique can give clients the probability of reaching their financial goals. For example, the simulation result may indicate that 95 percent of the time, the client's portfolio will be above a specific amount for retirement. However, the technique does have some shortcomings.

Before planners initiate running a Monte Carlo simulation, they should ask, "Are the client's boots in the water?"

IS SUCCESS OR FAILURE MORE IMPORTANT?

Perhaps an analogy will help. Suppose an electrician and a mathematician were reviewing a new product and analyzing the number of shocks that occurred when the product's electric cord was plugged into a socket. The wiring was properly installed, but the electrician would occasionally be shocked when he touched the cord.

The mathematician recorded the number of times the electrician touched the cord and determined that the probability of being shocked was less than 5 percent. Hence, the probability of success--not being shocked--was 95 percent!

How many times can you beat 95 percent?

Having never been shocked, the mathematician felt that the probability of shock was low enough to encourage use of the product.

The electrician, however, had been shocked a number of times and was interested in finding out more.

One rainy day, he realized he was getting shocked not 5 percent of the time, but every time he touched the cord. Looking down, he noticed his boots were standing in a thin film of water. He pulled over a stepladder, removed his boots and dried his feet. Cautiously touching the cord, he was not shocked.

The electrician noticed water accumulating on the floor from a leak in the roof. He stopped the leak, eliminated the shocks and supported the release of the new product with one caveat--don't stand in water when you plug it in.

The electrician discovered that the mathematician included too much of the universe of possible outcomes in his answer. When the count was confined only to the relevant data for failure, the electrician discovered that shocks occurred 100 percent of the time when standing in water.

Advisers and investors, like the electrician, should be less concerned about the probability of success and more concerned about the consequence of failure. While clients may be dazzled by a 95 percent probability of success, they should prefer to know under what type of situation a 5 percent failure occurs.

SIMILAR SIMULATIONS

Since Monte Carlo randomly generates thousands of simulated rates of return based on user input, the simulations produce similar probabilities of success whenever they are run with the same client variables.

A financial plan's 5 percent draw-down simulation run in March 2000--when equity markets were at record heights--would result in similar probabilities of success as a 5 percent draw-down simulation run in February 2003, when significant market values had already been lost.

Draw-down is used here as a client input variable to describe the annual percentage rate that a portfolio is consumed by an investor. The results are similar, rather than the same, because both simulations consider the same market variables or user input variables--just reordered in a new set of 1,000 random sequences.

Misunderstood, this could create a dangerous misconception for the unwary.

By simulating statistics related to all market environments at each starting point, Monte Carlo simulation lessens the weight given to the importance of the current market environment.

The thousand iterations include periods when markets are priced at five, seven, 10 or 14 price-to-earnings multiples, even though the current market may be priced at 30 times earnings. Hence, the simulation may not be related to decision-making for the current market situation.

SEQUENCE IS IMPORTANT

The sequence of rates of return for the client's investment portfolio has a lot to do with whether or not clients can achieve their financial goals.

For example, if the simple average rate of return for the following series of returns is 8 percent, the impact of the client's portfolio will be different.

Portfolio        A      B

Year 1           8%     8%
Year 2           6%     -6%
Year 3           10%    22%

Returns
Simple Average   8.%    8%
Compound Annual  7.99%  7.39%

Assume a beginning investment balance of $100,000 on Jan. 1 of Year 1:

Portfolio   A         B

Year 1      $108,000  $108,000
Year 2      $114,480  $101,520
Year 3      $125,928  $123,894

If the investor had withdrawn money for a large purchase or for retirement in Year 2, the impact of the sequence of returns would have reduced the portfolio by even more.

It is important for the planner to communicate to clients the impact of the sequence of rates of return on their portfolio and that the sequence of returns for equities is outside the planner's control.

Monte Carlo does a good job of showing the wide variance of possible results and the probability of success over thousands of different market environments. But it does not address the consequences based on the relevant market environment that exists over an investor's lifetime.

Let's return to the 5 percent failures given by the Monte Carlo simulation. Under what environments do they occur? If you measured all trailing 10-year market returns for each month since 1871 and compared those returns with the beginning-of-period price-earnings ratios, the results--not surprisingly--would suggest that linking simulations to current market conditions is imperative for reasonable conclusions to be drawn.

THE IMPACT OF INCREASING DRAW-DOWN RATES

By increasing the draw-down rate from 5 percent, much higher failure rates were experienced than in the original simulation. Constant client draw-down rates also have a tendency to produce more failures--that is, running out of money--when the sequence of returns are low or include negative returns.

Perhaps the best way to test the validity of a Monte Carlo simulation is to prepare a 30-year simulation using an initial draw-down rate increased each year by a rate to keep pace with inflation--5 percent initial draw-down on the portfolio with a 3.1 percent annual inflation increase.

That simulation can be compared with a 20-year simulation with an increased initial draw-down rate, assuming that the portfolio did not grow during the first 10 years.

A 5 percent initial draw-down on the portfolio, increased by 3.1 percent each year for 10 years, will become a 6.785 percent draw-down 10 years later--5 percent compounded at 3.1 percent for 10 years--if the portfolio remained at the same value at the end of the 10-year period as it was at the beginning.

On the other hand, if the portfolio value declined to 80 percent of the initial value at the end of the 10-year period, the new draw-down rate would be 8.49 percent (6.785 percent divided by 80 percent). If the portfolio stood at only 60 percent of the initial value after 10 years, the new draw-down rate would be 11.31 percent.

Applying the new draw-down rates to the remaining 20 years of our original 30-year simulation resulted in much higher financial plan failure rates than the original simulation would suggest. A seemingly modest original 15 percent failure probability for a portfolio that is 60 percent stock and 40 percent bonds becomes a 53 percent or 87 percent failure, if the first 10 year's performance results in ending values of only 80 percent or 60 percent of the initial portfolio value.

This is exactly the kind of result to be concerned about if your client's boots are already in the water.

SO, ARE THEIR BOOTS IN THE WATER?

If you begin draw-down in a market priced at 30 times earnings or after portfolio value has already been significantly reduced, their boots may be in the water.

What is the environment when you start to run the simulation?

Just as the 5 percent of electric shocks occurred 100 percent of the time when the electrician was standing in water, so too could the 5 percent investor shock occur with a much higher probability than Monte Carlo simulations suggest.

Monte Carlo simulations are driven by statistics. Advocates of Monte Carlo argue that no valid statistical inference could be drawn if the simulation used a sequence of returns that was limited to the few times the markets were unusually priced, such as more than 30 times earnings.

But to include highly unlikely sequences of returns in a simulation to achieve statistical validity is worse than a flip of the coin. At least with a coin flip, you can only be wrong 50 percent of the time.

The return sequence in the initial 10year period can make a large difference on account values and achievement of client financial goals.

WHAT DO YOU DO ABOUT THE WATER?

Those using Monte Carlo software may want to consider running additional simulations, assuming the portfolio equaled 80 percent or less of the original starting balance after the initial 10 years.

Using an 8.49 percent adjusted draw-down rate, (a 5 percent draw-down grows to 6.785 percent in 10 years if the account value remains the same and 8.49 percent if the account is only 80 percent of the initial value) compare the probability results of the new 20-year simulation to the original 30-year simulation.

You may find similar results.

And you may need to help your client develop contingency strategies in case of projected failure.

Using Monte Carlo simulations can be a good way to educate clients that portfolio values will vary, perhaps significantly, with changing rates of return and market environments.

In actuality, portfolios will not climb relentlessly year to year based on an average positive rate of return, which is commonly used in financial plans.

Advisers would be wise to add more questions to their due diligence checklist for Monte Carlo simulation software that includes: does the package contain normal or log-normal distributions; cross, serial and cross-serial correlation; standard deviations; and arithmetic or geometric average returns?

And, of course, one of the major questions will be, does the software consider if your client's boots are in the water?

Jerry Nightingale, MBA, CPA/PFS is president of Nightingale Financial Advisory in Palo Alto, is chair of CalCPA's Peninsula Silicon Valley Chapter's Personal Financial Planning Committee and a member of CalCPA's Board of Directors. You can reach him at [e-mail] or [phone].

James A. Shambo CPA/PFS is president of Lifetime Planning Concepts, P. C. in Colorado Springs, Colo, and former chair of the AICPA Personal Financial Planning Division. You can reach him at [e-mail]