Overview: Below is a commentary regarding Eleanor Laise’s article on Monte Carlo simulation that appeared in the May 2, 2009 edition of The Wall Street Journal. The article was titled, “Odds-On Imperfection: Monte Carlo Simulation.” 
 

The article in The Wall Street Journal points out several flaws of Monte Carlo simulation (MCS). While we agree with many of the critiques made, the article does not mention how investors and advisors should determine prudent spending rates and the appropriate asset allocation if they do not use MCS. At BAM, we continue to believe that MCS is a valuable tool available to the investment community.

 

We agree that MCS is not perfect, so it is key to communicate to clients that Monte Carlo results are not a certainty. The simulations are a way to gauge a plan’s chances of success.

 

Further, we agree with critics when they argue “the problem isn’t Monte Carlo itself, but the assumptions that go into it.”¹ We feel that our returns assumptions are on the conservative side. We are also confident in our methodology as it has been reviewed by DFA’s Ken French, who believes that our methodology uses the best available assumptions in current academic research. That said, the best in current academic research is still just an estimate.

 

The major premise of the article is that events like the fourth quarter of 2008 are not modeled to happen frequently enough in MCS. This is the primary source of disagreement between BAM and the author. In our specific case, we examined our Monte Carlo assumptions to see how frequently our assumptions had large negative numbers. We looked at a 100 percent equity portfolio using 2008’s assumptions (10.3 percent expected return and 17.4 percent volatility), running 3,000 scenarios lasting 42 years. We found that 308 scenarios had at least one year worse than –30 percent and three scenarios had at least one year worse than –40 percent.

 

It is not the case that our assumptions did not account for a year like 2008; we simply did not have a year like 2008 occurring as often as the author of the article might like. The article says “While a bell-curve model shows a negligible risk of a greater than 50 percent decline in the S&P 500 over extended time periods, a fatter-tailed model assigns it a probability of 4 or 5 percent, odds high enough to grab the attention of risk-adverse investors (emphasis added).”²

 

At BAM, our goal with MCS is to model reality using the best research and tools available to us, not to grab the attention of investors. The tone of the article is “How do you explain the occurrence of this extreme negative event when your model assigned it a relatively small probability?” The logic of the argument doesn’t make sense: Just because something happened does not prove that the odds of it happening are higher than estimated.

 

Although we consider an 85 percent success rate as a good run in a particular simulation, it is important for advisors and clients to consider what actions will be taken should the bottom 15 percent of runs materialize (or bottom 10, 5 or 1 percent depending upon the success rate of the run). These actions could include cutting discretionary spending or selling a vacation home. This is especially important if a year like 2008 occurred early in a client’s withdrawal phase.

 

Another point made in the article is that some advisors run too few scenarios when running MCS. The article argues that running 1,000 or fewer scenarios is too few. We run 3,000 scenarios when running MCS.

 

In conclusion, we feel MCS is an excellent tool as long as advisors and clients are educated about what it is and what it is not. While it helps determine an investor’s need to take risk and also with asset allocation, it is not a crystal ball that will tell precisely how likely a plan is to succeed or fail. MCS is an approximation of reality, not a replication of reality.