It is impossible to identify the end value of an investment portfolio that has variable returns. That said, it would appear that financial planning would be a gamble at best. Fortunately, there are statistical tools which we can use to help us to estimate how well a specific portfolio will perform.

One feature of statistics that can give us some measure of certainty is the ability to measure variability. For example, looking at the individual quarterly returns of the S&P 500 from 10/1/01 to 9/30/05 (4 full years)*, we can interpolate that the annual return in any year will range between 23.89% and -10.75% in 95% of the years.**

We use stochastic (meaning conjecture or guess) analysis to make reasonable guesses as to what end values are possible for a set of facts (starting amount, additions, withdrawals, time period, average return, standard deviation, desired ending balance). The form we use most often is referred to as the Monte Carlo method.

The Monte Carlo method is credited to Stanislaw Ulam, a Polish-born mathematician who worked on the Manhattan Project and was the co-designer of the hydrogen bomb. It started with a game of solitaire when he wondered what the chances were that you can be successful at Canfield solitaire. He figured that, instead of spending much time calculating combinations, it would be more practical to play the game a thousand times and count the number of successful games. Ulam then saw that this calculation method would need very fast computers but could be used for such things as determining what it would take to trigger fusion.

Between the Manhattan Project and the H-bomb, Ulam came up with a way to convert the differential equations to create the equivalent of a succession of random operations that could be calculated by computer. Reportedly a collaborator named this statistical sampling methodology after the casinos in Monte Carlo because his uncle spent a lot of time there.

We use the Monte Carlo method to determine the likelihood of success of an endeavor, such as, retirement. We determine the average return and standard deviation of the recommended investment portfolio. This tells us the likely range of returns for each year. A return is randomly chosen from that range and applied to the balance, deposits and withdrawals. The process is repeated with the new balance and new random rate of return until we have approximated each year between now and the selected end point. We repeat this process for 999 more times in essence, approximating 1,000 lifetimes. We compare the end values to the desired end value to determine how many times the process was successful. Generally, 75% or more successes tells us that the cash flow and investment portfolio together has a good chance of meeting or exceeding the client's goal.

We know that investment portfolios' average returns and standard deviations change over time. Additionally, clients' goals change as circumstances change. That's why we recommend that we and the client meet annually and re-run the Monte Carlo method to assure that the client's portfolio is still in line with his/her goals.

In essence then, we avoid the problem of the 5-foot man and the 7-foot hole in the 2-foot deep river. Rather than accepting the average over the whole river, we examine 1,000 ways to cross the river step-by-step. Then, we get our feet wet only after examining multiple ways to make it all the way across.

*Please note that the S&P 500 is an index, and you cannot invest directly in it. The following statistics are based on quarterly returns reported by Rydex Investments.

**We have ignored taxes, the fact that Standard & Poors changes the stock in the S&P 500 periodically, and that equities are affected by the world economy. Past performance is no guarantee of future results.