Towards the end of our class, we have been paying attention to Monte Carlo techniques. Monte Carlo simulation, which randomly generates values for uncertain variables over and over to simulate a model, have the advantage of factoring uncertainty into the processes where it is applied. Stanislow Ulam might be amused to learn that his Monte Carlo method is now gaining increasing popularity in financial planning:

Many people are fed up with what they say are outdated, simple-minded methods for estimating how much investors should save for retirement and other long-term goals. Their main beef is that the myriad computerized planning programs available ignore the uncertainty inherent in most financial projections. What will you earn on your investments over the next 30 years? What will the inflation rate be? When will you live till? The answers to these questions, of course, are unknowable. Yet the standard programs churn out precise recommendations with remarkable confidence, giving investors a dangerously false sense of security about their financial future. So far Monte Carlo software is pretty much available only to financial planners, but that will also soon change. Similar analysis, under the name of Stochastic Modeling or Probability Analysis, are the most reliable methods in which to test one’s financial plan’s success probabilities.

Among these uncertainty thinkers, investment advisors warn personal financial planners to think probabilistically rather than deterministically when advising their clients. 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. Most investment opportunities in the real world do not follow tidy patterns such as the “+ 20%/ - 80%” returns. But such patterns, albeit in more complicated states, do exist, and certain financial advisors make extensive use of them. 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. 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.

A Monte Carlo analysis would highlight some of the problems that might arise in a down market. To make it easier to see, a pretty illustrative example was given In Business Week’s “Will You Have Enough?“:

“A 40-year old male earns $150,000 a year and contributes the maximum to a 401(k), which is invested in stock and bond funds worth $300,000. His annual expected return is 9.43%. He hopes to retire at 65 with an income of $120,000 in today’s dollars (including Social Security). The projections are adjusted for inflation.

HE’S GOLDEN USING TRADITIONAL FINANCIAL PLANNING…

WEALTH: $1,700,000

INCOME: $123,000

CHANCE OF MAKING INCOME GOAL 100%

…BUT FALLS SHORT WITH A MONTE CARLO SIMULATION

WEALTH: $1,440,000 (with a 5% chance of $563,000 and a 5% chance of $3,420,000)

INCOME: $107,000 (with a 5% chance of $53,000 and a 5% chance of $228,000)

CHANCE OF MAKING INCOME GOAL 40%

(DATA: FINANCIAL ENGINES, BUSINESS WEEK)”

Therefore, to build uncertainty into these forecasts in order to determine the likelihood of reaching your goal, enter the Monte Carlo method. Nobel laureate William Sharpe-through his company, Financial Engines - already sells Monte Carlo-type asset allocation advice to employers with 401(k) plans, which then offer it via the Web (www. financialengines.com). A direct-to-consumer version is there. Morningstar ClearFuture (www.morningstar.com) has a familiar name behind its retirement tools. Also, check out www.wagner.com - It previews a similar financial-planning software product from consultants Daniel H. Wagner Associates.

This is amazing: Years ago it was virtually impossible to use regressive analysis, because computers and programs were not yet developed that could handle these extensive calculations. Today, computer technology allows for the development of highly sophisticated tools that utilize actual historic market statistics, and use these statistics randomly over 1,000 hypothetical lifetimes.

Monte Carlo Simulation helps us understand that capital markets are subject to risk, even over long periods of time. As you mentioned in your question, it is extremely important for you to get a sense of confidence in your planning, because it not only affects your future, but impacts your life right now.

This confidence can be achieved by discovering your odds (chances) of exceeding your goals, falling short of your goals, or being on target for your goals. This is accomplished by generating 1,000 random trials that match your investment structure (current or proposed) along with your prioritized goals. Each planning scenario will have either an acceptable success probability, an unacceptable success probability, or a success probability that is so high that it would indicate you are either taking on too much risk in your portfolio, saving too much, or spending too little income in retirement, etc.

Conversely, an unacceptable probability of success would call for a different set of adjustments, which could include a compromise on savings, retiring later, living on less, or being more aggressive in your portfolio. Once on target, you should monitor that scenario on a quarterly or annual basis making sure that your goals have remained the same, or making adjustments if new goals have been added.

One final point, however, is that even using a Monte Carlo Simulation approach can be misleading, if the sole criteria for your calculations are based on your maximum risk tolerance level, which is not something you really want to experience. Also, the projections or other information generated by Monte Carlo tools regarding the likelihood of various investment outcomes are hypothetical in nature, do not reflect actual investment results, and are not guarantees of future results. Results may vary with each use and over time.

Sources:

A Better Way to Size Up Your Nest Egg. Businessweek Online: January 22, 2001.

http://www.businessweek.com/2001/01_04/b3716156.htm

Geer,Carolyn. Personal finance - factoring uncertainty into retirement planning: the monte carlo method. New York: Jan 11, 1999. Vol. 139, Iss. 1; pg. 200.

Financial Problem Solved! Medical Economics.

http://medicaleconomics.modernmedicine.com/memag/Medical+Economics/Financial-Problem-Solved/ArticleStandard/Article/detail/108753

Introduction to Monte Carlo Methods.

http://arxiv.org/PS_cache/hep-ph/pdf/0006/0006269v1.pdf

Kraten, Michael. Using ‘Monte Carlo’ Simulations to Enhance Planning Recommendations. The CPA Journal. New York: Sep 2007. Vol. 77, Iss. 9; pg. 56, 4 pgs.

Money management. (January 2008). Dermatology Times, 29(1), 126,128,130. Retrieved April 26, 2008, from Research Library database. (Document ID: 1426043641).

Yakal, Kathy. The electronic investor: Investing in (your) futures. Barron’s. Chicopee: Mar 24, 2003. Vol. 83, Iss. 12; pg. T7, 1 pg.