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What Physician Investors Need to Know about Monte Carlo Simulation

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Probability Forecasting and Investing

By Dr. David Edward Marcinko MBA CMP™

[Editor-in-Chief] www.CertifiedMedicalPlanner.org

dr-david-marcinko1Recently, I had a physician-client ask me about Monte Carlo simulation. You know the routine: what it is and how it works, etc.

From Monaco

Named after Monte Carlo, Monaco, which is famous for its games of chance, MCS is a technique that randomly changes a variable over numerous iterations in order to simulate an outcome and develop a probability forecast of successfully achieving an outcome.

In endowment management, MCS is used to demonstrate the probability of “success” as defined by achieving the endowment’s asset growth and payout goals.  In other words, MCS can provide the endowment manager with a comfort level that a given payout policy and asset allocation success will not deplete the real value of the endowment.

Quantitative Tools Problematic

The problem with many quantitative tools is the divorce of judgment from their use. Although useful, MCS has limitations that should not supplant the endowment manager’s, FA or physician-investor’s, experience.

MCS generates an efficient frontier by relying upon several inputs: expected return, expected volatility, and correlation coefficients. These variables are commonly input using historical measures as proxies for estimated future performance. This poses a variety of problems.

  • First, the MCS will generally assume that returns are normally distributed and that this distribution is stationary.  As such, asset classes with high historical returns are assumed to have high future returns.
  • Second, MCS is not generally time sensitive. In other words, the MCS optimizer may ignore current environmental conditions that would cause a secular shift in a given asset class returns.
  • Third, MCS may use a mean variance optimizer [MVO] that may be subject to selection bias for certain asset classes. For example, private equity firms that fail will no longer report results and will be eliminated from the index used to provide the optimizer’s historical data.

Healthcare Investment Risks

A Tabular Data Example

This table compares the returns, standard deviations for large and small cap stocks for the 20-year periods ended in 1979 and 2010.

Twenty Year Risk & Return Small Cap vs. Large Cap (Ibbotson Data)

[IA Micro-Cap Value 14.66 17.44 24.69 0.44]









Small   Cap Stocks 30.8% 17.4% 78.0% 18.1% 26.85% 59.0%
Large   Cap Stocks 16.5% 8.1% 13.1% 15.06%

[Reproduced from “Asset Allocation Math, Methods and Mistakes.” Wealthcare Capital Management White Paper, David B. Loeper, CIMA, CIMC (June 2, 2001)]

The Problems

Professor David Nawrocki identified a number of problems with typical MCS in that their mean variance optimizers assume “normal distributions and correlation coefficients of zero, neither of which are typical in the world of financial markets.”

Dr. Nawrocki subsequently described a number of other issues with MCS including nonstationary distributions and nonlinear correlations.

Finally, Dr. Nawrocki quoted financial advisor, Harold Evensky MS CFP™ who eloquently notes that “[t]he problem is the confusion of risk with uncertainty.” Risk assumes knowledge of the distribution of future outcomes (i.e., the input to the Monte Carlo simulation). Uncertainty or ambiguity describes a world (our world) in which the shape and location of the distribution is open to question.


Contrary to academic orthodoxy, the distribution of U.S. stock market returns is “far from normal.”[1] Other critics have noted that many MCS simulators do not run enough iterations to provide a meaningful probability analysis.


Your thoughts and comments on this ME-P are appreciated. Feel free to review our top-left column, and top-right sidebar materials, links, URLs and related websites, too. Then, subscribe to the ME-P. It is fast, free and secure.

Speaker: If you need a moderator or speaker for an upcoming event, Dr. David E. Marcinko; MBA – Publisher-in-Chief of the Medical Executive-Post – is available for seminar or speaking engagements. Contact: MarcinkoAdvisors@msn.com


[1]   Nawrocki, D., Ph.D. “The Problems with Monte Carlo Simulation.” FPA Journal (November 2001).

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One Response

  1. Dark Pools threaten all investors

    So called, Dark Pools, began in the 1980s when the Securities and Exchange Commission decided that stock brokers could bring together buyers and sellers to trade anonymously.

    Rather than routing customer orders to the traditional exchanges, brokers could send them to an outside trading service or execute orders on their own internal systems, pocketing the spreads on prices and trading fees.


    Today, as much as 40 percent of trading in U.S. equities takes place away from the public stock exchanges. This fosters inefficiency and high fee spreads for Wall Street.

    Way to go, SEC.



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