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Financial Services Monte Carlo Simulation’s Flaws and Fixes

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Physicians Must Understand Deus ex Machina

[By Wayne J. Firebaugh Jr; CPA, CFP®, CMP™]


wayne-firebaughNamed after Monte Carlo, Monaco, which is famous for its games of chance, MCS is a software 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.

Endowment Fund Perspective

In private portfolio and fund 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.

Divorce from Judgment

The problem with many quantitative software and other tools is the divorce of judgment from their use. Although useful, both mean variance optimization MVO and MCS have limitations that make it so they should not supplant the physician investor or endowment manager’s experience. MVO 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.

Problems with MCS 

First, the MVO 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, an MVO optimizer is not generally time sensitive. In other words, the optimizer may ignore current environmental conditions that would cause a secular shift in a given asset class returns.

Finally, an MVO optimizer 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 [1].


As an example, David Loeper, CEO of Wealthcare Capital Management, made the following observation regarding optimization:

Take a small cap “bet” for our theoretical [endowment] with an S&P 500 investment policy. It is hard to imagine that someone in 1979, looking at a 9% small cap stock return premium and corresponding 14% higher standard deviation for the last twenty years, would forecast the relationship over the next twenty years to shift to small caps under-performing large caps by nearly 2% and their standard deviation being less than 2% higher than the 20-year standard deviation of large caps in 1979 [2].

Table: Compares the returns, standard deviations for large and small cap stocks for the 20-year periods ended in 1979 and 1999.  Twenty Year Risk & Return Small Cap vs. Large Cap (Ibbotson Data).

1979 1999
Risk Return Correlation Risk Return Correlation
Small Cap Stocks 30.8% 17.4% 78.0% 18.1% 16.9% 59.0%
Large Cap Stocks 16.5% 8.1% 13.1% 18.6%

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

More Problems with MCS

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

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

Finally, Dr. Nawrocki quotes Harold Evensky 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” [3]. Other critics have noted that many MCS simulators do not run enough iterations to provide a meaningful probability analysis.


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Some of these criticisms have been addressed by using MCS simulators with more robust correlation assumptions and with a greater number of iterative trials. In addition, some simulators now combine MVO and MCS to determine probabilities along the efficient frontier.


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1. Clark, S.E. and Yates, T.T., Jr. “How Efficient is your Frontier?” Commonfund Institute White Paper (November 2003).

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

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

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4 Responses

  1. More on the Role of Judgment

    Wayne – despite their limitations, Monte Carlo simulators and other financial portfolio optimizers are useful tools for developing asset allocations for endowments. They represent another tool in ensuring rational and consistent investor behavior.

    Most personal endowments will also use bottom-up analysis to examine the opportunities within a given asset class and to make adjustments to the allocations across asset classes.



  2. Monte Carlo

    A Monte Carlo simulation is a useful tool to give individual investors perspective regarding how their portfolio might perform during retirement.

    The retiree is more likely to be successful in a situation where some of the negative returns occur early in retirement if he or she is able to “tighten the belt” and reduce spending in such instances. Retiring with a lower level of debt can give a person more flexibility to make such adjustments in spending and survive the inevitable bear markets.

    Brian J. Knabe MD, CMP™


  3. Mis-Leading Monte Carlo

    Monte Carlo simulations are misleading as the “% of success” is based on such a small sampling, and unfortunately, physicians and clients then rely on that confidence when it’s just a sham.

    The Financial Advisor


  4. More on Monte Carlo

    The MCS methodology has been used for financial services and among other fields, such as medical physics to predict the radiation shielding and the travel distance that neutrons pass through various materials. However, MCS is especially useful for simulating phenomena with high uncertainty in inputs and systems.

    MCS is best used to model simulations and aggregate estimates for best-case, and worse-case scenarios, and the duration over the project.

    But, the results from MCS simulation typically lack accuracy without any meaningful MVO to achieve them.

    Ken Yeung MBA CMP™ candidate


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