Physicians Must Understand Deus ex Machina

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

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Named 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].

Example:

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).

*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”. Other critics have noted that many MCS simulators do not run enough iterations to provide a meaningful probability analysis.

Assessment 

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.

Conclusion

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References:

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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Filed under: Financial Planning, Investing, Portfolio Management | Tagged: CMP, David Loeper, david marcinko, David Nawrocki, Harold Evensky, Ibbotson, mean variance optimization, Monte Carlo simulation, S&P 500, Wayne Firebaugh, Wealthcare Capital Management | 4 Comments »