Probability Forecasting and Investing
By Dr. David Edward Marcinko MBA CMP™
[Editor-in-Chief] www.CertifiedMedicalPlanner.org
Recently, 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.
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]
|
|
1979
|
|
|
2010
|
|
|
Risk
|
Return
|
Correlation
|
Risk
|
Return
|
Correlation
|
| 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.
Assessment
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.
Conclusion
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[1] Nawrocki, D., Ph.D. “The Problems with Monte Carlo Simulation.” FPA Journal (November 2001).
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Filed under: CMP Program, Investing, Portfolio Management | Tagged: certified medical planner, correlation coefficients, david marcinko, David Nawrocki, Endowment Management, Harold Evensky, Monte Carlo simulation, variance optimizer | 2 Comments »
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