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Sampling James R. Thompson's inspired nonparametric portfolio approaches

Focus Article

John A. Dobelman

Published Online: Dec 22 2020

DOI: 10.1002/wics.1542

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Abstract Asset or security returns are an example of phenomena whose distributions still cannot be convincingly modeled in a parametric framework. James R. (Jim) Thompson (1938–2017) used a variety of nonparametric approaches to develop workable investing solutions in such an environment. We review his ground breaking exploration of the veracity of the capital asset pricing model (CAPM), and several nonparametric approaches to portfolio formulation including the Simugram™, variants of his Max‐Median rule, and Tukey weightings. This article is categorized under: Applications of Computational Statistics > Computational Finance Statistical and Graphical Methods of Data Analysis > Transformations Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms

Returns obtained by varying lookback period in trading days ν and power means p (reparameterized as θ)

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Annual returns and compound growth of $1 for the period 1970–2012

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Simugram outperformance over the S&P 500 for the period 1970–2002. Solid dots are S&P 500 return for the year, and light dots are various Simugram results for that year

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Stochastically dominating Simugrams: F₂≤_stF₁. T_c is the lower 20th percentile of returns r

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Simugram percentile optimization, taken from U.S. Patent No. 7,720,738

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The fraction of random portfolios that outperform the market portfolio by year. It is clear from random selection that there are many opportunities for a competent portfolio manager to do better than the market portfolio

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Annual returns and annualized volatility of each of the random portfolios (of size 30) generated for the year 1971. Open circles are the random portfolios; the black dot is the Market portfolio (combined NYSE/AMEX/NASDAQ) which is situated on the Capital Market Line (CML)

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The Capital Market Line (CML)

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Comparison of geometric Brownian motion (GBM) and actual security returns, 1960–2017

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Realized security returns, 1985–2008 versus normal variates

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Market returns, 1926–2017 and representative index levels (linear and log₁₀) based on the market returns. Ending level is 25,044

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Antonio Gramsci (1891–1937) and Oleg Deripaska (1968–)

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James R. Thompson

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Cumulative log₁₀ returns for 1958 to 2015 for the eight Tukey transformational ladder portfolios. This calculation includes dividends and frictions and assumes that $100,000 is invested on January 2, 1958 and left to grow until December 31, 2015. The major avowed recessions are depicted in the shaded zones

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References

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Further Reading

Ali,, H., Broadkey, D., Rieden, R., & Shenoy, S. (2018). Extensions on CAPM validation and exploration of portfolio growth, STAT 486 final project, Rice University, Spring.
Glover,, K., Hulley,, H., & Peskir,, G. (2013). Three‐dimensional Brownian motion and the golden ratio rule. Annals of Applied Probability, 23(3), 895–922.
Greg,, W. W. (Ed.). (1904). Everyman from the edition by John Skot. Louvain, Belgium: Uystpruyst.
Roberts,, H. (1959). Stock price `patterns` and financial analysis: Methodological suggestions. Journal of Finance, 14(10), 1–10.
Thompson,, J. R. (2003b). Methods and apparatus for determining a return distribution for an investment portfolio. U.S. Patent 7,720,738, Filed 1/3/2003b, and issued 7/8/2004.
Thompson,, J. R. (2011). Empirical model building: Data, models, and reality (2nd ed., p. 356). Hoboken, NJ: Wiley.
Thompson,, J. R. (2014b). Simulation‐based estimation: A case study in oncology (SIMEST) and a case study in portfolio selection (SIMUGRAM). WIREs Computational Statistics, 6, 379–385.
Thompson,, J. R. (2017b). Putting speed bumps on the road to serfdom. Presentation to Rice University, Houston, TX, February 2017b. Retrieved from https://scholarship.rice.edu/handle/1911/109317
Traflet,, J., & Coyne,, M. P. (2007). Ending a NYSE tradition: The 1975 unraveling of broker`s fixed commissions and its long term impact on financial advertising. Essays in Economic and Business History, 25, 131–141.
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Treynor,, J. (1999). Towards a theory of market value of risky assets,” originally an unpublished manuscript (1961) but published recently in. In R. A. Korajczyk, (Ed.), Asset pricing and portfolio performance (pp. 15–22). London, England: Risk Publication.
Tukey,, J. W. (1970). Exploratory data analysis, limited preliminary edition. Reading, MA: Addison‐Wesley.

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