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Sampling James R. Thompson's inspired nonparametric portfolio approaches

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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: F2stF1. Tc 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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Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms
Statistical and Graphical Methods of Data Analysis > Transformations
Applications of Computational Statistics > Computational Finance

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