Some Biases and Evolutionary Homomorphisms Implicit in the Calculation of Returns

Abstract

Investment returns are a core element of decisions in various “end-uses”. Investment returns are often calculated in different ways and over different horizons, and regardless of the method of computation, they often contain substantial Biases which distort results in the “end-uses”. These biases tend to have adverse multiplier effects because investment returns are the foundation or core elements in various statistical analysis such as: i) developing distributions of expected returns, ii) time series analysis; iii) developing options pricing models; iv) estimating various types of risk; v) developing pricing models for insurance; vi) for the evaluation of, and capital-budgeting for large billion-dollar projects. The two most popular methods for calculating long terms returns are simple-returns and compounded returns (sometimes expressed as natural-logs) which yield vastly different results that have significant computational consequences. Thus, more awareness of the effects of compounding is necessary. This article contributes to the existing literature by: i) explaining the biases and effects inherent in the calculation of compounded returns (distinct from human biases that can affect returns, and vice versa) – which in turn, implies that various investment approaches (such as “minimum variance investing”; “geometric mean maximization”; etc.) are wrong and inaccurate; ii) some of the Biases introduced herein are new types of Evolutionary Homomorphisms; iii) showing how biases in returns and the calculation methods can affect the analysis of Pattern Formation, Chaos and Adaptive Systems – the discussions in Preis, Kenett, et. al. (2012); Kenett, Preis, et. al. (2012); Preis (2011); Podobnik, Horvatic, Petersen & Stanley (2009); Fenn, et al. (2011); Kriener, Helias, Rotter, et. al. (2014); Hsieh (1993); Menna, Rotundo & Tirozzi (2002); and Hommes (2002) omitted such effects; and iv) explaining some of the effects of market volatility on compounded returns.

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Keywords: portfolio management, risk management, compounding, returns, Indices, complexity