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 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 analyses such as: (1) developing distributions of expected returns; (2) time series analysis; (3) developing options pricing models; (4) estimating various types of risk; (5) developing pricing models for insurance; (6) for the evaluation, and capital-budgeting, of large billion-dollar projects. The two most popular methods for calculating long-term 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 chapter contributes to the existing literature by: (1) 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; (2) some of the biases introduced herein are new types of evolutionary homomorphisms; (3) showing how biases in returns, and the calculation methods, can affect the analysis of pattern formation, chaos and adaptive systems—the discussions in Preis et al. (2012), Kenett et al. (2012), Preis (2011), Podobnik et al. (2009), Fenn, et al. (2011), Kriener et al. (2014), Hsieh (1993), Menna et al. (2002), and Hommes (2002) omitted such effects; and (4) explaining some of the effects of market volatility on compounded returns.

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