An Example of an Investment Model That Makes Something Out of Nothing (Sort of): Implications for Building Applied Mathematical Models

Abstract

Two related and under-studied components of modeling are: a) the process by which simplifying assumptions are derived; and b) the process by which tests of model validity are designed. This case study illustrates these processes for two simple investment models: a) a version of the model supporting classical portfolio theory; and b) a version of a mean-reverting model consistent with some of the tenets of behavioral finance. We perform a simulation that demonstrates that the traditional method of empirically assessing the performance of value investment strategies is underpowered. Indeed, the simulation illustrates in a narrow technical sense how to make something out of nothing; namely, how to generate increased returns while reducing risk. Analyzing the mechanism underpinning this counter-intuitive result helps to illustrate the close and sometimes unexpected relationship between the substantial assumptions made about the systems being modeled, the mathematical assumptions used to build models of those systems, and the structure of the experiments used to assess the performance of those models.