Trade off between simplicity and precision of index models

Abstract

In the basis of contemporary portfolio theory is Markowitz model of portfolio analysis which accurately defines a set of efficient portfolios for a relatively small number of securities in its composition. With the increase in the number of securities in the portfolio, the application of the Markowitz's model becomes complex, so financial theory found the solution of the problem in the single-index Sharpe's model. The later emergence of multi-index models, which better reflect reality, increased precision in determining a set of efficient portfolios, but at the cost of greater complexity of the model. The aim of the research is to analyze a kind of substitution between the simplicity and precision of the model, and to search answer to the question of what is the optimal number of explanatory factors of the model. Using qualitative economic analysis method, it was concluded that the number of factors (indexes) in the model should be increased until marginal benefits in the form of increased precision are equalized with marginal costs in the form of increased complexity, reduced applicability and associated costs of obtaining informations. In striving for greater precision of models, financial analysts must not overlook that the index models emerged from the practical necessity of simplifying the original Markowitz's model.