Examining heterogeneity in implied equity risk premium using penalized splines

Abstract

Financial data exhibit complex structures and relations and it is therefore not always possible or expedient to find a suitable parametric functional form to adequately describe the data. To overcome this problem, nonparametric techniques can be used to extract the functional process directly from the data without any a priori specification of the functional shape. We take advantage of this flexibility and use a penalized spline approach to model, over time, the implied equity risk premiums of companies that belong to a local stock exchange index. In finance and macroeconomic research it is common practice to use simple averaging techniques to aggregate the single values, thus obtaining an overview of the stock market of a country or particular groups defined by stock-specific characteristics. The objective is to obtain common patterns or dependencies from individual characteristics. A precondition here is a substantial heterogeneity of the individual stocks, because otherwise one constituent can represent the whole index and the required diversification effect fails. Hence, in this paper we explore if and how this assumption is justified. The examined stock indices are the Dow Jones Industrial Index and the German DAX 30. It turns out that the constituents of both indices show very stock-specific behaviors of their equity risk premium over time. Thus the application of these indices in, e.g., macroeconomic research seems adequate.

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