A solution to the risk-return conundrum: Return exposure and the nonparametric Bayesian approach

Abstract

The topic of the risk-return relationship is of broad importance in the fields of finance and economics. It has been widely investigated on an international scale, especially by developed markets from as early as the 1950's, with the primary motive being to help market participants optimize their chance to earn higher returns. According to conventional economic theory, the relationship between risk and return is a positive and linear relationship – the higher the risk, the higher the return. However, there are many studies documented in literature which show a positive or negative or no relationship at all. As a result, due to the magnitude of conflicting results over the years, this has caused an ongoing debate to arise regarding the risk-return relationship. International studies have explored a number of theories and models to attempt resolving the inconclusive empirical backing of the risk-return relationship. A valuable contribution of this study is the introduction of the novel concept “returns exposure” which refers to the risk that arises from the asymmetric nature of returns. This measure has a certain level of uncertainty attached to it due to its latent and stochastic nature. As a result, it may be ineffectively accounted for by existing parametric methods such as regression analysis and GARCH type models which are prone to model misspecification. This motivates the use of a more robust method, namely, the nonparametric Bayesian approach. The Bayesian approach has the ability to average out sources of uncertainty and measurement errors and thus effectively account for “return risk” or “returns exposure.” The Bayesian approach can be modelled within a parametric or nonparametric framework. The nonparametric approach is considered more robust as it relaxes modelling assumptions such as normality. Thus, in combination with the nonparametric approach, this provides a more robust estimation of the risk-return relationship.