On the Empirical Importance of the Conditional Skewness Assumption in Modelling the Relationship Between Risk and Return

TL;DR

This paper uses Bayesian inference to test how the skewness of the conditional return distribution influences the risk-return relationship, focusing on the Warsaw Stock Exchange.

Contribution

It introduces a novel approach to model skewness in financial returns using inverse probability transformations within a Bayesian framework.

Findings

Conditional skewness significantly affects the risk-return relationship.

Bayesian analysis provides posterior probabilities supporting the importance of skewness.

The model demonstrates empirical relevance on Warsaw Stock Exchange data.

Abstract

The main goal of this paper is an application of Bayesian inference in testing the relation between risk and return on the financial instruments. On the basis of the Intertemporal CAPM model we built a general sampling model suitable in analysing such a relationship. The most important feature of our assumptions is that the skewness of the conditional distribution of returns is used as an alternative source of relation between risk and return. This general specification relates to GARCH-In-Mean model. In order to make conditional distribution of financial returns skewed we considered a constructive approach based on the inverse probability integral transformation. In particular, we apply the hidden truncation mechanism, two equivalent approaches of the inverse scale factors, order statistics concept, Beta and Bernstein distribution transformations, and also the constructive method. Based on the daily excess returns on the Warsaw Stock Exchange Index we checked the empirical importance of the conditional skewness assumption on the relation between risk and return on the Warsaw Stock Market. We present posterior probabilities of all competing specifications as well as the posterior analysis of positive sign of the tested relationship.