  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.
