In the study we introduce an extension to a stochastic volatility in mean model (SV-M), allowing for discrete regime switches in the risk premium parameter. The logic behind the idea is that neglecting a possibly regimechanging nature of the relation between the current volatility (conditional standard deviation) and asset return within an ordinary SV-M specication may lead to spurious insignicance of the risk premium parameter (as being ‛averaged out’ over the regimes). Therefore, we allow the volatility-in-mean eect to switch over dierent regimes according to a discrete homogeneous two-state Markov chain. We treat the new specication within the Bayesian framework, which allows to fully account for the uncertainty of model parameters, latent conditional variances and hidden Markov chain state variables. Standard Markov Chain Monte Carlo methods, including the Gibbs sampler and the Metropolis-Hastings algorithm, are adapted to estimate the model and to obtain predictive densities of selected quantities. Presented methodology is applied to analyse series of the Warsaw Stock Exchange index (WIG) and its sectoral subindices. Although rare, once spotted the switching in-mean eect substantially enhances the model t to the data, as measured by the value of the marginal data density.

The study aims at a statistical verification of breaks in the risk-return relationship for shares of individual companies quoted at the Warsaw Stock Exchange. To this end a stochastic volatility model incorporating Markov switching in-mean effect (SV-MS-M) is employed. We argue that neglecting possible regime changes in the relation between expected return and volatility within an ordinary SV-M specification may lead to spurious insignificance of the risk premium parameter (as being ’averaged out’ over the regimes).Therefore, we allow the volatility-in-mean effect to switch over different regimes according to a discrete homogeneous two- or
three-state Markov chain. The model is handled within Bayesian framework, which allows to fully account for the uncertainty of
model parameters, latent conditional variances and state variables. MCMC methods, including the Gibbs sampler, Metropolis-Hastings algorithm and the forward-filtering-backward-sampling scheme are suitably adopted to obtain posterior densities of interest as well
as marginal data density. The latter allows for a formal model comparison in terms of the in-sample fit and, thereby, inference on the
’adequate’ number of the risk premium regime