The authors analyse relation between expected return and conditional variance, mainly whether it is time-varying or constant (and also linear). It is assumed that for specified period of time investors expect higher returns from assets with higher risk. However there is no agreement whether positive relation between expected returns and variance is 'dynamic'. Investment over short horizons may sometimes be influenced by portfolio balance and transaction cost consideration or by unexpected immediate consumption needs. All these factors may obscure the risk and return relation in the short horizon. The risk and return relation may also be nonlinear or time varying. The authors analyse this relation for 26 stocks and 2 indices quoted on the Warsaw Stock Exchange with the aim to provide additional insight into the nature of stocks volatility and its relation to expected returns. The GARCH-M models with constant and time-varying parameter are implemented. For most stocks there are no reasons to reject the hypothesis of no autocorrelation of returns. Observable higher serial correlations in portfolio returns are in agreement with the results of other investigations. According to the estimates of the parameters in the conditional variance, current information remains important for forecasts of the conditional variance for very long horizons. Large persistence in variance in financial time series is perplexing because currently no theory predicts that this should be the case. Estimates of the GARCH-M model with constant parameter indicate that for most assets the relation between expected, return and conditional variance is not significant. However the results are sensitive to specification of conditional mean. Only for two stocks the relation between expected return and conditional variance is time-varying. Estimates of the GARCH-M model with time-varying parameter can explain different empirical results concerning the GARCH-M model with constant parameter. Wide range of confidence intervals for time-varying parameter may explain insignificance of analyzed relation for the GARCH-M model with constant parameter.