The CAPM model tries to describe the behaviour of capital markets. It is often used by financial market practitioners for example to estimate expected returns, to estimate the cost of capital or to evaluate portfolio managers. In this article tests of the CAPM model with the application of the multivariate GARCH models are presented. It has been shown by numerous studies that conditional variances, covariances of returns and betas are time-varying. Most of the CAPM tests ignore those properties of financial time series. If conditional variance of the error term is time-varying then OLS estimators of the parameters in the mean equation are less efficient. Variability of betas may significantly influence the results of CAPM tests. The multivariate GARCH-M model is able to capture those properties of asset returns and simultaneously describes relations between expected returns and conditional...

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The CAPM model tries to describe the behaviour of capital markets. It is often used by financial market practitioners for example to estimate expected returns, to estimate the cost of capital or to evaluate portfolio managers. In this article tests of the CAPM model with the application of the multivariate GARCH models are presented. It has been shown by numerous studies that conditional variances, covariances of returns and betas are time-varying. Most of the CAPM tests ignore those properties of financial time series. If conditional variance of the error term is time-varying then OLS estimators of the parameters in the mean equation are less efficient. Variability of betas may significantly influence the results of CAPM tests. The multivariate GARCH-M model is able to capture those properties of asset returns and simultaneously describes relations between expected returns and conditional covariances of returns. That is why it can be applied to test the restrictions of the CAPM model. Two new specifications of the GARCH-M model are proposed in the paper: the GARCH-M model with the price of market risk evolving over time according to the random walk process and the GARCH model with the asymmetric GARCH-M effect. In the empirical part of the paper tests of the CAPM model are performed for sectors quoted on the Warsaw Stock Exchange. Estimated market risk premia are changing over time. The highest estimates of risk premia are for financial crisis in Russia and Brazil. Estimated conditional betas are also time-varying. Some of the results support the restrictions of the CAPM model; however, the relation between expected returns and covariances of sector returns and market portfolio analysed for standard specifications of the GARCH-M model is not significant. Moreover there are strong relations between the S&P 500 index and all analysed sector portfolios. The WIG index is not a proper market portfolio or the CAPM model should include additional factors like a portfolio of the overall stock market (for instance the S&P 500 index). Results of the estimation for the proposed model with an asymmetric GARCH-M effect suggest that the relation between expected returns and covariances is significant, but the price of market risk is positive when return of the S&P 500 index is positive and negative when return of the S&P 500 is negative. During the bull market the price of market risk is positive and during the bear market negative. It seems that the GARCH-M model with price of risk dependent on the sign of a portfolio of the overall stock market gives a better description of relations between expected returns and conditional covariances of returns.

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