Conventional and downside CAPM with higher-order moments: Evidence from emerging markets

Research background: Conventional CAPM is a well-known and tested theory on various capital markets. It was also repeatedly rejected as a model of capital pricing. This article proposes a different approach to both CAPM testing and the use of other risk measures. In addition, research is global, including emerging countries.<br /> Purpose of the article: This paper investigates the standard CAPM, and this model is based on higher moments of the return distribution for the global emerging market. In addition, this paper aims to compare the conventional and downside CAPM versions using the beta coefficient and co-moments. Methods: Contrary to the classical unconditional tests for the risk premium, conditional relationships are also estimated considering the market portfolio condition. Moreover, the studies considered conventional and downside approaches to risk measures. The cross-sectional regressions are based on the Fama-MacBeth (F-M) procedure and panel models. Findings & value added: The findings contribute to the debate on whether beta coefficient and higher order co-moments in conventional and downside approaches can explain the crosssectional emerging indices returns. The unconditional models using all measures do not significantly describe the cross-sectional volatility of returns. The cross-sectional regressions in up and down-market based on both the classic F-M procedure and panel models show that the beta and co-kurtosis risk premium is significant and depends on market conditions. The risk premium for co-skewness is not valid, and the direction of the relationships is opposite than expected. Research also demonstrates that the test results of CAPM relationships are not robust to the presence of outliers and shocks resulting from the Covid-19 pandemic in the context of risk-return space. Research provides strong support for the importance of downside risk in the context of standard CAPM and, above all, higher co-moments.