This paper investigates the role of the third and fourth moments which impact on weeklystock return for the all twenty-five emerging stock markets (featured by MSCI - Morgan Stanley Capital International) during the period from April 2005 to November 2017. We employ the traditional CAPM combined with co-skewness and co-kurtosis representing nonlinear shape in risk measurement to estimate return generating under quantile regression in descending order by sorting equally weighted portfolios. The findings show that three of premium including market premium, co-skewness premium and co-kurtosis premium has influenced stock return in each country by 1%; 5%; 10% significance level with five-quantile regression approach. Then, our models with higher co-moments have better explanation for securities in emerging markets rather than traditional CAPM. Importantly, the investors should add more co-skewness securities and eliminate co-kurtosis (or less this factor) to generate more returns among 25 developing markets.