We study the multifractal nature of daily price and volatility returns of Latin-American stock markets employing the multifractal detrended fluctuation analysis. Comparing with the results obtained for a developed country (US) we conclude that the multifractality degree is higher for emerging markets. Moreover, we propose a stock market inefficiency ranking by considering the multifractality degree as a measure of inefficiency. Finally, we analyze the sources of multifractality quantifying the contributions of two factors, the long-range correlations of the time series and the broad fat-tail distributions. We find that the multifractal structure of Latin-American market indices can be mainly attributed to the latter.