This paper offers a comprehensive view of four time properties that emerge from the empirical time series literature on asset returns. It examines: (1) the predictability of returns from past observations; (2) the auto-regressive behavior of conditional volatility; (3) the asymmetric response of conditional volatility to innovations; (4) and the conditional variance risk premium. Three emerging markets previously under-researched in this respect are considered: South Africa (ALSI, IND, GOLD indexes), Kenya (NSE index) and Nigeria (LSE index). The paper employs exponential GARCH (EGARCH) framework for analysis. The results indicate that asymmetric volatility found in the U.S. and other developed markets does not appear to be a universal phenomenon. Significant asymmetric volatility is found in both South Africa and Nigerian stock markets. However, in one market, NSE (Kenya), the asymmetric volatility coefficient is significant but positive, suggesting that positive shocks increase volatility more than negative shocks of an equal magnitude. LSE (Nigeria), GOLD (the post-announcement sample) and IND (the pre-announcement sample) return series exhibit a significant and positive time-varying risk premium. NSE (Kenya) and ALSI (South Africa) return series report negative but insignificant risk-premium parameters. The results also indicate that expected returns in these emerging markets are predictable. The auto-regressive return parameter (Ø1) is significant in all the markets. The auto-regressive structure, however, is more severe in Nigeria and Kenya than in South Africa. This implies that the percentage of stocks that do not trade in a time interval in the Lagos and Nairobi Stock Exchanges are less than that of the Johannesburg Stock Exchange. Finally, volatility persistence is significant in all the return series of the markets. The GARCH parameter ($b$) is statistically significant in all cases indicating that volatility persistence found in the develo