Nigerian capital market has an essential role in stimulating economic growth by mobilizing domestic savings and encouraging static financial resources to be allocated to more productive activities. Considering this pivotal role of the capital market, this study explores the behavior of the Nigerian capital market excess stock return via the asymmetric and symmetric conditional volatility over the period January 2, 2001, to November 8, 2018. By assessing the comparison among various conditional volatility models, the results are i) there is strong persistence volatility in the stock returns, that is, the presence of ARCH and GARCH, ii) no evidence of asymmetric in the volatility, and iii) no risk premium from the best-fitted models. The study, therefore, concludes that there is no linear relationship between risk and returns as the coefficient is insignificant and that there are no differential effects between positive and negative shocks in the Nigerian capital market. This study offers some insight into the portfolio management strategy and contributes to the growing stock conditional volatility literature in portfolio optimization.