This study is aimed to investigate what is happening in the Nigeria Stock Market under its new name, “Nigeria Exchange Group”, with respect to the uncertainty nature of share price behaviour in the capital market. Hence, the month end stock prices of four listed consumer companies from the period January 2017 to December 2022 were used as proxies. The study made use of the Autoregressive Conditional Heteroskedasticity (ARCH) to estimate and find out the presence of the volatility. The study identified the presence of volatility in all the four consumer stock prices used, while the volatility of stock price was then regressed against stock prices to determine their certainty. The results however revealed that out of the four consumer goods companies, only two consumer goods companies’ stock prices were predicted by volatility, while past stock prices predicted current stock prices implying that the market does not follow a random walk. The study therefore recommended that activities of corporate insiders should be critically scrutinized to reduce the predictability of stock prices. Also, that Information should be made available and in clear terms to stakeholders and all investors in particular. Also, that policy makers should carefully review their economic policies in their use of the Nigerian bourse as a barometer to measure performance in the general economy to avoid misleading the investing public.