This study aimed at understanding the Nigerian Stock Market with regards to volatility and prediction, to this effect the month end stock prices of four major companies from the period January 2005 to December, 2009 was used as proxy. The study made use of the Autoregressive Conditional heteroskedasticity (ARCH) to estimate and find out the presence of volatility. The study found the presence of volatility in all the four stock prices used, while stock price volatility was then regressed against stock prices to determine their predictability. The results however, revealed that out of the four companies, only two companies' stock prices were predicted by volatility in their stock prices, while past stock prices predicted current stock prices implying that the market does not follow a random walk. As a result of these, it is recommended that activities of corporate insiders should be properly checked, to reduce the predictability of stock prices, information should be known and made public to all investors. Also policy makers are advised to review their economic policies and should be careful in their use of the Nigerian bourse as a barometer to reflect performance in the general economy as our findings suggests that this could be misleading.
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