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This paper was set out to validate the random walk hypothesis on security returns in the Nigeria. The primary objective was to investigate the hypothesis of random walk on security returns in the Nigeria capital market.This study made use of data collected annually from the Nigerian stock exchange (NSE) between 1986- 2017. However, in order to validate the theory of RW in the Nigeria bourse, unit ischolar_main test was adopted and the hypothesis was tested at a critical value of 5% and 10% respectively. It was revealed from the analysis that the Nigeria capital market is currently nonrandom. This implies that and participant can outperform the market with past return if they can efficiently allocate their asset. We therefore recommended that investors should put into consideration the trend of movement of returns in other to maximize their portfolio.


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