> Problem statement: The stock exchange market has been one of the most popular investments in the recent past due to its high returns. The market has become an integral part of the global economy to the extent that any fluctuation in this market influences personal and corporate financial lives and the economic health of a country. The daily behavior of the market prices revealed that the future stock prices cannot be predicted based on past movements. Approach: In this study, we analyzed the behavior of daily return of Nigerian stock market prices. The sample included daily market prices of all securities listed in the Nigeria Stock Exchange (NSE). Results: The result from the study provided evidence that the Nigerian stock exchange is not efficient even in weak form and that NSE follow the random walk model. The idealized stock price in the Nigerian stock exchange is a martingale. Conclusion: Martingale defines the fairness or unfairness of the investment and no investor can alter the stock price as defined by expectation.
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