Market efficiency is defined as a case when the prices in a market reflects the information, which is currently available within the market, or otherwise, the market is said to be inefficient whenever the prices of a financial security in not reflected by the information available to all local and international investors who are trading in the securities market. Having a better understanding of the market efficiency when trading an Exchange Traded Fund of any given set of securities in an exchange market is extremely vital for any prospective investor who need to make sound investment decisions as well as market predictions. When trading in a market with few traders who likes dominating the market through insider trading, it is more likely to experience securities exchange market without confidence of investors thus depicting weak form of the efficient market efficiency. Nairobi Securities Exchange market is important in the economy especially for those companies that are looking forward to capital or startups in the Kenyan Market from a global perspective. While testing of the weak form of efficient market hypothesis or EMH of the Nairobi stock exchange (NSE) is done through daily as well as weekly securities index data from NSE 20 share index over the period, 2nd February 2002 to May 2nd 2019. The research study applies the use of secondary NSE data that was derived from Nairobi Stock Exchange market website. This research has deviated from the normal and conventional linear approach to test market efficiency and use of using unit roots to test serial correlation. The daily returns in aspect to skewness as well as kurtosis was found to be non-normal. Similar demonstrations resulted from the Kolmogorov Smirnov test. From the results, null hypothesis of the normality was not rejected. In this research, there is the use of fractional integration thus utilization of ARFIMA to test long term memory and even the traditional unit root test is incorporated to compare both results thus giving a perfect conclusion on whether NSE stock market is definitely weak form efficient. Moreover, NSE-20 share Index stocks are used to make an Exchange Traded Fund that is priced and forecasted that is important for investors looking forward to make investments at the NSE Market in Kenya due to its mimicking ability. Ultimately, the forecasted values of ETF is done on the trendlines similar to the NSE-20 share Index trends, which investors to make informed financial decisions when buying any securities traded in NSE market.

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