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- 1. Random Walk Hypothesis An Empirical Analysis of KSE 100 Index From Paper of: Haroon Mahmood Shaheed Zulfiqar Ali Bhutto Institute of Science & Technology)
- 2. what is random walk? The advocates of random walk holds that it is impossible to predict the prices of a security from the past performance because changes in economic condition, securities valuations, corporate profits and market as a whole all occur in a countless of different ways.
- 3. introduction Capital market plays a crucial role in mobilization of domestic resources and channeling them efficiently to raise economic production and productivity. (Fama, 1965) define The random walk theory that states that all information is reflected in the current stock prices, therefore, it can be said that any new information would also take little time to be fully incorporated in the prices, and market participants, thus, would have little time to utilize this new information to realize above normal profits.
- 4. Literature Review The first researcher who linked the random walk process to economic processes was French mathematician Louis who noticed that changes of prices of French government papers (rentes) are unpredictable what forced him to conclude that "The mathematical expectation of the speculator is zero". It cannot be denied that some studies have produced evidence against the random walk hypothesis, showing that stock returns contain predictable elements.
- 5. Literature Review Much of this work has centered on the world‟s largest stock markets, including the United States, developed economies in Europe, and Japan and studied by (Poterba & Summers, 1988) and (Lo and MacKinlay, 1988). More recently, mixed evidence on the randomwalk hypothesis has been found for emerging markets in Latin America (Urrutia, 1995); (Grieb & Reyes, 1999) and inAsia (Ayadi & Pyun, 1994); (Huang, 1995); (Chang & Ting, 2000).
- 6. Purpose of study This research, thus, wants to test the phenomena of random walk theory in Karachi Stock Exchange-whether past stock price movements follow a trend or not, so they can or cannot be used to predict their future movement. The results of the study are aimed to confirm the perceptions that stock prices in KSE do follow the random walk theory.
- 7. Data In this research, historical stock prices on a monthly and daily basis have been used from a sample period of July 1996 to June 2006 of KSE 100 Index Companies. A time line of 10 years has been chosen to test the efficiency of the Pakistani Stock market. Thus, the total number of observations is 121 for monthly data and 2218 for daily data. Consequently, a quantitative method has been used.
- 8. Procedure After data collection, it was treated and the statistical tool- ANOVA was applied. First, as the data available from the site, only specified the dates, the day effect needed each day specified too. Subsequent to this the daily and monthly return was calculated as the logarithmic difference between two consecutive daily or monthly prices respectively, yielding continuously compounded returns, by using: Ln {Pt /P(t-1) } where, Ln = Logarithm Pt = Stock prices in time period t P(t-1) = Stock price in time period t-1
- 9. Hypothesis The acceptance of the hypotheses would show that the mean returns on all the weekdays and months are not significantly different from each other and the rejection would mean that mean returns on at least one day of the week and in at least one month are significantly different from each other.
- 10. Conclusion The results lead us to the conclusion that the Random-walk hypothesis can be accepted for both monthly and daily returns. There is no “day of the week effect” or the „month effect‟. Thus, the random walk theory is valid for the KSE which can be termed as an efficient market. This is well-matched with Fama‟s conclusion of existence of random walk phenomena. This result indicates that daily stock market returns are independent and cannot be used to make forecasts of next trading session stock returns.
- 11. Conclusion Therefore, the stock returns in KSE are independent and they cannot be used to predict future returns. Since changes in stock prices are random, we can do no better than to predict that the next period‟s price will be somewhere around where it was the last time we knew it. This conclusion is consistent with modern efficient market studies.

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