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
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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.