This up of. An efficient market is defined

This essay is going to focus on the weak form of the
efficient market hypothesis in order to analyse the US market.

In order to understand the hypotheses of an efficient market
it is important to understand what an efficient market is made up of. An
efficient market is defined as a place where a large number of rational profit
maximisers are actively competing with each other in order to predict the
future market value of individual securities. At any point in time actual
prices of individual securities reflect the events that have already occurred
and also the events that are to happen in the near future.

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Over the course of the previous 5 decades, efficient market
hypothesis has been subject to intense research and debates. Efficient market
hypothesis is an investment theory according to which it is impossible to beat
the market. According to this theory stocks always trade for their real/fair
value, which makes it impossible for the investors to either sell stocks for
inflated prices or purchase undervalued stocks. Based upon this it should be
more or less impossible to outperform the entire market through market timing
or expert stock selection, making the only way to obtain higher returns by
investing in riskier stocks that other will be sceptical putting their money

While there is substantial evidence in support of the
efficient market hypothesis there is an equal amount of dissent. In the
investment world there are investors such as Warren Buffet who have
consistently beaten the market, which by definition is almost impossible to

There are three
forms of efficient market hypothesis that are all based on different
assumptions of price efficiency.

The strong form of
efficient market hypothesis reflects asset prices based, not just on public
knowledge, but private inside information as well.

The semi strong
version reacts instantly to new information while maintaining efficiency in the

of efficient market hypothesis is a theory based on investment analysis based on
what future stock prices cannot be readily estimated by historical trends and
values as well as past prices.




After the financial crisis
of 2007-2008 many of the major economics in the world suffered dreadfully.

Policy makers due to this reconsidered their commitment towards the efficient
market hypothesis. The Efficient Market Hypothesis has three levels at which it
is likely to work efficiently. The three levels include the strong form, semi
strong and weak form of the efficient market hypothesis.

This essay aims to focus on the Us market and data from S%P
500 from 1997 to 2007 the weak
form of efficient market hypothesis, the weak form of efficient market
hypothesis unlike the semi strong and strong form, considers that stock prices
are unpredictable meaning that there are no patterns that are based on price
fluctuations. Moreover the theory also states that there is no momentum in
price and that the price movements of the stocks are independent. The only way
of beating the market is through insider trading and fundamental analysis but
this too is effective in the long run. This paper will analyse a number of
tests in order to see if a pattern can be find in the Us market based upon
which a conclusion will be made which will show whether the us market is
efficient in the weak form of efficient market hypotheses.


Data and

The data that will be used to analyse the weak form of the
efficient market hypothesis, contains the daily volume traded and the closing
prices of the S&P 500 index, which will cover the period from November 1997
to November 2017.

To analyse the hypotheses, tests for the weak form of EMH
will be conducted. The tests that are going to be explained will be the
Augmented Dickey-Fuller test, Runs test and Ljung Box test.









Augmented Dickey-Fuller test;

A unit root test means that the results either follow a trend
or are random. This test will show us if the prices have a link with each

The null hypotheses for this test are that there is a unit
root. The alternative hypothesis is that the time series is trend stationary.

Augmented Dickey-Fuller test is estimated by the equation



The hypothesis is written as:

H0: a=0 (The data are not distributed independently as they
show serial correlation)


Statistic test;

 is the estimate of  and  is the coefficient standard error.




The degree of freedom is N-K, for lag k= 1, df =n-1. The
p-value is 1, which means that we accept the null hypotheses, which imply that
the data are not distributed independently as they show serial correlation.











The Ljung Box test:

Ljung box test is a statistical test that is based on an
autocorrelation plot. It tests the randomness based on a number of lags. This test
tells us if the data that is being analysed is random or not random. For the
weak form of EMH this is a good way to check whether the prices in the S$P 500
index have a pattern or the value are random.

H0: the data are distributed independently, this means that
the correlation is 0 which means that any correlation in the data would be a
result of randomness of the sampling process)

H1: the data are not distributed independently as they show
serial correlation.


The sample autocorrelation function is denoted by  which is evaluated at lag
K, for k=1.  can be computed using the



 The degrees of freedom is k, for lag k=1 df=1.

p-value that is obtained,


Looking at the p value from the result,
which is 0, the null hypothesis will be rejected, as it is less than 0.05.  This means that the data are not independently
distributed as they show serial correlation.
















A runs test
is also referred to as the Geary test, it is a non parametric test  as per which the sequence of consecutive
negative and positive returns are compared against its sampling distribution
under the random walk hypothesis. A run by definition refers to a series of
increasing or decreasing values. The runs tests analyses two parameters, the
type of run and the length of it. Stock price runs can either be negative or
positive or in other cases have no changes in it at all.

H0: a=0 the
data produced had a random sequence.

H1: a



R is the
observed number of runs, ?, is the expected number of runs.

sR refers to the standard deviation
of the runs.



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