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.

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

into.

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

do.

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

prices.

Weak

form

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

methodology

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

other.

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

below;

Where

and

The hypothesis is written as:

H0: a=0 (The data are not distributed independently as they

show serial correlation)

H1:a

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.

Statistic

test:

The sample autocorrelation function is denoted by which is evaluated at lag

K, for k=1. can be computed using the

formula;

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

The

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.

Runs

Test:

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

Statistic

test;

R is the

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

sR refers to the standard deviation

of the runs.