This essay is going to focus on the weak form of theefficient market hypothesis in order to analyse the US market.In order to understand the hypotheses of an efficient marketit is important to understand what an efficient market is made up of. Anefficient market is defined as a place where a large number of rational profitmaximisers are actively competing with each other in order to predict thefuture market value of individual securities. At any point in time actualprices of individual securities reflect the events that have already occurredand also the events that are to happen in the near future.Over the course of the previous 5 decades, efficient markethypothesis has been subject to intense research and debates.

Efficient markethypothesis is an investment theory according to which it is impossible to beatthe market. According to this theory stocks always trade for their real/fairvalue, which makes it impossible for the investors to either sell stocks forinflated prices or purchase undervalued stocks. Based upon this it should bemore or less impossible to outperform the entire market through market timingor expert stock selection, making the only way to obtain higher returns byinvesting in riskier stocks that other will be sceptical putting their moneyinto. While there is substantial evidence in support of theefficient market hypothesis there is an equal amount of dissent. In theinvestment world there are investors such as Warren Buffet who haveconsistently beaten the market, which by definition is almost impossible todo. There are threeforms of efficient market hypothesis that are all based on differentassumptions of price efficiency. The strong form ofefficient market hypothesis reflects asset prices based, not just on publicknowledge, but private inside information as well.

The semi strongversion reacts instantly to new information while maintaining efficiency in theprices.Weakformof efficient market hypothesis is a theory based on investment analysis based onwhat future stock prices cannot be readily estimated by historical trends andvalues as well as past prices. After the financial crisisof 2007-2008 many of the major economics in the world suffered dreadfully.Policy makers due to this reconsidered their commitment towards the efficientmarket hypothesis. The Efficient Market Hypothesis has three levels at which itis likely to work efficiently. The three levels include the strong form, semistrong and weak form of the efficient market hypothesis.

This essay aims to focus on the Us market and data from S%P500 from 1997 to 2007 the weakform of efficient market hypothesis, the weak form of efficient markethypothesis unlike the semi strong and strong form, considers that stock pricesare unpredictable meaning that there are no patterns that are based on pricefluctuations. Moreover the theory also states that there is no momentum inprice and that the price movements of the stocks are independent. The only wayof beating the market is through insider trading and fundamental analysis butthis too is effective in the long run. This paper will analyse a number oftests in order to see if a pattern can be find in the Us market based uponwhich a conclusion will be made which will show whether the us market isefficient in the weak form of efficient market hypotheses.

Data andmethodology The data that will be used to analyse the weak form of theefficient market hypothesis, contains the daily volume traded and the closingprices of the S&P 500 index, which will cover the period from November 1997to November 2017.To analyse the hypotheses, tests for the weak form of EMHwill be conducted. The tests that are going to be explained will be theAugmented Dickey-Fuller test, Runs test and Ljung Box test. Augmented Dickey-Fuller test;A unit root test means that the results either follow a trendor are random. This test will show us if the prices have a link with eachother.The null hypotheses for this test are that there is a unitroot. The alternative hypothesis is that the time series is trend stationary.Augmented Dickey-Fuller test is estimated by the equationbelow;Where and The hypothesis is written as: H0: a=0 (The data are not distributed independently as theyshow serial correlation)H1:a<0 (the data are distributed independently, this meansthat the correlation is 0 which means that any correlation in the data would bea result of randomness of the sampling process).

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. Thep-value is 1, which means that we accept the null hypotheses, which imply thatthe 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 anautocorrelation plot. It tests the randomness based on a number of lags. This testtells us if the data that is being analysed is random or not random.

For theweak form of EMH this is a good way to check whether the prices in the S$P 500index have a pattern or the value are random. H0: the data are distributed independently, this means thatthe correlation is 0 which means that any correlation in the data would be aresult of randomness of the sampling process) H1: the data are not distributed independently as they showserial correlation.Statistictest:The sample autocorrelation function is denoted by which is evaluated at lagK, for k=1. can be computed using theformula; The degrees of freedom is k, for lag k=1 df=1.

Thep-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 independentlydistributed as they show serial correlation. RunsTest:A runs testis also referred to as the Geary test, it is a non parametric test as per which the sequence of consecutivenegative and positive returns are compared against its sampling distributionunder the random walk hypothesis. A run by definition refers to a series ofincreasing or decreasing values. The runs tests analyses two parameters, thetype of run and the length of it.

Stock price runs can either be negative orpositive or in other cases have no changes in it at all.H0: a=0 thedata produced had a random sequence.H1: a<0the data produced did not have a random sequence to it.Statistictest; R is theobserved number of runs, ?, is the expected number of runs.sR refers to the standard deviationof the runs.