Random Walk Hypothesis - Efficient MarketTherandom walk hypothesisis afinancial theorystating thatstock marketpricesevolve according to arandom walkand thus cannot be predicted. It is consistent with the efficient-market hypothesis. The efficient market theory is a simple concept which says that the share prices basically reflect all the available information -in the strongest efficient market practically all the information including insiders information and in the weak efficient market publically available information. So practically its impossible to beat the market.This hypothesis is only as good as knowledge of market participants. So if market participants dont understand economics and when the central bank does something it is likely that they may misinterpret and imply the prices or impact prices which may be totally wrong and even they might not realize the impact as implication may be long term. Many times this resulted in market crisis for example crisis of 2008. Even if we assume that there are people who understand economics and impact but they are not significant player in market. So this correct information is not going to impact the market. In this way the market is not efficient and its possible to beat the market by the people who are having more information.In this project first we are going to test the Random Walk hypothesis for NIFTY. Random movement of share prices goes in favor of EMH(Efficient Market Hypothesis). According to EMH if there is possibility to predict the future price of share, that is the first sign of inefficient market. Randomness, one can say, is necessary condition for EMH.Random walk theory claims that stock market can be analyzed as random walk according to next three facts: efficient markets respond very fast to new information;

if the share price is a reflection of all available information, it is impossible to use that information for market predictions; it is impossible to predict market movement other than randomly.

RUN TESTTo test our hypothesis Run Test will be usedThe Run test is also known as Geary test and it is a non-parametric statistical test whereby the number of sequences of consecutive positive and negative returns is tabulated and compared against its sampling distribution under the random walk hypothesis. A run is defined as the repeated occurrence of the same value or category of a variable. It is indexed by two parameters, which are the type of the run and the length. Stock price runs can be positive, negative, or have no change. The length is how often a run type occurs in succession. Under the null hypothesis that successive outcomes are independent, the total expected number of runs is distributed as normal with the following mean:

and the standard deviation

where n is the total number of observations, nA is the number of first run cycle, and nB is the number of second run cycle. Number of runs is marked with R. If the number of observations is large its distribution is almost equal to normal distribution. The test for serial dependence is carried out by comparing the actual number of runs in the price series. If the number of observations is large its distribution is almost equal to normal distribution. That is why we can use standard normal Z distribution for implementing the Run Test.

H0: the sequence was produced in a random mannerH1: the sequence was not produced in a random manner

Significance Level : = 5%, critical value 1.96Null hypothesis will be rejected ifZ>1.96

Historical data for NIFTY is downloaded from NSE website from 2004. Run test for each year is conducted separately and also for all years together. An increase in NIFTY is marked as "1" and decrease is marked as "0".

Conclusion/Insight

We accept the hypothesis with 5% significance level till 2012 that our market is efficient in digesting the information. For 2013 and 2014 the null hypothesis is rejected and market becomes inefficient (MODI effect- not economics) On long term basis null hypothesis is rejected and there is probability of predicting the market.

The insight from this assignment presents some interesting behavior of our stock market. The daily movement of NIFTY is in line with the Random Walk Hypothesis (Except for 2013 and 2014) and suggests that the movement is random and the market cannot be predicted based on past data. The movements in 2013 and 2014 are against the efficient market hypothesis (not random) and suggest inefficiency. This may be because of this new government and there may be a large number of investors expecting some economic reform from this new government. -. This need to be investigated further with help of some more macroeconomic parameters. 200420052006200720082009201020112012201320142004-14

R=127110111121121129127111126106971296

n0=11410898108129111120141111130941245

n1=1391431521411161311321061401191341472

n=2532512502492452422522472512492282717

E(R)=126.26124.06120.17123.31123.16121.17126.71122.02124.82125.26111.491350.02

Var(R)=61.7760.0856.5559.8360.6559.4362.4659.0460.8361.7653.29669.55

StdDev(R)=7.867.757.527.747.797.717.907.687.807.867.3025.88

Z=0.09-1.81-1.22-0.30-0.281.020.04-1.430.15-2.45-1.99-2.09

P-value=0.540.030.110.380.390.850.510.080.560.010.020.02

H0H0H0H0H0H0H0H0H0H1H1H1

On a longer time horizon the market is not efficient and investors can make money by proper technical and fundamental analysis based on past data like volume and price.

What if one use Technical Analysis for prediction?

To further investigate and test the random walk hypothesis for NIFTY movement in case investor uses some technical analysis and try to understand the predictive behavior, a 5 days

simple moving average is considered for investment decision and the results are significantly against the random walk hypothesis and the hypothesis can be rejected with very high significant level. The movement is almost predictable and our market is not efficient. Investors can make big money by predicting the market by using technical analysis as simple as simple moving average.R=466

n0=1124

n1=1589

n=2713

E(R)=1317.65

Var(R)=638.7357

StdDev(R)=25.27322

Z=-33.6977

P-value=3.1E-249

A very large Z value and p value almost equal to zero!Happy investing- -