Graphical Analysis

CHAPTER 5. EMPIRICAL RESULTS, FINDINGS AND ANALYSIS

5.1. Over all graphical analysis

For any index the best way to gauge its long term movement is to plot its movement over a period of time. So here to start with the analysis part , first the overall movement of the daily "close" data for S&P CNX NIFTY FIFTY is examined for the period starting from 2nd May 2002 till 3rd Feb 2012. There are in total 2347 observations and the econometric package EViews 7 has been used to track the movement. The plot is shown in Fig No 5.1.

Fig No 5.1. Daily movement of Nifty Fifty "close" during 02/05/2002 - 03/02/2012

From the graph it is clear that Nifty has shown an upward trend over the period of time. While the upward trend is pretty evident from 2002 to 2007 however since 2007 Nifty movement has been somewhat unstable due to frequent market fluctuation and thus the market seems to be more volatile during this period. In terms of volatility another aspect is visible from the graph that is an upward trend is being followed by further upward trend while a downward trend is being followed by further downward trend and this feature is known as "volatility clustering" and this volatility clustering seems to be present in the index. More about the volatility and the movement of the index will be explored in the further subsections where the task of comparing Nifty movement at times is being taken.

5.2. Over all statistics

The performance of Nifty over the years is tabulated in the Table No5.1. The statistics is collected from the NSE website. The link to the website is

http://www.nseindia.com/content/indices/ind_cnx_nifty.pdf

Period Returns (%) Volatility (%) Avg Daily Return (%)

1 year -9.23 1.29 -0.03

3 years 75.29 1.46 0.09

5 years 38.57 1.87 0.04

10 years 368.82 1.66 0.08

Since inception 429.56 1.69 0.05

Table No 5.1. Over all statistics of Nifty Fifty (source - NSE website)

Histogram and Normality Test

One of the very important assumption to test is whether the stock market index conforms to the pattern of normality and for the normality test both graphical analysis and statistical tests have been adopted.

First the histogram is plotted for the daily "close" data of S&P CNX NIFTY.

The histogram is represented in the fig no 5.2.

Fig no 5.2. Histogram for daily "close" of NIFTY during 03/05/2002 - 03/02/2012

The histogram suggests that the index Nifty conforms to a non normal pattern. To confirm this, the results of statistical tests for normality is solicited. The normality tests that have been adopted are -

a. Kolmogorov - Smirnov test

b. Cramer-von Mises test

c. Anderson - Darling test

d. Jarque - Bera test

The rationale and the methodology of each test is being discussed in the section "methodology" so here only the test statistic and the corresponding probability is represented to understand whether the index follows a normal or a non normal pattern. While for the first three tests the help of the software SAS 9.1 is adopted, for Jarque Bera test the econometric package EViews 7 is used

The test statistics for each test with its corresponding probability is given in the table no 5.2.

TEST STATISTIC P-VALUE REMARKS

Kolmogorov - Smirnov test .107335 Less than .01 Not Normal

Cramer-von Mises test 8.336493 Less than .005 Not Normal

Anderson - Darling test 54.05025 Less than .005 Not Normal

Jarque - Bera test 191.3551 0.0000 Not Normal

Table 5.2. Normality Test Results For Nifty "Close" during 03/05/2002-03/02/2012

For the normality test the null hypothesis ( H0) is that the index conforms to the normal pattern while the alternative hypothesis (Ha) is that the index does not conform to the normal pattern. The level of significance (α) is set at .05 i.e 5% so the logic is if the p-value that is obtained from the software is below the α then the null hypothesis (H0) will be rejected and the inference will be that the index conforms to a non normal pattern , however if the value of p-value is greater than level of significance (α) then the null hypothesis ( H0) can't be rejected and hence it will be accepted that the index conforms to a normal pattern. From the test result presented in the table no 5.2. it is seen that for each test the p-value is below the level of significance (α) which is .05 or 5% and hence the null hypothesis ( H0) is rejected . Thus the test statistics confirms the pattern obtained from the histogram that is the index conforms to a non normal pattern.

5.3. Other aspects of Nifty trading - shares traded and turnover

Another indicator that how strong a stock market is performing is in terms of its growth in number of traded shares and its growth in turnover.

Table 5.3.presents -

i. The number of traded shares on the first day of the data collection along

with the number of traded shares on the last day of the data collection to

give a intuitive report on how the index has grown in terms of volume.

ii. The turnover on the first day of the data collection along with the turnover

on the last day of the data collection so as to give a intuitive report on how

the index has grown in terms of daily turnover.

PARAMETER 2/5/2002 3/2/2012 GROWTH (IN %)

SHARES TRADED 44413724 217358188 389.3941972

TURNOVER ( IN CRORES) 1325.68 7573.02 471.2555066

Table