a study on random walk of equity futures market with

A Study on Random Walk of Equity Futures Market with Reference to National Stock Exchange, India

Prakash Pinto Dept. of Business Administration

St Joseph Engineering College Mangalore-575028

email: [email protected]

Ajaya MSNM Besant Institute of PG

Studies Mangalore-575008


Preeti Menezes Dept. of Business Administration

St Joseph Engineering College Mangalore-575028


Abstract: Efficient market emerges when new information is quickly incorporated into the price so that price becomes information. Efficient market hypothesis[EMH] is the idea that information is quickly and efficiently incorporated into asset prices at any point in time, so that old information cannot be used to foretell future price movements. The study is conducted to test the random walk of futures prices. It comprises of the daily returns of Nifty futures and 19 individual stock futures of the National Stock Exchange. The study is based on the data compiled for the period of 3 years, i.e., from 19th December 2008 to 20th December 2011.

Keywords- Random walk; Efficient market hypothesis; Equity futures; Nifty futures

I. INTRODUCTION In an efficient market, the stock prices respond rapidly

and accurately to all relevant and available information. The efficient market hypothesis [EMH] assumes that stock prices adjust rapidly to the arrival of new information, and thus current prices fully reflect all available information. There are three forms of market efficiency namely weak form, semi strong form and strong form. The weak form says that the current prices of stocks already fully reflect all the information that is contained in the historical sequence of prices. This weak form of the efficient market hypothesis is popularly known as the Random Walk hypothesis.

The random walk hypothesis of stock market prices is concerned with the question of whether one can predict future prices from past prices. The fundamental ideas behind the random walk hypothesis are that successive price changes (or successive one period returns) in individual securities are independent over time and that its actual price fluctuates randomly around its intrinsic or theoretical value.

One of the speculative markets gaining popularity both in the developed as well as developing economies is the equity futures market. In India, the equity futures are actively traded on Bombay Stock Exchange (BSE) and National Stock Exchange (NSE). Since futures offer the traders an opportunity to hedge their risk exposure to the underlying asset, it has become the favorite instrument for most of the traders (investors, arbitrageurs, speculators and hedgers).

II. STATEMENT OF THE PROBLEM Several studies have been conducted in India testing the

random walk of stock prices [1],[6],[8],[10]. However, very

few studies have tested the random walk of stock index futures and equity futures prices [7]. The present study is conducted to test the Random walk of Equity Futures market with reference to S&P CNX Nifty Futures and selected Equity Futures from the National Stock Exchange, India.

A. Objectives The objectives of the study are as follows: • To test the validity of the Random Walk hypothesis

for return series of S&P CNX Nifty Index Futures. • To test the validity of the Random Walk hypothesis

for return series of 19 individual stock futures. • To empirically test the validity of the Random Walk

hypothesis or weak form efficient market hypothesis in the Indian Equity futures market.

B. Hypothesis 1. H0: The S&P CNX Nifty Future returns series is

random. H1: The S&P CNX Nifty Future returns series is not random.

2. H0: The individual stock future return series is random. H1: The individual stock future return series is not random.

C. Scope of the Study The study is restricted to only one index of National

Stock Exchange i.e. S&P CNX Nifty Futures and 19 individual stock futures. The analysis is limited for a period of 3 years, from 19th December 2008 to 20th December 2011.

III. RESEARCH METHODOLOGY The universe of the study comprises of the daily closing

values of Nifty Futures and individual stock futures traded on NSE. The daily closing values of S&P CNX Nifty futures and 19 individual stock futures of the NSE are taken for a period of 3 years, from 19th December 2008 till 20th December 2011. The individual stock futures have been selected using random sampling technique. Price series data were obtained from the website of NSE.

The returns on Nifty futures and individual stock futures were calculated in the following manner.

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Returns on Nifty Futures: RNt= [(Pnt –Pnt-1)/ Pnt-1] ×100

Where, RNt = Returns on Nifty futures, in period t Pnt = Price of nifty futures at day t Pnt-1= price of nifty futures at day t-1

Returns on Stock Futures: RSt= [(Pnt –Pnt-1)/ Pnt-1]×100 Where:

RSt=Returns on stock futures, in period t Pnt = Price of stock futures at day t Pnt = Price of stock futures at day t-1

The present study used run test, autocorrelation and Ljung- Box statistic to arrive at the findings.

A. Run Test The run test is an approach to test and detect statistical

dependencies (randomness). A run test is performed by comparing the actual number of runs with the expected number of runs on the assumption that price changes are independent. If the observed runs are not significantly different from the expected number of runs, then it is inferred that successive price changes are independent. On the contrary, if this difference is statistically significant, the series of changes would be regarded as dependent. The measurements employed are as below: R 2 1

Where, Rexp= Expected number of runs n1 = Number of positive signs n2 = Number of negative signs n3 = Number of zeroes (no change in price)

The Standard error (S.E) of expected number of runs of all signs may be obtained as follows:

. 2 2─1

The difference between actual and expected number of

runs can be expressed by a standardized variable ‘Z’ as under: 0.5

Where, R= Total observed number of runs of all signs Rexp = Expected number of runs 0.5 = continuity adjustment δ (Rexp) = standard error

For testing the significance of the difference between observed and expected number of runs, the test statistic employed will be ‘Z’. In the absence of an alternative

hypothesis about the direction of the deviation from random series, a two tailed test is applied.

The null hypothesis (randomness hypothesis) will be accepted at 5 % level of significance if ‘Z’ value < 1.96 and it will be rejected if ‘Z’ value is > 1.96.

B. Auto-correlation Test Auto correlation is a reliable measure for testing of

independence of random variables in return series. The serial correlation coefficient measures the relationship between the values of random variable at time (t) and its value (k) in the previous period. They will indicate whether price change at time (t) is influenced by the price changes occurring (k) periods earlier. The serial correlation of time series is given by autocorrelation function of lag k.

Auto-correlation test is used to identify whether the correlation coefficient are significantly different from zero. Auto correlation [ rk ] is estimated by using:

rk = Ck/ C0 Where, ∑ – ; 0, 1 … ∑ t, ; C0 = Variance of X1

IV. RESULTS OF THE STUDY

A. Results of Run Test Runs test is employed to check if the futures return series

follow random walk or not. The null hypothesis (randomness hypothesis) will be accepted at 5 % level of significance if ‘Z’ value < 1.96 and it will be rejected if ‘Z’ value is > 1.96. The results are shown in the Table I and Table II respectively.

1) Results of Run Test- Median as Base: The results of runs test reveal that the null hypothesis is accepted in the case of almost all the 20 futures as the Z values are less than 1.96 (i.e. Z< 1.96) except for AMBUJACEM and CIPLA future returns. AMBUJACEM futures has the Z value of 2.974 and CIPLA has Z value 2.904 both of which are greater than 1.96. Hence, the null hypothesis is cannot be accepted for these two return series.

2) Results of Run Test- Mean as Base: The results of runs test reveal that the null hypothesis is accepted in the case of almost all the 20 futures as the Z values are less than 1.96 (i.e. Z< 1.96) except for AMBUJACEM and CIPLA futures returns. AMBUJACEM futures has a Z value of 3.008 which is greater than 1.96 and CIPLA futures has Z value of 3.406 which is greater than 1.96. Hence, the null hypothesis is rejected and the return series does not follow random walk. All the other futures have Z values less than 1.96 and hence null hypothesis is accepted which proves that the return series follow random walk. To conclude, the results of runs test show that the futures return series follow random walk.

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TABLE I. RESULT OF RUNS TEST FROM MEDIAN

V. RESULTS OF AUTOCORRELATION TEST Autocorrelation refers to the correlation of a time series

with its own past and future values. Autocorrelation is also sometimes called “lagged correlation” or “serial correlation”, which refers to the correlation between members of a series of numbers arranged in time.

Auto correlation tests whether the return series confirms to zero correlation. At 5% level of significance if the autocorrelation coefficient is > 0.05, then we conclude that it is significant and hence return series is not independent so the null hypothesis (H0: Return series follows random walk) will be rejected.

TABLE II. RESULT OF RUNS TEST FROM MEAN

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Suppose the autocorrelation coefficient is < 0.05 at 5% significance level, and then we can infer that the return series is independent and so null hypothesis is accepted. The summary results of autocorrelation test are shown in the Table III and individual results are tabulated in Table IV.

TABLE III. SUMMARY RESULTS OF AUTOCORRELATION

In the Table III we observe that at lag 1, the futures

BAJAJHLDNG, BHEL and SBIN having the coefficient values 0.083, 0.05 and 0.117 respectively violate the white noise at 5% correlation and all other futures conform to zero correlation, which says that the null hypothesis is accepted and hence the futures return series follow random walk.

At lag 4, we have 2 stock futures i.e. INFY and MTNL having the coefficient values 0.095 and 0.058 respectively violate the zero correlation at 5% significance level. All other futures have coefficient value < 0.05, which says that they conform to zero correlation and so null hypothesis is accepted.

At lag 8, we can observe that the results are similar as that of lag 4. The futures ACC, INFY and MTNL having the coefficient value 0.051, 0.084 and 0.07 respectively violate the white noise at 5% significance level. All other future returns conform to zero correlation and they follow random walk hypothesis.

At lag 16, we can observe that only SBIN futures having coefficient value 0.05 violates the zero correlation and all other futures conform to white noise accepting the null hypothesis and confirming random walk.

Thus, the summary result of autocorrelation test gives mixed results. But, as we have majority of the futures conforming to zero correlation, we can conclude that the futures market follows random walk hypothesis.

Individual results of autocorrelation test are shown in Table IV

1) NIFTY: At lag 1, the coefficient value is 0.035, at lag 4 it is 0.027, lag 8 the coefficient is 0.041 and at lag 16 it is 0.012. We can observe that at all the lags, the nifty

TABLE IV. AUTOCORRELATION RESULTS

futures confirm to zero correlation and hence provides evidence for random walk hypothesis.

2) ACC: At lag 1, the coefficient value is 0.011, at lag 4 it is 0.001, lag 8 the coefficient is 0.051 and at lag 16 it

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is 0.044. We can observe that at all the lags with an exception of lag 8, the ACC futures are close to zero correlation and hence the return series follows the random walk hypothesis.

3) AMBUJACEM: At lag 1, the coefficient value is -0.129, at lag 4 it is -0.044, lag 8 the coefficient is 0.026 and at lag 16 it is -0.032. We observe that at all the lags the futures conform to zero correlation.

4) BAJAJHLDNG: At lag 1, the coefficient value is 0.083, at lag 4 it is -0.018, lag 8 the coefficient is 0.035 and at lag 16 it is -0.043. We observe that at all the lags except at lag 1, the BAJAJHLDNG futures are close to zero implying no dependencies and hence it follows the random walk hypothesis.

5) BHEL: At lag 1, the coefficient value is 0.05, at lag 4 it is -0.044, lag 8 the coefficient is -0.008 and at lag 16 it is 0.004. We can observe that at all the lags except at lag 1, the futures are close to zero implying no dependencies and hence supports the random walk hypothesis.

6) BPCL: At lag 1, the coefficient value is -0.059, at lag 4 it is 0.022, lag 8 the coefficient is -0.032 and at lag 16 it is -0.031. We observe that at all the lags, the futures are close to zero implying no dependencies.

7) CIPLA:At lag 1, the coefficient value is -0.099, at lag 4 it is 0.048, lag 8 the coefficient is -0.059 and at lag 16 it is -0.051. We observe that at all the lags, the futures are close to zero implying no dependencies and hence supports the random walk hypothesis.

8) DR REDDY:At lag 1, the coefficient value is -0.036, at lag 4 it is 0.029, lag 8 the coefficient is -0.01 and at lag 16 it is -0.042. We observe that at all the lags, the futures are close to zero implying no dependencies and hence it follows the random walk hypothesis.

9) GRASIM:At lag 1, the coefficient value is 0.039, at lag 4 it is 0.018, lag 8 the coefficient is -0.078 and at lag 16 it is 0.009. We observe that at all the lags, the futures are close to zero implying no dependencies and hence it follows the random walk hypothesis.

10) HDFC:At lag 1, the coefficient value is -0.013, at lag 4 it is 0.015, lag 8 the coefficient is -0.019 and at lag 16 it is 0.011. We observe that at all the lags, the futures are close to zero implying no dependencies and hence it follows the random walk hypothesis.

11) HINDALCO:At lag 1, the coefficient value is -0.002, at lag 4 it is -0.013, lag 8 the coefficient is -0.019 and at lag 16 it is 0.007. We observe that at all the lags the futures are close to zero implying no dependencies and hence follows the random walk hypothesis.

12) HINDUNILVR:At lag 1, the coefficient value is 0.028, at lag 4 it is 0.000, lag 8 the coefficient is -0.014 and at lag 16 it is 0.009. We can observe that at all the lags, the futures are close to zero implying no

dependencies and hence it follows the random walk hypothesis.

13) HINDPETRO:At lag 1, the coefficient value is -0.043, at lag 4 it is -0.006, lag 8 the coefficient is -0.032 and at lag 16 it is -0.004. We observe that at all the lags, the futures conform to zero correlation and hence it follows the random walk hypothesis.

14) INFY:At lag 1, the coefficient value is 0.033, at lag 4 it is 0.095, lag 8 the coefficient is 0.084 and at lag 16 it is 0.018. We can observe that at all the lags except at lag 4 and lag8, the INFY futures conform to zero correlation. Since it’s a mixed result, we cannot come to any conclusion.

15) ITC:At lag 1, the coefficient value is -0.037, at lag 4 it is 0.005, lag 8 the coefficient is -0.042 and at lag 16 it is -0.016. We observe that at all the lags, the futures conform to zero correlation and hence the returns follows the random walk.

16) M&M:At lag 1, the coefficient value is 0.046, at lag 4 it is -0.03, lag 8 the coefficient is -0.034 and at lag 16 it is 0.005. We observe that at all the lags, the M&M futures conform to zero correlation and hence the return series follows the random walk.

17) MTNL:At lag 1, the coefficient value is -0.053, at lag 4 it is 0.058, lag 8 the coefficient is 0.07 and at lag 16 it is 0.035. We observe that at all the lags except at lag 4 and lag 8, the MTNL futures conform to zero correlation. Since it’s a mixed result, we cannot reach to any conclusions.

18) RANBAXY:At lag 1, the coefficient value is 0.027, at lag 4 it is -0.027, lag 8 the coefficient is 0.049 and at lag 16 it is -0.031. We observe that at all the lags, the futures conform to zero correlation supporting the random walk hypothesis.

19) RELIANCE:At lag 1, the coefficient value is 0.017, at lag 4 it is -0.033, lag 8 the coefficient is 0.013 and at lag 16 it is -0.015. We observe that at all the lags, the futures conform to zero correlation and hence follows the random walk .

20) SBIN: At lag 1, the coefficient value is 0.117, at lag 4 it is -0.011, lag 8 the coefficient is 0.016 and at lag 16 it is 0.05. Since it’s a mixed result, it is difficlult to provide an evidence of random walk.

The overall conclusion of autocorrelation test is that, majority of the futures at different lags conform to zero correlation and so the null hypothesis stating that the return series follow random walk is accepted.

VI. RESULTS OF LJUNG-BOX STATISTIC TEST The Ljung- Box Statistic was used to test joint

hypothesis about the significance of all autocorrelation matrices at a given lag. The results are shown in Table III and IV respectively. The Ljung- Box Statistic was tested at 5 % significance level for 16 degree of freedom. If the

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test statistic value is less than 26.30 at 5% significance level, we conclude that the return series conform to zero correlation and the null hypothesis stating that the returns follow random walk will be accepted. From the tables III and IV we observe that at lag1 and lag 4, all the futures conform to zero correlation the null hypothesis is accepted.

At lag 8, we can see that INFY returns violate the white noise as the statistic value 27.831 is greater than 26.30 at 5% significance level. All other futures conform to zero correlation. At lag 16, we have 6 futures violating the zero correlation as they have statistic value greater than 26.30 at 5% significance level. The futures are AMBUJACEM, CIPLA, INFY, MTNL, RANBAXY and SBIN. All other futures confirm to zero correlation.

VII. FINDINGS AND RECOMMEMNDATION

A. Findings The major findings of the test conducted are:

1) Runs test: The results of runs test considering mean and median as the base indicates that the standard normal variate ‘Z’ is less than 5% level of significance for almost all the futures except for AMBUJACEM and CIPLA futures. So the null hypothesis is accepted in most of the futures stating that the futures market follow random walk.

2) Autocorrelation test: The autocorrelation results also support the results of run analysis.Out of 20 serial correlation coefficient at lag 1, three futures (BAJAJHLDNG, BHEL and SBIN) are greater than 0.05 at 5% significance level all other futures are insignificant conforming to zero correlation .At lag 4, two serial correlation coefficients (INFY and MTNL) are significant at 5% significance level. All other futures confirm to zero correlation. At lag 8, we have three serial correlation coefficients (ACC, INFY and MTNL) significant at 5% level of significance and other futures conforming to zero correlation.Finally at lag 16, we have only one coefficient (SBIN), violating the zero correlation and all other futures conforming to zero correlation ensuring the acceptance of null hypothesis.

3) Box- Ljung Statistic: The overall outlook at the results shows that majority of the futures conform to zero correlation at different lags and hence the null hypothesis that the returns follow random walk holds good.

VIII. CONCLUSION The study tested the weak form efficiency for Indian

Futures market considering NIFTY futures and 19 individual stock futures of the National Stock Exchange using Runs test, Autocorrelation test and Box- Ljung statistic. The evidence of runs test indicated that the null hypothesis was accepted in majority of the futures where the return series follow random walk. The auto correlation

test, although had mixed results, majority of the futures conformed to zero correlation. The Box- Ljung statistic test also supported the results of autocorrelation test. Thus, we conclude that the Indian Equity Futures Market follows the random walk hypothesis.

ACKNOWLEDGMENTS The authors are grateful to Dr. Demian Antony

D’Mello, Professor CSE for the valuable suggestions and Rev. Fr. Joseph Lobo, Director, St. Joseph Engineering College, Mangalore for the support.

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a study on random walk of equity futures market with

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