efficiency of commodity futures market

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A Test of Efficiency of Commodity Futures Market M.P.Birla Institute of management 1 ARE S EARC H RE P O R T ON A test of Efficiency of Commodity Futures MarketSubmitted in partial Fulfillment of the requirements for MBA Degree of Bangalore University Submitted By SUDHEER REDDY Reg.No.05XQCM6095 UNDER THE GUIDENCE OF Prof.B.V.Rudra Murthy Professor, MPBIM M.P.Birla Institute of Management Associate Bharatiya Vidya Bhavan Bangalore-560001 2005-2007

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Page 1: Efficiency of Commodity Futures Market

A Test of Efficiency of Commodity Futures Market

M.P.Birla Institute of management 1

A RESEARCH REPORT

ON

“A test of Efficiency of Commodity Futures Market”

Submitted in partial Fulfillment of the requirements for MBA

Degree of Bangalore University

Submitted

By

SUDHEER REDDY Reg.No.05XQCM6095

UNDER THE GUIDENCE

OF

Prof.B.V.Rudra Murthy Professor, MPBIM

M.P.Birla Institute of Management Associate Bharatiya Vidya Bhavan

Bangalore-560001 2005-2007

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M.P.Birla Institute of management 2

DECLARATION

I hereby declare that the Project report on “A test of Efficiency of

Commodity Futures Market” is a record of independent work carried

out by me, towards partial fulfillment of the requirements for MBA

course of Bangalore University at M.P.Birla Institute of Management.

This has not been submitted in part or full towards any other degree

or Diploma of Bangalore University or any other University

Date: Sudheer M Reddy Place: Bangalore (05XQCM6095)

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PRINCIPAL’S CERTIFICATE

This is to certify that Sudheer M Reddy, bearing Registration No:

05XQCM6095 has done a research project on “A test of Efficiency of Commodity Futures Market” under the guidance of Prof.B.V.Rudra

Murthy , M P Birla Institute of Management, Bangalore. This has not

formed a basis for the award of any degree/diploma for any other university.

Place: Bangalore Dr.N.S.MALAVALLI Date: MPBIM, Bangalore

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M.P.Birla Institute of management 4

GUIDE’S CERTIFICATE

This is to certify that the dissertation entitled “A test of Efficiency of Commodity Futures Market” is an original study conducted by

Sudheer M Reddy, bearing register number 05XQCM6095, of M. P.

Birla Institute of Management, Associate Bharatiya Vidya Bhavan,

under my guidance.

This has not formed the basis for the award of any Degree/Diploma

by Bangalore University or any other University.

I also certify that he has fulfilled all the requirements under the

covenant governing the submission of dissertation to the Bangalore

University for the award of MBA Degree.

Date : Prof.B.V.Rudra Murthy Place : Bangalore MPBIM, Bangalore

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M.P.Birla Institute of management 5

ACKNOWLEDGEMENT

A teacher is a perennial source of inspiration and guidance in all the

academic activities of his students throughout. I whole-heartedly extend

my deep and sincere gratitude to Dr.T.V.Narasimha Rao, faculty for

Finance, MPBIM, for his continuous guidance and help provided for

completing this research study.

I am also grateful to Dr N S Malavalli, Principal, M.P Birla Institute of

Management for his full support and encouragement while I was

conducting this research.

I am also thankful to Prof. S.S. Santhanam, M.P Birla Institute of

Management for sharing his expertise in the field of Statistics with me

whenever I approached him.

I am also thankful to Prof.B.V.Rudra Murthy, M.P Birla Institute of

Management for sharing his expertise in the field of Finance with me

whenever I approached him.

I also express my gratitude to all friends and family members for extending

their helping hand whenever I approached them. Without their help this

research could not have been presented in a proper manner.

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TABLE OF CONTENTS

ABSTARCT 01 1. INTRODUCTION

Introduction and Background of the study 02 2. REVIEW OF LITERATURE

Past literature 09 3. RESEARCH METHODOLOGY

Hypothesis statement 19 Methodology 21

Theory of stationarity 23 Gangers co-integration test 26 4. DATA ANALYSIS AND INTERPRETATION

Empirical Results 27 5.CONCLUSION 40 BIBLIOGRAPHY 41 ANNEXURES 42

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ABSTRACT

This paper addresses the Efficiency of commodity futures market of soy bean, chana and

sugar. Whether, the Futures contracts trading has significant impact on the spot prices or

not. Using unit root test it is confirmed that the data is stationary. The residual based

Ganger co-integration test also indicates that the spot prices have co-integrated, with the

NCDEX Futures prices. After doing unit root test for the first order difference data, when

we found data is stationary then this data is tested for residual values. Then once again

the residual values are tested for unit root test to see the both the future series and spot

series are co-integrated with each other. The unit root test conducted for residual values

also found that the data is stationary. Hence the unit root tests conducted for both the

values are stationary, we can say that the market is efficient in these three commodities.

The volatility in the short run prices has corrected over a period in the long run.

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INTRODUCTION

Market efficiency has an influence on the investment strategy of an investor because if

market is efficient, trying to pickup winners will be a waste of time. In an efficient

market there will be no undervalued commodities offering higher than deserved expected

returns, given their risk. On the other hand if markets are not efficient, excess returns can

be made by correctly picking the winners. In this paper, analysis of three popular

commodities are carried out to test the efficiency level in Indian commodity market by

using the ADF test and the Ganger co-integration test. In India, the first commodity futures exchange was set up in 1875, in Mumbai, under the

aegis of Bombay Cotton Traders Association. A clearing house for clearing and

settlement of these trades was set up in 1918. In oilseeds, a futures market was

established in 1900. Wheat futures market began in Hapur in 1913. Futures market in raw

jute was set up in Calcutta in 1912 and the bullion futures market in Bombay in 1920.

During the post Independence period commodity trading saw various regulatory

decisions. The Forward Contract (Regulation) Act was enacted in 1952 and the FMC or

the Forward Markets Commission was established in 1953 under the Ministry of

Consumer Affairs. FMC acts as a regulatory body, which regulates the commodity

markets in India. The mid-1960s witnessed an unprecedented rise in the prices of major

oils and oilseeds as a result of a sharp fall in output. Futures trade was banned in most

commodities to contain speculation, which the government attributed to rising inflation.

In 2002-03, The Government of India took two steps that gave a fillip to the commodity

markets. The first one was setting up of nation wide demutualized multi commodity

exchanges and the second one was expansion of list of commodities permitted for

trading. Today we have three nationalized exchanges in India viz. MCX, NCDEX and

NMCE; and more than 21 regional exchanges in India.

In May 2006, the commodity futures markets have average daily volumes of more than

Rs.4000 crores at NCDEX and MCX each and have surpassed that of the Bombay Stock

Exchange (BSE) which has a volume of Rs.2500 crores. The total volume of commodity

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futures trading in the country has reached Rs. 190000 crores ($44 billion) during the first

quarter of the 2006-2007, showing a significant growth of 800 percent as per the statistics

by Forward Market Commission (FMC). The commodity exchanges in India can be

considered to be in a growth trajectory and the total volume of trade as at the end of

December 2005 has been in the order of Rs 13.88 lakh crore, compared to Rs 5.71 lakh

crore during the previous year. The growth in the volume of trade is phenomenal in the

context of the recent emergence of the exchanges, also facilitated by the increase in the

number of commodities (more than 89) available for trading and the provision of an

online trading platform.

The objectives of the commodity markets introduction can be summarized as price

discovery of the underlying commodity, cross commodity risk hedging, hedge price risk

resulting from export-import activities and development of specialized warehouses and

treasuries for facilitation of trade. Moreover, the —dual price system “under which

different prices for same commodities exist, the administration of a part of market for the

commodity by the government is expected to give rise to inefficiency.

The study aims at testing the efficiency of the commodity markets, specifically in soy

bean, chana and sugar. An efficient market is one in which the spot market —fully

reflects“the available information and no one can consistently make profits and futures

eliminate the possibility of guaranteed profits. An efficient market would provide reliable

forecasts of spot prices in future. This would also provide export-import oriented firms

with better risk management capabilities.

There has also been a debate in Indian Parliament regarding commodity futures markets

affecting inflation in economy. After the reintroduction of commodity markets in 2002-

03, there have been a few studies on commodity futures market in India. With

tremendous growth in commodity markets, it would be desirable to test the efficiency of

the commodity futures markets.

As a result of the revival of commodity futures in a big way in 2003, the nature of

commodity trade in India has undergone a sea change. Going by trade volume and also

possibly as an identifiable influence on the price-making processes with respect to the

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traded commodities, both the futures market and actual merchandising have undergone a

big change. The disproportionately large size of the former compared to the latter

underlines the financial market character of the futures trade. Not surprisingly, for the

majority of the futures traders, the physical commodities seem to be, in effect, no more

than the denominator in terms of which the deals are expressed, as they switch from one

commodity to another very easily as demanded by their financial calculus – a case of

instant business substitutability! A mind-boggling amount of financial resources have

been deployed in these markets. Consequently the form, purpose, volume and modus

operandi of the commodity trade, along with its role and impact on the economy at the

macro, sector-specific, regional and local levels and in socio-economic terms, no longer

retain their conventional patterns associated largely with physical merchandising. Hence

there is a need for a fresh look at the futures markets and the policy decisions that led to

their present enormous size, especially in view of the recent controversy regarding their

role in accentuating inflationary pressures in 2006-07. Prior to attempting such an

examination, it may be pointed out that trade in general and commodity futures in

particular have not attracted much academic attention and remain a somewhat opaque

area of the economy.

India has three national level multi commodity exchanges with electronic trading and

settlement systems. The National Commodity and Derivative Exchange (NCDEX). The

Multi Commodity Exchange of India (MCX) and the National Multi Commodity

Exchange of India (NMCE) the National Board of Trading in Derivatives (NBOT), offers

trading on a national level, but is not completely online. Currently, the annual value of all

commodity futures traded in India is $135 billion, far less than the potential $ 600 billion.

What is significant, however, is the speed at which the gap is being narrowed.Volumes in

commodity futures have perked up from Rs 20,000 crore to 30,000 crore per annum

before the liberalization of futures trading to around Rs 5.71 lakh crore per annum by the

end of 2004.

Commodities’ trading is now one of the hottest games in town. Volumes grew by 900

percent between financial years 2005-2006 and 2006-2007. The growth of the

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commodities business has been beyond what was originally projected. With national level

exchanges like Multi Commodity Exchange of India (MCX) and the National

Commodities Derivatives Exchange (NCDEX) of full-fledged commercial operations, the

growth in commodities futures trading is almost as spectacular as India’s success in

business process outsourcing. A large potion of daily trading volumes in commodity

futures is concentrated in a handful of commodities like precious metals (primarily gold

and silver), Soya and its derivatives.

The commodity market is a market where forwards, futures and options contracts are

traded on commodities. Commodity markets have registered a remarkable growth in

recent years. The stage is now set for banks to trade in commodity futures. This could

help producers of agricultural products bankers and other participants of the commodity

markets. Banks have started acknowledging the commodity derivatives market. In this

context the Punjab National Bank and the Corporation Bank have sanctioned loans worth

Rs 50 crore to commodity futures traders over the past six months. However, the loans

are not given to pure speculators. A precondition for the loans is that the futures contract

must result in the delivery of the commodity.

Commodity exchanges in India are expected to contribute significantly in strengthening

Indian economy to face the challenges of globalization. Indian markets are poised to

witness further developments in the areas of electronic warehouse receipts (equivalent of

dematerialized shares), which would facilitate seamless nationwide spot market for

commodities.

Sugar

With over 450 sugar mills, India is the largest sugar producer in the world. Over 11

million tons of refined sugar is produced, accounting for 60% of the total sugar cane

cultivated. Following is the Indian export statistics for sugarcane that counts to about

811027.5 M. Tonnes in the year 2000- 2001.

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The first prerequisite of decontrol -commencement of futures trading in sugar - has

already been fulfilled by NCDEX. Futures trading in Sugar commenced on National

Commodity & Derivatives Exchange Limited (NCDEX) on July 27, 2004. The

Government should now announce decontrol of sugar industry by way of dismantling the

sugar release mechanism immediately now that futures trading in sugar is available to the

industry on a national level exchange like NCDEX.

Regular options trade on futures contracts having March, May, July and October delivery

periods as well as a January expiration option which is based upon the March futures

contract. Serial options are short-life options contracts providing additional option

expirations on existing futures contracts. Perhaps the greatest change in the international

sugar trade has been the trend toward price stabilization. Historically at the mercy of

everything from war to weather, the price of sugar has always been extremely volatile.

Soy bean In India Madhya Pradesh, Maharashtra, Rajasthan and Andhra Pradesh are the major

producers of soybeans. Madhya Pradesh tops the list. Nearly 88% of soyabean is

produced in the state. During 1997-98 total soyabean production in the state was 49.19

metric tonnes which was about 84.2% of the total produce. The domestic market is

improving a lot. Some years back, the (DOC) De-oiled Cake consumption of the soybean

was 10% of the total production. But now it is 25%. It is increasing because of the rise in

cattle population in the country, which in turn results in high consumption. The

remaining 75% is exported and the industry is earning nearly Rs 3,000 crore annually

through exports. Futures trading in soy bean commenced on National Commodity &

Derivatives Exchange Limited (NCDEX) on December 15, 2003.

Chana

India accounted for 60-70% of world production during this period. Production in India

was variable, which was the main reason for the large range in world production.

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On average, world production consisted of about 75% desi type and 25% kabuli type.

Production of the kabuli type is more dispersed and therefore less variable than for the

desi type. Futures trading in chana commenced on National Commodity & Derivatives

Exchange Limited (NCDEX) on April 12, 2004.

Trading Systems in Exchanges:

Trading in commodity futures took place just the way the physical commodities

themselves have always traded, through an “open outcry” system. Of late, however, there

is a distinct move towards “de-materialization” or online electronic trading. Three of the

four major national-level exchanges use screen-based electronic trading and the oldest

(NBOT) is moving towards it as well. In most of the other regional exchanges, trading

takes place primarily through an open outcry system.

Apart from the trading that goes on in the exchanges, there is a significant gray market

outside the exchanges where futures change hands. According to some estimates, trading

in the gray market may account for as much as 25-30% of the total futures trading in

India.

A complex and potentially problematic part of futures trading is the settlement of futures

contracts. It must be borne in mind, that a relatively small fraction of the futures traded

actually come up for delivery – most are “squared off” before maturity. For those sellers

who intend to deliver on their contracts exchanges follow more or less the same system.

Usually about a week before the maturity of the futures contract, the sellers and buyers

have to notify the exchange whether they want to deliver/take delivery on the contract or

“square it off” on maturity, i.e. pay/accept cash. The exchange then matches up the

buyers and sellers intending on making delivery. The actual delivery almost always takes

the form of warehousing receipts. A warehousing receipt is a receipt issued by a

government recognized warehouse, certifying that a certain quantity of an agricultural

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commodity is kept in storage there. The receipt itself is negotiable and is acceptable as

settlement of claims.

Margins in India typically fall in the 5-10% range and one can start trading in

commodities with as low a balance as Rs. 5,000. In addition there are brokerage and other

fees. Brokerage charges usually range from 0.10-0.25 per cent of the contract value and

generally higher for a contract resulting in delivery. There are also transaction charges of

approximately Rs 6 to Rs 10 per contract. The brokerage varies from commodity to

commodity and is below maximum limits set by the relevant exchange.

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Literature review The relationship between spot and futures market has been the focus of much literature

for some time. This include the fact that futures markets tend to have less trading

constraints than the cash markets, leading to future markets being more informational

efficient as the marginal cost from trading will be less than in the cash markets. This is

further compounded by the fact that futures market tend to have lower transaction cost

and higher liquidity. There is wide body of research which clearly indicates futures

market lead spot market and suggest that this provides evidence of futures markets are

acting as a vehicle for price discovery within the corresponding spot markets.

PAST STUDIES

1. Commodity Futures Market Efficiency in India and Effect on Inflation by

Gaurav Raizada, Gurpreet Singh Sahi

Abstract The paper aims to study the commodity futures market efficiency in India and analyzing

its effect on social welfare and inflation in the economy. The wheat futures market at

National Commodity & Derivatives Exchange Ltd. (NCDEX) has been studied and

efficiency has been estimated through Johansen‘s Co-integration approach for different

futures forecasting horizons ranging from one week to three months. The commodity

futures market is not efficient even in the short run. The social loss statistic also indicates

poor price discovery. The growth in commodity futures markets volumes also has a

significant impact on the inflation in the economy.

Methodology

A non-stationary time series is said to be integrated in order one, often denoted by I(1), if

the series is stationary after the first-order differencing. The theory of co-integration

applies to the study of testing the efficiency of a futures market where, St is the spot price

at time t and Ft-i is futures price taken at i periods before the contract matures at time t

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and i is the number of periods to maturity. If the futures price can prove some prediction

of the spot price i periods ahead, then some linear combination of St and Ft-i is expected

to be stationary, in the sense that there exists a and b such that zt is stationary with mean

0.

If both St and Ft-i are I(1), the co-integration of the vector (St,Ft-i) is a necessary

condition for market efficiency (Lai and Lai, 1991). Co-integration ensures that there

exists a long-run equilibrium relationship between the two series, spot and futures. If St

and Ft-i are not co-integrated, they will move without bound, as a result futures price

would provide no or little information about the movement of the spot price. In addition

to co-integration, tests of market efficiency also requires that futures price must be an

unbiased predictor of spot price i.e. a=0 and b=1 in equation (1).

In effect, the market efficiency should be tested in two steps; first to examine the co-

integration between the two price series St and Ft-I; if co-integration exists then the

parameters restriction a=0 and b=1 is tested. The second step may consist of multiple

tests: a=0 and b=1 jointly or individually for different time series. The constraint b=1 is

more important indicator for market efficiency, because a is non-zero under the existence

of risk premium and/or transportation costs even when the market is efficient. The co-

integration relationship and the parameter restrictions can be tested using Johansen‘s

approach and standard likelihood ratio test.

Initially each individual price series is examined for stationarity. The stationarity is

checked using the Augmented Dickey-Fuller (ADF) unit root tests. If both the

futures price and spot prices are I (1), then Johansen‘s co-integration tests are

conducted. Consider a general kth

order VAR model.

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where Yt is an (nx1) vector to be tested for co-integration and xYt = Yt -Yt-1 is the

deterministic term which may take different forms such as a vector of zeros or non-zero

constants depending on properties of the data to be tested; x and x are matrices of

coefficients; and k is chosen so that t (the errors) is a multivariate normal white noise

process with mean 0 and finite covariance matrix.

The co-integration relationship can be detected by examining the rank of the coefficient

matrix x, because the number of co integration vectors equals the rank of x. In particular,

the 0 rank i.e. x= 0 ---implies no co integration. In a bi-variable case, i.e., n=2, the two

variable are co integrated only if the rank of = equals 1 (Johansen and Juselius, 1990).

Johansen (1988) suggested two test statistics to test the null hypothesis that there are at

most r co integration vectors. The null hypothesis can be equivalently stated as the rank

of x is at most r, for r = 0,1..,n-1. The two test statistics are based on trace and maximum

eigenvalues, respectively,

where 1…… r are the r largest squared canonical correlations between the residuals

obtained by regressing ΔYt and Yt-1 on ΔYt-1, ΔYt-2… ΔYt-k-1 and 1 respectively.

In our test for efficiency of futures market, Y = (S ,F )

, n = 2, and the null hypothesis should

be tested for r =

0 and r = 1. If r = 0 cannot be rejected, we will conclude that there is no cointegration

vector, and therefore, no cointegration. On the other hand, if r = 0 is rejected, and r = 1

cannot be rejected, we conclude that there is a cointegration relationship.

Tests of Restrictions on Cointegration Vectors

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If the futures price and the spot price are not cointegrated, inefficiency can be concluded

since cointegration is a necessary condition for market efficiency. If the futures price and

the spot market price are cointegrated, then and only then can we test restrictions on the

parameters in equation (1).

'* β Y

t

Cointegration implies that there exists a cointegration vector Y such that is stationary,

where in the case

*' '*'β = (1,−b,−a) Y = (S , F ,1) z = β Y

of equation (1), and t tt −i

, so that tt

is stationary.

The market efficiency hypotheses can therefore be tested by imposing

restrictions on the cointegration'

β = (1,−1,−0)

vector Y. For example, the hypothesis of a=0 and b=1 can be expressed as . We can then

apply the standard likelihood ratio test in this case. The test statistics is twice the negative

log ratio of the two maximum likelihood values under the restricted model versus the full

model. Specifically, the test statistics can be expressed by the canonical correlations as

(Johansen and Juselius, 1990):

where

λ1…..

λr are the r largest squared canonical correlations under the null hypothesis,

i.e., the restricted model; and 1… are the r largest squared canonical correlations under

the full or unrestricted model. The test statistic follows an asymptotic {2

distribution with

degree of freedom equaling the number of restrictions imposed. When we fit the VECM

model, in case the price series are cointegrated, and weak exogeneity test is performed to

determine whether {i=0, Weak exogeneity means that there is no information about {i in

the marginal model or that one set of variables do not react to disequilibrium.

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Test of social loss

Stein (1991) has proposed that if the there is mispricing of futures i.e. there is a forecast

error FE where

where FE (i) is i.i.d. with a zero expectation. Then the evaluation of the performance of

such speculative markets is based upon the social welfare generated by different

intertemporal allocations of resources. Welfare is evaluated in terms of the present value

of the utility of per capita consumption.

where MSE(i)=E(FE(i))2

. MSE (j) is the unavoidable error in pricing the futures. We

believe that for the Indian market one week prior to expiration of contract the participants

will know as much about the expected spot price as they ever will and hence MSE (1

week) will be social loss due to an unavoidable error by the rational participants. MSE (i)

refers to the social loss for the commodity where the futures price has a maturity i months

in the future. Lower the value of SL better is the market functioning. This statistic is

compared with critical value of F statistic to test the null hypothesis that there is no social

loss.

Test of inflation

Subject to the futures market being inefficient and the subsequent mispricing leading to a

social loss in terms of welfare, regression for testing the hypothesis that mispricing of

commodity futures contracts leads to inflation can be performed. For this wholesale price

index inflation can be regressed on the growth in volumes of trade in leading two futures

exchanges in India (NCDEX and MCX), growth in money supply (M3) and growth in oil

prices index. The latter two are perceived to be important determinants of inflation in an

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economy. The null hypothesis that inflation is caused by the growth in volume of trade in

futures market can be rejected in case the coefficient corresponding to the same in

significant in the regression.

Data

Only three month wheat futures at NCDEX have been included in this study of the

commodity futures market. The spot market rates and the futures prices have been taken

from the NCDEX database. Daily spot and futures prices from July 2004 to July 2006

provided by NCDEX online database have been used for the study. There are three

contracts running simultaneously for wheat futures and twelve contracts each year. The

daily closing prices have been taken to be spot prices. Futures market efficiency has been

tested for five horizons œ one week, two weeks, one month, two months, three months

prior to maturity of each contract. For every horizon, there is one spot price series and

one future price series, a total of ten, five spot price series and five futures prices series

for the study. For NCDEX the contracts start on 21st

of a month and end on 20th

of the

third month.

For the estimation of inflation, the data for monthly volumes of the commodity traded has

been taken from NCDEX and MCX data. The data for oil index, WPI inflation and M3

money supply has been taken from the Reserve Bank of India (RBI) database.

Conclusion

The formal statistical tests on the efficiency of the commodity futures markets show that

it is not even weakly efficient in the short term. The weak exogeneity of the spot price

shows that spot leads the futures price determination and that futures market are not

performing their main role of allowing for price discovery. The social loss statistics for

commodities futures market indicate a poor price discovery process as well. The social

loss statistics for pre-futures and post-futures needs to be determined for further insight.

The regression for inflationary effects of commodity futures markets provides significant

results. It can be said that inflation is persistent as it depends on its past values. The

inflationary effect of rising crude prices has not been observed as its prices are

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administered by the government. The commodity futures market trade volumes and

Money Supply have significant impact on inflation. The maturity of commodity futures

markets in times to come will allow for efficient price discovery and reducing the

inflationary impact on economy as well.

2.EFFICIENCY OF INDIAN STOCK MARKET by Anand Pandey Abstract Market efficiency has an influence on the investment strategy of an investor because if

market is efficient, trying to pickup winners will be a waste of time. In an efficient

market there will be no undervalued securities offering higher than deserved expected

returns, given their risk. On the other hand if markets are not efficient, excess returns can

be made by correctly picking the winners. In this paper, an analysis of three popular stock

indices is carried out to test the efficiency level in Indian Stock market and the random

walk nature of the stock market by using the run test and the autocorrelation function

ACF (k) for the period from January 1996 to June 2002. The study carried out in this

paper has presented the evidence of the inefficient form of the Indian Stock Market. From

autocorrelation analyses and runs test we are able to conclude that the series of stock

indices in the India Stock Market are biased random time series. The auto correlation

analysis indicates that the behavior of share prices does not confirm the applicability of

the random walk model in the India stock market. Thus there are undervalued securities

in the market and the investors can always excess returns by correctly picking them.

METHEDOLOGY

Since the test of weak form of EMH, in general, have come from the random walk

literature, so I am interested in testing whether or not successive price changes were

independent of each other. In this paper, I will use Autocorrelation and Runs Test for

testing the efficiency of the stock market.

Autocorrelation ACF (k)

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M.P.Birla Institute of management 24

Autocorrelation is one of the statistical tools used for measuring the dependence of

successive terms in a given time series. Therefore it is used for measuring the dependence

of successive share price changes. It is the basic tool used to test the weak form of EMH.

The autocorrelation function ACF(k) for the time series Yt and the k-lagged series Yt-k is

defined as :-

where _y is the overall mean of the series with n observations.

The standard error of ACF(k) is given by:

where n is sufficiently large (n _ 50), the approximate value of the standard

error of ACF(k) is given by:-

To test whether ACF (k) is significantly different from zero, the following distribution of

't' is used, i.e. t=ACF (k)/ Se ACF(k). For both random variable series and series with

trends, ACF (k) are very high and decline slowly as the lag value (k) increases. At the

same time the ACF (k) of the first difference series (price changes or returns) are

statistically insignificant when the series is a random walk series. A random walk series

drifts up and down over time. In some situation it may be difficult to judge whether a

trend or drift is occurring. Hence to determine whether a series has significant trend or

whether it is a random walk, the t-test is applied on the series of first differences.

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Run Test Run test is a non-parametric test. It depends only on the sign of the price changes but not

on the magnitude of the price. It does not require the specification of the probability

distribution. It depends only on the sign of the price. They are essentially concerned with

the direction of changes in the time series. " A Run test may be defined as a sequence of

price changes of the same sign preceded and followed by price changes of different sign."

In a given time series of stock prices there are three possible types of price changes,

namely positive, negative and no change. This gives three types of runs. A positive

(negative) run is a sequence of positive (negative) price changes preceded and succeeded

by either negative (positive) or zero price change. Similarly, a zero run is sequence of

zero price changes preceded and succeeded by either negative or positive price change.

Under the hypothesis that the successive price changes are independent and the sample

proportion of positive, negative and zero price changes are unbiased estimates of the

population proportions, the expected number of runs of all the types is computed as

follows, (by Wallis, Robert (1956)).

where M = Expected number of runs,

ni = Number of price changes of each sign (i = 1,2,3) and

N = Total number of price changes = n1 + n2 + n3

The standard error of the expected number of runs of all signs may be obtained as :-

When N is sufficiently large, the sampling distribution of expected number of runs of all

types is approximately normally distributed with mean M and standard error _m .

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DATA

The sample period is January 1996 to June 2002. The data consist of daily

and weekly closing values of three leading stock indices namely CNX defty,

CNX Nifty, CNX Nifty Junior.

CONCLUSION The assumption that the stock prices are random is basic to the Efficient Market

Hypothesis and Capital Asset Pricing Models. The study carried out in this paper has

presented the evidence of the inefficient form of the Indian Stock Market. From

autocorrelation analyses and runs test we are able to conclude that the series of stock

indices in the India Stock Market are biased random time series. The auto correlation

analysis indicates that the behavior of share prices does not confirm the applicability of

the random walk model in the Indian stock market. Thus there are undervalued securities

in the market and the investors can always make excess returns by correctly picking

them.

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RESEARCH METHODOLOGY

HYPOTHESIS STATEMENT COINTEGARTION TEST HYPOTHESIS STATEMENT Ho: There is no significant co-integration between spot and futures markets and the

market is not efficient.

H1: There is significant co-integration between spot and futures market and the market is

efficient

DATA COLLECTION

The spot market rates and the futures prices have been taken from the NCDEX database.

Daily spot and futures prices from July 2004 to march 2007 provided by NCDEX online

database have been used for the study. The daily closing prices have been taken to be

spot prices. Futures market efficiency has been tested. To test the efficiency, three

commodities spot prices and futures prices have been taken for the study. For NCDEX

the contracts start on 21st

of a month and end on 20th

of the third month.

The commodities considered for the study are soy bean, chana, sugar. Both closing and

future prices are obtained from official website NCDEX (www.ncdex.com).

DATA TYPE

The present research makes use of secondary data available in the NCDEX website

pertaining to the daily closing prices data of spot and futures.

DATA SAMPLE

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Daily spot and future prices of soy bean, chana, and sugar have been taken.

PERIOD OF SAMPLE

Daily observation from 27th july 2004 to 20th march 2007

STATISTICAL MODELS APPLIED

• Augmented Dickey Fuller test to test the stationary of the series.

• Granger’s co integration approach test for co integration between the series.

STATISTICAL SOFTTWARE PACKAGES USED

• E views

This software has been used to conduct the Augmented Dickey Fuller Unit root Test,

Johansen Co integration Test.

• SPSS

To test the data for skew ness and kurtosis and to find the data is normally distributed or

not, this software is used.

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METHODOLOGY

If the series is stationary after the first-order differencing. The theory of co-integration

applies to the study of testing the efficiency of a futures market where, St is the spot price

at time t and Ft-i is futures price taken at i periods before the contract matures at time t

and i is the number of periods to maturity. If the futures price can prove some prediction

of the spot price i periods ahead, then some linear combination of St and Ft-i is expected

to be stationary, in the sense that there exists a and b such that zt is stationary with mean

0.

z = S −a −bF (1)

tt t−i

If both St and Ft-i are I(1), the co-integration of the vector (St,Ft-i) is a necessary

condition for market efficiency (Lai and Lai, 1991). Co-integration ensures that there

exists a long-run equilibrium relationship between the two series, spot and futures. If St

and Ft-i are not co-integrated, they will move without bound, as a result futures price

would provide no or little information about the movement of the spot price. In addition

to co-integration, tests of market efficiency also requires that futures price must be an

unbiased predictor of spot price i.e. a=0 and b=1 in equation (1).

In effect, the market efficiency should be tested in two steps; first to examine the co-

integration between the two price series St and Ft-I; if co-integration exists then the

parameters restriction a=0 and b=1 is tested. The second step may consist of multiple

tests: a=0 and b=1 jointly or individually for different time series. The constraint b=1 is

more important indicator for market efficiency, because a is non-zero under the existence

of risk premium and or transportation costs even when the market is efficient. The co-

integration relationship and the parameter restrictions can be tested using Gangers co-

integration test approach.

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Initially each individual price series is examined for stationarity. The stationarity is

checked using the Augmented Dickey-Fuller (ADF) unit root tests. If both the

futures price and spot prices are I (1), then Gangers co-integration tests are

conducted.

The co-integration relationship can be detected by examining the rank of the coefficient

matrix x, because the number of co integration vectors equals the rank of x. In particular,

the 0 rank i.e. x= 0 ---implies no co integration. In a bi-variable case, i.e., n=2, the two

variable are co integrated only if the rank of = equals 1 (Johansen and Juselius, 1990).

Johansen (1988) suggested two test statistics to test the null hypothesis that there are at

most r co integration vectors. The null hypothesis can be equivalently stated as the rank

of x is at most r, for r = 0,1..,n-1. The two test statistics are based on trace and maximum

eigenvalues, respectively,

^ n

λtrace =−T ∑ln(1−λi) i=r +1 (3)

^ λ max =−T ln(1−λr+1) (4)

where 1…… r are the r largest squared canonical correlations between the residuals

obtained by regressing ΔYt and Yt-1 on ΔYt-1, ΔYt-2… ΔYt-k-1 and 1 respectively.

In our test for efficiency of futures market, Y = (S ,F )

, n = 2, and the null hypothesis should

be tested for r = 0 and r = 1. If r = 0 cannot be rejected, we will conclude that there is no

co-integration vector, and therefore, no co-integration. On the other hand, if r = 0 is

rejected, and r = 1 cannot be rejected, we conclude that there is a co-integration

relationship.

In this study, Gangers co-integration. Before doing co-integration analysis, it is necessary

to test whether the time series are stationary at levels by running Augmented Dickey

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fuller (ADF) test on the series. Because most time series are non stationary in levels, and

the original data need to be transformed to obtain stationary series.

STATIONARITY

According to Engle and Granger, a time series is said to be stationary if displacement

over time does not alter the characteristics of a series in a sense that probability

distribution remains constant over time. In other words, the mean, variance and co-

variance of the series should be constant over time. The degree of co-integration is

closely related with stationary.

The empirical works based on time series data assumes that the underlying time series is

stationary. In regressing a time series variable on another time series variables, one often

obtains a very high R2

(residuals) even though there is no meaningful relationship

between the two variables. This situation exemplifies the problem of spurious or

nonsense regression, which arises when data is non stationary.

A series is said to be integrated of order one [I (1)] if it has to be differentiated once

before becoming stationary. Similarly, a series is of order two [I(2)] if it has to be

differentiated twice before becoming stationary.

THEORY OF STATIONARITY

Following are different ways of examining about whether a time series variable Xt is

stationary or has a unit root:

• In the AR (1) model, if ρ =1, then X has a unit root. If ρ |< 1 then X is stationary.

• If X has a unit root, and then its autocorrelations will be near one and will not

drop much as a lag length increases.

• If X has a unit root, and then it will have a long memory. Stationary time series do

not have long memory.

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• If X has a unit root then the series will exhibit trend behavior.

• If X has a unit root, then ΔX will be stationary. For this reason, series with unit

root are often referred to as difference stationary series.

This means that if the appropriate order of the AR process is lag2 rather than lag1, the

term ΔYt-1 should be added to the regression model. A test of whether there is a unit root

can be carried out in the same way as for the ADF test, with the test statistics provided by

the ‘t’ statistics of the ρ coefficient. If ρ = 0 then there is a unit root. The same reasoning

can be extended for a generic AR (p) process.

TESTING STATIONARITY BY UNIT ROOT TEST OF DICKEY FULLER

HYPOTHESIS STATEMENT

H0: Series has Unit root : Non Stationary

H1: Series does not have Unit root : Stationary

Dickey Fuller test involve estimating regression equation and carrying out the hypothesis

test. The AR (1) process is….

Yt = C + ρYt-1

+ εt

Where c and …..are parameters and is to be white noise. If -1 < ρ < 1, then Y is

stationary series. While if ρ = 1, y is non stationary series. Therefore, the hypothesis of a

stationary series is involves whether the absolute value of b is strictly less than one. The

test is carried out by estimating an equation with Yt-1 subtracted from both sides of the

equation.

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Δyt = C + γt-1

+ εt

Where …… and the null and alternative hypotheses are

Ho: = 0 …..Non Stationary

H1: = 0 …..Stationary

The usual t-statistic under the null hypothesis of a unit root does not have the

conventional t-distribution. Dickey and fuller (1979) showed that the distribution under

the null hypothesis is nonstandard and simulated the critical values for selected sample

sizes. More recently, Mackinnon (19991) has implemented a much larger set of

simulations than those tabulated by Dickey and Fuller.

UNIT ROOT TEST BY AUGMENETD DICKEY FULLER TEST

The simple Unit root test is valid only if the series as an AR (1) Process. If the series is

correlated at high order lags, the assumption of white noise disturbances is violated. The

ADF controls for high- order correlation by adding lagged difference terms of the

dependent variable to the right-hand side of the regression

Δyt = C + γt-1

+ δ1Δ y

t-1 + δ

2Δ y

t-2 + …..+ δpΔ y

t-p + ε

t

This augmented specification is then tested

H0: = 0 Non Stationary

H1: = 0 Stationary

In general, the procedure start with whether the variables X and Y in its level form is

stationary. If the hypothesis is rejected, then the series is transformed into first difference

of the variable and tested for stationarity. If first difference series is stationary, this

implies that X and Y are I(1).

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GRANGERS CO-INTEGRATION TEST

Granger introduced the concept of co-integration when he wrote that two variables may

move together though individually they are non stationary. Co-integration is based on the

long run relationship between variables. The idea arises from considering equilibrium

relationships, where equilibrium is a stationary point characterized by forces that tend to

push the variables back toward equilibrium.

In general, if Yt and Xt are both integrated of order I(d), then any linear combination or

the two series will also be I(d).. That is, the residuals obtained on regressing Yt on Xt are

I(d).

If two or more series are co integrated then even though the series themselves may be non

stationary, they will move closely together over time and their difference will be

stationary. Their long run relationship is the equilibrium to which the system converges

overtime and the disturbance term Et can be construed as the disequilibrium error or the

distance that the system is away from equilibrium at time t

The Engle granger co integration test is a two step process:

1. First estimating an ordinary least square (OLS) regression on the data. A

regression of one integrated variable on the other integrated variables (x on y and y on x).

Yt = a + bx

t + e

t

X & Y will be co-integrated if and only if et is stationary.

2. Then testing these residuals from regression equation for stationarity using a

unit root test of ADF.

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Empirical results

Graphs showing daily price movements

Movement of future prices from 1st sep 2004 to

20th mar 2007

0

500

1000

1500

2000

1 49 97 145 193 241 289 337 385 433 481 529 577 625 673 721

No.of observations

soy be

an

log natural for the above data

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

1 49 97 145 193 241 289 337 385 433 481 529 577 625 673 721

No.of observations

soy

bean

INTERPRETATION The above graphs show the daily price movements of soy bean in futures market from 1st

sep 2004 to 20th mar 2007. These movements show that the volatility in the series since

they are showing a upward trend as the time changing. This data has been further tested

for stationarity.

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Movement of spot prices from 1st sep 2004 to 20th mar 2007

0200400600800

100012001400160018002000

1 50 99 148 197 246 295 344 393 442 491 540 589 638 687 736

No.of observations

soy be

an

Log naturals for the above data

-0.16-0.14-0.12

-0.1-0.08-0.06-0.04-0.02

00.020.040.06

1 55 109 163 217 271 325 379 433 487 541 595 649 703

No.of observations

soy

bean

INTERPRETATION The above graphs show the daily price movements of soy bean in spot market from 1st

sep 2004 to 20th mar 2007. These movements show that the volatility in the series since

they are showing a upward trend as the time changing. In this the graph shows initially

the prices are highly volatile. This data has been further tested for stationarity.

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Movement of future prices from 21st oct 2004 to 20th mar 2007

0500

100015002000250030003500

1 47 93 139 185 231 277 323 369 415 461 507 553 599 645 691

No.of observations

chan

a

Log naturals for the above data

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

1 47 93 139 185 231 277 323 369 415 461 507 553 599 645 691

No.of observations

chan

a

INTERPRETATION The above graphs show the daily price movements of chana in futures market from 21st

oct 2004 to 20th mar 2007. These movements show that the volatility in the series since

they are showing a upward trend as the time changing. This data has been further tested

for stationarity.

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Movement of spot prices from 21st oct 2004 to 20th mar 2007

0500

100015002000250030003500

1 47 93 139 185 231 277 323 369 415 461 507 553 599 645 691

No.of observations

chan

a

Log naturals for the above data

-0.08-0.06-0.04-0.02

00.020.040.060.08

1 47 93 139 185 231 277 323 369 415 461 507 553 599 645 691

No.of observations

chan

a

INTERPRETATION The above graphs show the daily price movements of chana in spot market from 21st oct

2004 to 20th mar 2007. These movements show that the volatility in the series since they

are showing a upward trend as the time changing. This data has been further tested for

stationarity.

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Movement of future prices for the above period

0

500

1000

1500

2000

2500

1 28 55 82 109 136 163 190 217 244 271 298 325 352 379 406

No.of observations

suga

r

Log naturals for the above period

-0.04-0.03-0.02-0.01

00.010.020.030.040.05

1 28 55 82 109 136 163 190 217 244 271 298 325 352 379 406

No.of observations

suga

r

INTERPRETATION The above graphs show the daily price movements of sugar in futures market from 21st

oct 2004 to 20th mar 2007. These movements show that the volatility in the series since

they are showing a upward trend as the time changing. This data has been further tested

for stationarity.

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Movement of spot prices

0

500

1000

1500

2000

2500

1 28 55 82 109 136 163 190 217 244 271 298 325 352 379 406

No.of observations

suga

r

Log naturals for the above data

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

1 28 55 82 109 136 163 190 217 244 271 298 325 352 379 406

No.of observations

suga

r

INTERPRETATION The above graphs show the daily price movements of sugar in spot market from 21st oct

2004 to 20th mar 2007. These movements show that the volatility in the series since they

are showing a upward trend as the time changing. This data has been further tested for

stationarity.

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ADF UNIT ROOT TEST RESULTS FOR STATIONARITY OF THE SERIES AT LEVELS H0 = Unit root : Non Stationary H1 = No Unit root : Stationary Table 1 ADF Test Statistic -10.82136 1% Critical Value* -3.4418

Soy bean future prices 5% Critical Value -2.8658

10% Critical Value -2.5691

Table 2 ADF Test Statistic -9.170110 1% Critical Value* -3.4418

Soy bean spot prices 5% Critical Value -2.8658

10% Critical Value -2.5691

INTERPRETATION The ADF test has been conducted on both the future and spot time series at their levels.

The first order difference data is taken for the unit root test to test the stationarity. ADF

values for the SOY BEAN future price is -10.82136, spot price is -9.170110. The results

show that the null hypothesis is rejected since ADF calculated values for future and spot

series are lesser than the critical values at all the levels (1%, 5%, 10%). There exists no

unit root in the series. Therefore, both the series are Stationary.

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Table 3 ADF Test Statistic -11.40149 1% Critical Value* -3.4420

Chana future prices 5% Critical Value -2.8659

10% Critical Value -2.5691

Table 4 ADF Test Statistic -12.47645 1% Critical Value* -3.4420

Chana spot prices 5% Critical Value -2.8659

10% Critical Value -2.5691

INTERPRETATION The ADF test has been conducted on both the future and spot time series at their levels.

The first order difference data is taken for the unit root test to test the stationarity. ADF

values for the CHANA future price is -11.40149, spot price is -12.47645. The results

show that the null hypothesis is rejected since ADF calculated values for future and spot

series are lesser than the critical values at all the levels (1%, 5%, 10%). There exists no

unit root in the series. Therefore, both the series are Stationary.

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Table 5

ADF Test Statistic -8.060243 1% Critical Value* -3.4483

Sugar future prices 5% Critical Value -2.8688

10% Critical Value -2.5706

Table 6

ADF Test Statistic -8.193794 1% Critical Value* -3.4483

Sugar spot prices 5% Critical Value -2.8688

10% Critical Value -2.5706

INTERPRETATION The ADF test has been conducted on both the future and spot time series at their levels.

The first order difference data is taken for the unit root test to test the stationarity. ADF

values for the SUGAR future price is -8.060243, spot price is -8.193794.The results

show that the null hypothesis is rejected since ADF calculated values for future and spot

series are lesser than the critical values at all the levels (1%, 5%, 10%). There exists no

unit root in the series. Therefore, both the series are Stationary.

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RESIDUAL BASED GARNGER’S CO INTEGRATION TEST After obtaining the stationarity of the series at their first order difference, next residual

based granger’s co integration test has been conducted at their levels to know the long

run relationship between the future prices and spot prices. The residuals are obtained by

following the granger’s Ordinary Least Square method.

Residuals for Spot e

t = S

t -α - β F

t ------------------------(1) Residuals for futures e

t = F

t -α - β S

t ----------------------(2)

In the above equations α and β are the regression coefficients which are obtained by

regressing the spot prices against the futures prices. The regression coefficient β is

positive for both the series which gives a some idea that they are positively co integrated.

After obtaining the regression coefficients, the residuals are obtained form the equation

(1) and (2). But this relationship has been further studied by following ADF test.

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FOR RESIDUAL SERIES ADF UNIT ROOT TEST RESULTS FOR STATIONARITY OF THE SERIES AT LEVELS H0 = Unit root : Non Stationary H1 = No Unit root : Stationary Table 7 ADF Test Statistic -9.620079 1% Critical Value* -3.4437

Soy bean spot prices 5% Critical Value -2.8667

10% Critical Value -2.5695

Table 8 ADF Test Statistic -8.340894 1% Critical Value* -3.4437

Soy bean future prices 5% Critical Value -2.8667

10% Critical Value -2.5695

INTERPRETATION The above Table 7&8 shows the results regarding the ADF test statistics obtained for residuals obtained from the Granger’s Co integration Test .The ADF Test has been conducted to check the unit root in the series. The ADF test statistics calculated for soy bean spot prices are -9.620079, future prices are -8.340894. These calculated values are lesser than the Mac Kinnon Critical values at all the levels (1%, 5%, and 10%). This shows that the null hypotheses of Unit root is rejected at all the levels. Therefore the both the series are Stationary which shows that the series are co integrated.

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Table 9 ADF Test Statistic -10.42985 1% Critical Value* -3.4437

Chana spot prices 5% Critical Value -2.8667

10% Critical Value -2.5695

Table 10 ADF Test Statistic -11.18795 1% Critical Value* -3.4437

Chana future prices 5% Critical Value -2.8667

10% Critical Value -2.5695

INTERPRETATION The above Table 9&10 shows the results regarding the ADF test statistics obtained for

residuals obtained from the Granger’s Co integration Test .The ADF Test has been

conducted to check the unit root in the series. The ADF test statistics calculated for chana

spot prices are -10.42985, future prices are -11.18795. These calculated values are lesser

than the Mac Kinnon Critical values at all the levels (1%, 5%, and 10%). This shows that

the null hypotheses of Unit root is rejected at all the levels. Therefore the both the series

are Stationary which shows that the series are co integrated.

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Table 11

ADF Test Statistic -8.060243 1% Critical

Value* -3.4483

Sugar spot prices 5% Critical Value -2.8688

10% Critical Value -2.5706

Table 12

ADF Test Statistic -8.214633 1% Critical Value* -3.4483

Sugar future prices 5% Critical Value -2.8688

10% Critical Value -2.5706

INTERPRETATION The above Table 9&10 shows the results regarding the ADF test statistics obtained for

residuals obtained from the Granger’s Co integration Test .The ADF Test has been

conducted to check the unit root in the series. The ADF test statistics calculated for sugar

spot prices are -8.060243, future prices are -8.214633. These calculated values are lesser

than the Mac Kinnon Critical values at all the levels (1%, 5%, and 10%). This shows that

the null hypotheses of Unit root is rejected at all the levels. Therefore the both the series

are Stationary which shows that the series are co integrated.

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CONCLUSION The empirical results of the study show that the there exists a long run equilibrium

relationship between NCDEX Spot and futures. This long run relationship between

the prices of these three commodities is evidenced by the Granger’s Co integration

Test. These tests show positive results towards co integration between NCDEX

Spot Prices and Futures prices for the three commodities.

So finally we can conclude that the Future market is efficient in discovering the

Future Spot price compared to Spot market.

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BIBLIOGRAPHY REFERNCE BOOKS

Basic Econometrics - Damodar N.Gujarati, (fourth edition) Options and Futures . H C Hull

WEBSITES

www.ncdex.com www.finance.yahoo.com www.google.com www.mcx.com

REFERNCE ARTICLES

Commodity Futures market Efficiency In India and Effect on Inflation - by Gavrav Raizada, Gurupreet Singh Sahi---2006.

Efficiency of Indian Stock Market - by Anand Pandey---2003.

Commodity Futures in India - by Kamal Nayan Kabra---2007.

Commodity futures in India – by Rajesh Chakrabarthy.

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Annexures Table1 ADF results for Soy bean future prices ADF Test Statistic -10.82136 1% Critical Value* -3.4418

5% Critical Value -2.8658 10% Critical Value -2.5691

*MacKinnon critical values for rejection of hypothesis of a unit root.

Augmented Dickey-Fuller Test Equation Dependent Variable: D(SER01) Method: Least Squares Date: 05/15/07 Time: 11:11 Sample(adjusted): 6 743 Included observations: 738 after adjusting endpoints

Variable Coefficient Std. Error t-Statistic Prob. SER01(-1) -0.811671 0.075006 -10.82136 0.0000

D(SER01(-1)) -0.150657 0.068879 -2.187254 0.0290D(SER01(-2)) -0.110119 0.061064 -1.803332 0.0717D(SER01(-3)) -0.068128 0.050993 -1.336029 0.1820D(SER01(-4)) -0.016967 0.036829 -0.460700 0.6452

C 6.54E-05 0.000354 0.184888 0.8534R-squared 0.483332 Mean dependent var -2.34E-05Adjusted R-squared 0.479803 S.D. dependent var 0.013317S.E. of regression 0.009605 Akaike info criterion -6.444971Sum squared resid 0.067531 Schwarz criterion -6.407540Log likelihood 2384.194 F-statistic 136.9543Durbin-Watson stat 2.000420 Prob(F-statistic) 0.000000

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Table 2 ADF results for Soy bean spot prices ADF Test Statistic -9.170110 1% Critical Value* -3.4418

5% Critical Value -2.8658 10% Critical Value -2.5691

*MacKinnon critical values for rejection of hypothesis of a unit root.

Augmented Dickey-Fuller Test Equation Dependent Variable: D(SER02) Method: Least Squares Date: 05/15/07 Time: 11:13 Sample(adjusted): 6 743 Included observations: 738 after adjusting endpoints

Variable Coefficient Std. Error t-Statistic Prob. SER02(-1) -0.575519 0.062760 -9.170110 0.0000

D(SER02(-1)) -0.152454 0.060501 -2.519873 0.0120D(SER02(-2)) -0.209264 0.052940 -3.952825 0.0001D(SER02(-3)) -0.229862 0.044947 -5.114073 0.0000D(SER02(-4)) -0.042884 0.036955 -1.160453 0.2462

C -0.000149 0.000377 -0.395524 0.6926R-squared 0.395039 Mean dependent var 6.29E-06Adjusted R-squared 0.390907 S.D. dependent var 0.013101S.E. of regression 0.010225 Akaike info criterion -6.319954Sum squared resid 0.076524 Schwarz criterion -6.282524Log likelihood 2338.063 F-statistic 95.59905Durbin-Watson stat 2.007061 Prob(F-statistic) 0.000000

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Table 3 ADF results for Chana future prices ADF Test Statistic -11.40149 1% Critical Value* -3.4420

5% Critical Value -2.8659 10% Critical Value -2.5691

*MacKinnon critical values for rejection of hypothesis of a unit root.

Augmented Dickey-Fuller Test Equation Dependent Variable: D(SER03) Method: Least Squares Date: 05/15/07 Time: 11:17 Sample(adjusted): 6 725 Included observations: 720 after adjusting endpoints

Variable Coefficient Std. Error t-Statistic Prob. SER03(-1) -0.928633 0.081448 -11.40149 0.0000

D(SER03(-1)) -0.030327 0.072510 -0.418252 0.6759D(SER03(-2)) -0.019907 0.063081 -0.315575 0.7524D(SER03(-3)) -0.018850 0.052008 -0.362441 0.7171D(SER03(-4)) -0.052916 0.037536 -1.409758 0.1590

C 0.000654 0.000627 1.043321 0.2972R-squared 0.480534 Mean dependent var 8.31E-05Adjusted R-squared 0.476896 S.D. dependent var 0.023192S.E. of regression 0.016774 Akaike info criterion -5.329699Sum squared resid 0.200891 Schwarz criterion -5.291538Log likelihood 1924.692 F-statistic 132.0975Durbin-Watson stat 1.992918 Prob(F-statistic) 0.000000

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Table 4 ADF results for Chana spot prices ADF Test Statistic -12.47645 1% Critical Value* -3.4420

5% Critical Value -2.8659 10% Critical Value -2.5691

*MacKinnon critical values for rejection of hypothesis of a unit root.

Augmented Dickey-Fuller Test Equation Dependent Variable: D(SER04) Method: Least Squares Date: 05/15/07 Time: 11:19 Sample(adjusted): 6 725 Included observations: 720 after adjusting endpoints

Variable Coefficient Std. Error t-Statistic Prob. SER04(-1) -0.929216 0.074478 -12.47645 0.0000

D(SER04(-1)) 0.091146 0.065875 1.383621 0.1669D(SER04(-2)) 0.076553 0.058169 1.316044 0.1886D(SER04(-3)) 0.100306 0.048847 2.053470 0.0404D(SER04(-4)) -0.002268 0.037632 -0.060270 0.9520

C 0.000561 0.000548 1.024781 0.3058R-squared 0.426575 Mean dependent var -2.54E-06Adjusted R-squared 0.422560 S.D. dependent var 0.019264S.E. of regression 0.014639 Akaike info criterion -5.601999Sum squared resid 0.153004 Schwarz criterion -5.563838Log likelihood 2022.719 F-statistic 106.2300Durbin-Watson stat 1.995436 Prob(F-statistic) 0.000000

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Table 5 ADF results for Sugar spot prices ADF Test Statistic -8.193794 1% Critical Value* -3.4483

5% Critical Value -2.8688 10% Critical Value -2.5706

*MacKinnon critical values for rejection of hypothesis of a unit root.

Augmented Dickey-Fuller Test Equation Dependent Variable: D(SER05) Method: Least Squares Date: 05/15/07 Time: 11:21 Sample(adjusted): 6 417 Included observations: 412 after adjusting endpoints

Variable Coefficient Std. Error t-Statistic Prob. SER05(-1) -0.620464 0.075724 -8.193794 0.0000

D(SER05(-1)) -0.045418 0.073094 -0.621358 0.5347D(SER05(-2)) -0.044583 0.067991 -0.655720 0.5124D(SER05(-3)) 0.078300 0.059691 1.311758 0.1903D(SER05(-4)) 0.069844 0.049908 1.399460 0.1624

C 0.000371 0.000266 1.397545 0.1630R-squared 0.339174 Mean dependent var -8.29E-06Adjusted R-squared 0.331036 S.D. dependent var 0.006502S.E. of regression 0.005318 Akaike info criterion -7.620937Sum squared resid 0.011483 Schwarz criterion -7.562379Log likelihood 1575.913 F-statistic 41.67657Durbin-Watson stat 1.981641 Prob(F-statistic) 0.000000

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Table 6 ADF results for Sugar future prices ADF Test Statistic -8.060243 1% Critical Value* -3.4483

5% Critical Value -2.8688 10% Critical Value -2.5706

*MacKinnon critical values for rejection of hypothesis of a unit root.

Augmented Dickey-Fuller Test Equation Dependent Variable: D(SER06) Method: Least Squares Date: 05/15/07 Time: 11:23 Sample(adjusted): 6 417 Included observations: 412 after adjusting endpoints

Variable Coefficient Std. Error t-Statistic Prob. SER06(-1) -0.747389 0.092725 -8.060243 0.0000

D(SER06(-1)) -0.040442 0.084087 -0.480957 0.6308D(SER06(-2)) -0.030956 0.073490 -0.421233 0.6738D(SER06(-3)) -0.100833 0.062447 -1.614681 0.1072D(SER06(-4)) -0.044425 0.047683 -0.931679 0.3521

C 0.000303 0.000336 0.901989 0.3676R-squared 0.399844 Mean dependent var -1.08E-05Adjusted R-squared 0.392452 S.D. dependent var 0.008672S.E. of regression 0.006760 Akaike info criterion -7.141257Sum squared resid 0.018551 Schwarz criterion -7.082698Log likelihood 1477.099 F-statistic 54.09805Durbin-Watson stat 1.989930 Prob(F-statistic) 0.000000

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Table 7 ADf results for Soy been spot residual values ADF Test Statistic -9.620079 1% Critical Value* -3.4437

5% Critical Value -2.8667 10% Critical Value -2.5695

*MacKinnon critical values for rejection of hypothesis of a unit root.

Augmented Dickey-Fuller Test Equation Dependent Variable: D(SER01) Method: Least Squares Date: 05/15/07 Time: 16:21 Sample(adjusted): 6 601 Included observations: 596 after adjusting endpoints

Variable Coefficient Std. Error t-Statistic Prob. SER01(-1) -0.792334 0.082362 -9.620079 0.0000

D(SER01(-1)) -0.141197 0.075599 -1.867701 0.0623D(SER01(-2)) -0.115608 0.066888 -1.728383 0.0844D(SER01(-3)) -0.084333 0.055890 -1.508909 0.1319D(SER01(-4)) -0.037126 0.040959 -0.906408 0.3651

C -0.000364 0.000241 -1.511263 0.1313R-squared 0.468992 Mean dependent var -1.61E-05Adjusted R-squared 0.464492 S.D. dependent var 0.007948S.E. of regression 0.005816 Akaike info criterion -7.446291Sum squared resid 0.019959 Schwarz criterion -7.402094Log likelihood 2224.995 F-statistic 104.2190Durbin-Watson stat 2.002625 Prob(F-statistic) 0.000000

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Table 8 ADF results for Soy bean future residual values ADF Test Statistic -8.340894 1% Critical Value* -3.4437

5% Critical Value -2.8667 10% Critical Value -2.5695

*MacKinnon critical values for rejection of hypothesis of a unit root.

Augmented Dickey-Fuller Test Equation Dependent Variable: D(SER02) Method: Least Squares Date: 05/15/07 Time: 16:23 Sample(adjusted): 6 601 Included observations: 596 after adjusting endpoints

Variable Coefficient Std. Error t-Statistic Prob. SER02(-1) -0.641594 0.076921 -8.340894 0.0000

D(SER02(-1)) -0.198387 0.072989 -2.718034 0.0068D(SER02(-2)) -0.217295 0.062805 -3.459810 0.0006D(SER02(-3)) -0.282090 0.052610 -5.361922 0.0000D(SER02(-4)) -0.047642 0.041203 -1.156280 0.2480

C -0.000171 0.000380 -0.451799 0.6516R-squared 0.455736 Mean dependent var -1.22E-06Adjusted R-squared 0.451124 S.D. dependent var 0.012489S.E. of regression 0.009253 Akaike info criterion -6.517741Sum squared resid 0.050514 Schwarz criterion -6.473544Log likelihood 1948.287 F-statistic 98.80674Durbin-Watson stat 1.994690 Prob(F-statistic) 0.000000

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Table 9 ADF results for Chana spot residual values ADF Test Statistic -10.42985 1% Critical Value* -3.4437

5% Critical Value -2.8667 10% Critical Value -2.5695

*MacKinnon critical values for rejection of hypothesis of a unit root.

Augmented Dickey-Fuller Test Equation Dependent Variable: D(SER03) Method: Least Squares Date: 05/15/07 Time: 16:26 Sample(adjusted): 6 601 Included observations: 596 after adjusting endpoints

Variable Coefficient Std. Error t-Statistic Prob. SER03(-1) -0.931571 0.089318 -10.42985 0.0000

D(SER03(-1)) -0.031339 0.079680 -0.393304 0.6942D(SER03(-2)) -0.028134 0.069540 -0.404565 0.6859D(SER03(-3)) -0.004546 0.057068 -0.079660 0.9365D(SER03(-4)) -0.048763 0.041018 -1.188817 0.2350

C 0.000605 0.000237 2.556183 0.0108R-squared 0.484953 Mean dependent var -3.32E-06Adjusted R-squared 0.480588 S.D. dependent var 0.007763S.E. of regression 0.005595 Akaike info criterion -7.523899Sum squared resid 0.018469 Schwarz criterion -7.479702Log likelihood 2248.122 F-statistic 111.1053Durbin-Watson stat 1.998353 Prob(F-statistic) 0.000000

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Table 10 ADF results for Chana future residual values ADF Test Statistic -11.18795 1% Critical Value* -3.4437

5% Critical Value -2.8667 10% Critical Value -2.5695

*MacKinnon critical values for rejection of hypothesis of a unit root.

Augmented Dickey-Fuller Test Equation Dependent Variable: D(SER04) Method: Least Squares Date: 05/15/07 Time: 16:28 Sample(adjusted): 6 601 Included observations: 596 after adjusting endpoints

Variable Coefficient Std. Error t-Statistic Prob. SER04(-1) -1.088998 0.097337 -11.18795 0.0000

D(SER04(-1)) 0.037340 0.086134 0.433506 0.6648D(SER04(-2)) 0.027307 0.074238 0.367830 0.7131D(SER04(-3)) 0.039013 0.059895 0.651354 0.5151D(SER04(-4)) -0.005703 0.041375 -0.137828 0.8904

C 0.000713 0.000506 1.408070 0.1596R-squared 0.528030 Mean dependent var -1.81E-05Adjusted R-squared 0.524031 S.D. dependent var 0.017794S.E. of regression 0.012276 Akaike info criterion -5.952328Sum squared resid 0.088913 Schwarz criterion -5.908131Log likelihood 1779.794 F-statistic 132.0161Durbin-Watson stat 1.995714 Prob(F-statistic) 0.000000

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Table 11 ADF results for Sugar spot residual values ADF Test Statistic -8.060243 1% Critical Value* -3.4483

5% Critical Value -2.8688 10% Critical Value -2.5706

*MacKinnon critical values for rejection of hypothesis of a unit root.

Augmented Dickey-Fuller Test Equation Dependent Variable: D(SER05) Method: Least Squares Date: 05/15/07 Time: 16:30 Sample(adjusted): 6 417 Included observations: 412 after adjusting endpoints

Variable Coefficient Std. Error t-Statistic Prob. SER05(-1) -0.747389 0.092725 -8.060243 0.0000

D(SER05(-1)) -0.040442 0.084087 -0.480957 0.6308D(SER05(-2)) -0.030956 0.073490 -0.421233 0.6738D(SER05(-3)) -0.100833 0.062447 -1.614681 0.1072D(SER05(-4)) -0.044425 0.047683 -0.931679 0.3521

C 0.000420 0.000120 3.495209 0.0005R-squared 0.399844 Mean dependent var -3.48E-06Adjusted R-squared 0.392452 S.D. dependent var 0.002792S.E. of regression 0.002176 Akaike info criterion -9.408147Sum squared resid 0.001923 Schwarz criterion -9.349588Log likelihood 1944.078 F-statistic 54.09805Durbin-Watson stat 1.989930 Prob(F-statistic) 0.000000

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Table 12 ADF results for Sugar future residual values ADF Test Statistic -8.214633 1% Critical Value* -3.4483

5% Critical Value -2.8688 10% Critical Value -2.5706

*MacKinnon critical values for rejection of hypothesis of a unit root.

Augmented Dickey-Fuller Test Equation Dependent Variable: D(SER06) Method: Least Squares Date: 05/15/07 Time: 16:32 Sample(adjusted): 6 417 Included observations: 412 after adjusting endpoints

Variable Coefficient Std. Error t-Statistic Prob. SER06(-1) -0.710796 0.086528 -8.214633 0.0000

D(SER06(-1)) -0.106249 0.081141 -1.309443 0.1911D(SER06(-2)) -0.063225 0.074448 -0.849256 0.3962D(SER06(-3)) 0.050813 0.063937 0.794740 0.4272D(SER06(-4)) 0.053979 0.049552 1.089355 0.2766

C 3.02E-05 0.000250 0.120958 0.9038R-squared 0.411344 Mean dependent var -4.81E-06Adjusted R-squared 0.404094 S.D. dependent var 0.006562S.E. of regression 0.005066 Akaike info criterion -7.718219Sum squared resid 0.010418 Schwarz criterion -7.659660Log likelihood 1595.953 F-statistic 56.74126Durbin-Watson stat 1.987132 Prob(F-statistic) 0.000000