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1. INTRODUCTION TO CAPITAL MARKET Meaning: Capital markets are markets where people, companies, and governments with more funds than they need (because they save some of their income) transfer those funds to people, companies, or governments who have a shortage of funds (because they spend more than their income). Stock and bond markets are two major capital markets. Capital markets promote economic efficiency by channelling money from those who do not have an immediate productive use for it to those who do. Capital markets carry out the desirable economic function of directing capital to productive uses. The savers (governments, businesses, and people who save some portion of their income) invest their money in capital markets like stocks and bonds. The borrowers (governments, businesses, and people who spend more than their income) borrow the savers' investments that have been entrusted to the capital markets. For example, suppose A and B make Rs. 50,000 in one year, but they only spend Rs.40,000 that year. They can invest the 10,000 - their savings - in a mutual fund investing in stocks and bonds all over the world. They know that making such an investment is riskier than keeping the 10,000 at home or in a savings account. But they hope that over the long-term the investment will yield greater returns than cash holdings or interest on a savings account. The borrowers in this example are the companies that issued the stocks or bonds that are part of the mutual fund portfolio. Because the companies have spending needs that exceeds their income, they finance their spending needs by issuing securities in the capital markets. 1 The Structure of Capital Markets Primary markets: The primary market is where new securities (stocks and bonds are the most common) are issued. The corporation or government agency that needs funds (the borrower) issues securities to purchasers in the primary market. Big investment banks assist in this issuing process. The banks underwrite the securities. That is, they guarantee a minimum price for a business's securities and sell them to the public. Since the primary market is limited to issuing new securities only, it is of lesser importance than the secondary market. Secondary market: The vast majority of capital transactions, take place in the secondary market. The secondary market includes stock exchanges (like the New York Stock Exchange and the Tokyo Nikkei), bond markets, and futures and options markets, among others. All of these secondary markets deal in the trade of securities. Securities: The term "securities" encompasses a broad range of investment instruments. Investors have essentially two broad categories of securities available to them: 1. Equity securities (which represent ownership of a part of a company) 2. Debt securities (which represent a loan from the investor to a company or government entity). 2 Equity securities: Stock is the type of equity security with which most people are familiar. When investors (savers) buy stock, they become owners of a "share" of a company's assets and earnings. If a company is successful, the price that investors are willing to pay for its stock will often rise and shareholders who bought stock at a lower price then stand to make a profit. If a company does not do well, however, its stock may decrease in value and shareholders can lose money. Stock prices are also subject to both general economic and industry-specific market factors. In our example, if Carlos and Anna put their money in stocks, they are buying equity in the company that issued the stock. Conversely, the company can issue stock to obtain extra funds. It must then share its cash flows with the stock purchasers, known as stockholders. Debt securities: Savers who purchase debt instruments are creditors. Creditors, or debt holders, receive future income or assets in return for their investment. The most common example of a debt instrument is a bond. When investors buy bonds, they are lending the issuers of the bonds their money. In return, they will receive interest payments (usually at a fixed rate) for the life of the bond and receive the principal when the bond expires. National governments, local governments, water districts, global, national, and local companies, and many other types of institutions sell bonds. Internationalization of Capital Markets in the Late 1990s One of the most important developments since the 1970s has been the internationalization, and now globalization, of capital markets. Let's look at some of the basic elements of the international capital markets. 3 CAPITAL MARKET IN INDIA: - Coming to Indian context, the term capital market refers to only stock markets as per the common man's ideology, but the capital markets have a much broader sense. Where as in global scenario, it consists of various markets such as: 1. Government securities market 2. Municipal bond market 3. Corporate debt market 4. Stock market 5. Depository receipts market 6. Mortgage and asset-backed securities market 7. Financial derivates market 8. Foreign exchange market India’s presence in International Markets: India has made its presence felt in the IFMs only after 1991-92. At present there are over 50 companies in India, which have accessed the GDR route for raising finance. The change in situation has been due to the following factors: 1. Improved perception of India‘s economic reforms. 2. Improved export performance. 3. Healthy economic indicator. 4. Inflation at single digit. 5. Improved forex reserves. 6. Improved performance of Indian companies. 7. Improved confidence of FIIs. Reliance was the first Indian company to issue GDR in 1992. Since 1993, number of Indian companies successfully tapped the global capital markets & raised capital through GDR or foreign currency bond issues. Though there was a temporary setback due to Asian crisis in 1997. Since 1999 even IT majors have stepped the bandwagon of international markets & raised 4 capital. The average size of the issue was around 75USD. And the total amount raised was around USD 6.5billion. India has the distinction of having the largest number of GDR/ADR issues by any country. NSE’s Capital Market Segment The Trading on the NSE‘s capital market commenced on November 4, 1995 and has been witnessing a substantial growth over the years. The growth of NSE turnover figures shows a substantial rise from Rs. 1,805 crore (US $ 574.29 million) in the year 1994-95 to Rs. 2,752,023 crore (US $ 540,141.59 million) in 2008-09. With the increase in volumes, efficient and transparent trading platform, a wide range of securities like equity, preference shares, debt warrants, exchange traded funds as well as retail government securities, NSE upholds its position as the largest stock exchange in the country. The CM segment of NSE provides an efficient and transparent platform for trading of equity, preference shares, debentures, warrants, exchange traded funds as well as retail Government securities. 5 2. INTRODUCTION TO DERIVATIVE MARKET It is very well known that the Indian capital market has witnessed a major transformation and structural change from the past one decade as a result of ongoing financial sector reforms. Dr. L.C.Gupta (2002) has rightly pointed out that improving market efficiency, enhancing transparency, checking unfair trade practices and bringing the Indian capital market up to a certain international standard are some of the major objectives of these reforms. Due to such reforming process, one of the important step taken in the secondary market is the introduction of derivative products in two major Indian stock exchanges (viz. NSE and BSE) with a view to provide tools for risk management to investors and also to improve the informational efficiency of the cash market. Many emerging and transition economies had started introducing derivative contracts since 1865 when the commodity futures were first introduced on the Chicago Board of Trade. The Indian capital markets have experienced the launching of derivative products on June 9, 2000 in BSE and on June 12, 2000 in NSE by the introduction of index futures. Just after one year, index options were also introduced to facilitate the investors in managing their risks. Later stock options and stock futures on underlying stocks were also launched in July 2001 and Nov. 2001 respectively. In India, derivatives were mainly introduced with view to curb the increasing volatility of the asset prices in financial markets and to introduce sophisticated risk management tools leading to higher returns by reducing risk and transaction costs as compared to individual financial assets. Though the onset of derivative trading has significantly altered the movement of stock prices in Indian spot market, it is yet to be proved whether the derivative products has served the purpose as claimed by the Indian regulators. In an efficient capital market where all available information is fully and instantaneously utilized to determine the market price of securities, prices in the futures and spot market should move simultaneously without any delay. However, due to market frictions such as transaction cost, capital market microstructure effects etc., significant lead-lag relationship between the two markets has been observed. 6 As far as developed markets, such as USA, UK, Japan etc., are concerned, a number of important and in-depth studies have been carried out to examine the lead-lag relationship between the spot and derivative, viz. futures market and also to provide the possible explanations behind such relation and its changes over time. Therefore, the present study seeks to contribute to the existing knowledge base and literature for examining the actual lead-lag relationship among the Indian spot and futures market in terms of returns for the time period Jan-2007 to Dec-2008 2.1 HISTORY OF DERIVATIVE MARKET Derivatives can be found throughout the history of mankind. In the Middle Ages, engaging in contracts at predetermined prices for future delivery of farming products, for example, was quite frequent. Hundreds of years ago, Japan had a semblance of an actual futures exchange. But it was not until 1848 that the first modern, organized futures market in North America was created—the Chicago Board of Trade. Agricultural Futures Dominate the First 100 Years of Derivatives Trading After the Chicago Board of Trade first opened its doors, the grain market in Chicago almost exploded. Farmers needed to secure prices for their grain, needed to know those prices in advance of the crops, needed a place to store the grain, and needed someone to facilitate delivery and settlement of futures contracts. Around that time, the first customized option contracts were offered, too. To illustrate, a well known financier of the era, Russell Sage, offered customized options that effectively imitated loans at interest rates that were much higher than rates allowed under the then-existing usury laws. After the Chicago Board of Trade, other organized derivatives markets were established in the U.S., including the Chicago Mercantile Exchange, and later The New York Mercantile Exchange and the Chicago Board Options Exchange. The latter two subsequently became the main driving forces of the derivatives industry worldwide. 7 During the 1970s, Financial Derivatives Enter the Scene The new era for the derivative markets was ushered with the introduction of financial derivatives, and it continues to last to this day. Although commodity derivatives are still quite active, particularly oil and precious metals, financial derivatives dominate trading in the current derivative markets. In addition, although customized options existed since the 19th century at least, the introduction of standardized options in 1973 completely overshadowed their customized counterparts. Another important factor impacted the derivatives markets in the 1970s—deregulation of foreign exchange rates. When foreign exchange rates became freely floating, not only have new currency markets developed, but also the markets for trading customized forward contracts in foreign currencies. This market was later referred to as the interbank market because most of the participants were, and still are, domestic and international banks. Aside from facilitating trading in currency derivatives, the currency interbank market also set the stage for the banking industry to become more involved in trading of other types of financial derivatives. The Age of Deregulation in the 1980s More deregulation of the 1980s further blurred the regulatory lines among financial services providers, such as banks, insurance industries, securities dealers, etc. Banks in particular discovered they could create various types of derivatives that were to be sold to corporations, as well as to other financial institutions. The idea was to create tailored products that were designed to alleviate risk exposure specific to certain situations and certain players. Of course, banks were not the only ones profiting from financial derivatives designed to transfer or lay off risks elsewhere. Investment banking firms, also called derivatives dealers, soon joined in the burgeoning derivative markets. 8 The Age of Maturity in the 1990s Although the derivatives markets slowed down considerably by the end of the 20th century, that did not mean that there were not a steady offering of existing, as well as new derivative products. Derivatives exchanges also went through a period of change; some consolidated, some merged, some became for-profit institutions. Regardless, they all had something in common—the need for less regulation. Aside from structural changes, some derivative exchanges also changed the way they conducted trading. Old systems of face-to-face trading on trading floors have been replaced with electronic trading, and telephone and computer networks. With the advent of Internet, electronic trading evolved into e-trading. And although trading floors still dominate derivative markets in the U.S., it is obvious that to stay competitive, the U.S. will have to eventually embrace electronic trading. Derivatives Markets in the 21st century There is a general consensus that London and New York are the world‘s primary markets for over-the-counter derivatives. Notably, a significant derivative trading is also in Tokyo, Paris, Frankfurt, Chicago, Amsterdam, etc. In terms of size, today the U.S. accounts for almost 35% of futures and options trading worldwide. However, the Korea Stock Exchange is the largest derivative exchange in the world. The second largest by volume is the Eurex (German-Swiss), followed by the Chicago Board of Trade, the London International Financial Futures and Options Exchange, the Paris bourse, the New York Mercantile Exchange, the Bolsa de Mercadorias & Futuros of Brazil, and the Chicago Board Options Exchange. Note that in 2001, these exchanges traded in aggregate 70 million derivative contracts (Source: Futures Industry, January/February 2002). 9 2.2 TYPES OF DERIVATIVES OTC Exchange-Traded Broadly speaking there are two distinct groups of derivative contracts, which are distinguished by the way they are traded in market: Over-the-counter (OTC) derivatives are contracts that are traded (and privately negotiated) directly between two parties, without going through an exchange or other intermediary. Products such as swaps, forward rate agreements, and exotic options are almost always traded in this way. The OTC derivatives market is huge. Exchange-traded derivatives (ETD) are those derivatives products that are traded via specialized derivatives exchanges or other exchanges. A derivatives exchange acts as an intermediary to all related transactions, and takes Initial margin from both sides of the trade to act as a guarantee. The world's largest derivatives exchanges (by number of transactions) are the Korea Exchange (which lists KOSPI Index Futures & Options), Eurex and CME Group (made up of the 2007 merger of the Chicago Mercantile Exchange and the Chicago Board of Trade and the 2008 acquisition of the New York Mercantile Exchange). According to BIS, the combined turnover in the world's derivatives exchanges totaled USD 344 trillion during Q4 2005. Some types of derivative instruments also may trade on traditional exchanges. For instance, hybrid instruments such as convertible bonds and/or convertible preferred may be listed on stock or bond exchanges. Also, warrants (or "rights") may be listed on equity exchanges. Performance Rights, Cash experts and various other instruments that essentially consist of a complex set of options bundled into a simple package are routinely listed on equity exchanges. Like other derivatives, these publicly traded derivatives provide investors access to risk/reward and volatility characteristics that, while related to an underlying commodity, nonetheless are distinctive. 10 KINDS OF FINANCIAL DERIVATIVES As already discussed, the important financial derivatives are the following: Forwards Futures Options, and Swaps FORWARDS Forwards are the oldest of all the derivatives. A forward contract refers to an agreement between two parties to exchange an agreed quantity of an asset for cash at certain date in future at a predetermined price specified in that agreement. The promised asset may be currency, commodity, instrument etc. FUTURES A futures contract is very similar to a forward contract in all respect excepting the fact that it is completely a standardized one. Hence, it is rightly said that a futures contract is nothing but a standardized forward contract. It is legally enforceable and it is always traded on an organized exchange. The term ‗future trading‘ includes both speculative transactions where futures are bought and sold with the objective of making profits from the price changes and also the hedging or protective transactions where futures are bought and sold with view to avoiding unforeseen losses resulting from price fluctuations. A future contract is one where there is an agreement between two parties to exchange any assets or currency or commodity for cash at a certain future date, at an agreed price. Both the parties to the contract must have mutual trust in each other. It takes place only in organized futures market and according to well-established standards. 11 As in a forward contract, the trader who promises to buy is said to be in ‗long position‘ and the one who promises to sell is said to be in ‗short position‘ in futures also. SWAPS Swap is yet another exciting trading instrument. In fact, it is a combination of forwards by two counter parties. It is arranged to reap the benefits arising from the fluctuations in the market- either currency market or interest rate market or any other market for that matter. OPTIONS A derivative transaction that gives the option holder the right but not the obligation to buy or sell the underlying asset at a price, called the strike price, during, a period or on a specific date in exchange for payment of a premium is known as ‗option‘. Underlying asset refers to any asset that is traded. The price at which the underlying asset is traded is called the ‗strike price‘. 12 2.3 IMORTANCE OF DERIVATIVES Derivatives are becoming increasingly important in world markets as a tool for risk management. Derivative instruments can be used to minimize risk. Derivatives are used to separate the risks and transfer them to parties willing to bear these risks. The kind of hedging that can be obtained by using derivatives is cheaper and more convenient than what could be obtained by using cash instruments. It is so because, when we use derivatives for hedging, actual delivery of the underlying asset is not at all essential for settlement purposes. The profit or loss on derivative deal alone is adjusted in the derivative market. Moreover, derivatives do not create any new risk. They simply manipulate risks and transfer them to those who are willing to bear these risks. Hedging risk through derivatives is not similar to speculation. The gain or loss on a derivative deal is likely to be offset by an equivalent loss or gain in the values of underlying assets. 'Offsetting of risks' is an important property of hedging transactions. But, in speculation one deliberately takes up a risk openly. When companies know well that they have to face risk in possessing assets, it is better to transfer these risks to those who are ready to bear them. So, they have to necessarily go for derivative instruments. All derivative instruments are very simple to operate. Treasury managers and portfolio managers can hedge all risks without going through the tedious process of hedging each day and amount/share separately. But with the rapid development of the derivative markets, now, it is possible to cover such risks through derivative instruments like swap. Thus, the availability of advanced derivatives market enables companies to concentrate on those management decisions other than funding decisions. Derivatives also offer high liquidity. Just as derivatives can be contracted easily, it is also possible for companies to get out of positions in case that market reacts otherwise. This also does not involve much cost. Thus, derivatives are not only desirable but also necessary to hedge the complex exposures and volatilities that the companies generally face in the financial markets today. 13 2.4 EMERGENCE OF DERIVATIVE MARKET IN INDIA With globalization of the financial sector, it's time to recast the architecture of the financial market. The liberalized policy being followed by the Government of India and the gradual withdrawal of the procurement and distribution channel necessitated setting in place a market mechanism to perform the economic functions of price discovery and risk management. Till the mid – 1980's, the Indian financial system did not see much innovation. In the last 18 years, financial innovation in India has picked up and it is expected to grow in the years to come, as a more liberalized environment affords greater scope for financial innovation at the same time financial markets are, by nature, extremely volatile and hence the risk factor is an important concern for financial agents. To reduce this risk, the concept of derivatives comes into the picture. Derivatives are products whose values are derived from one or more basic variables called bases. India is traditionally an agriculture country with strong government intervention. Government arbitrates to maintain buffer stocks, fix prices, impose import-export restrictions, etc. This paper focuses on the basic understanding about derivatives market and its development in India. The emergence of the market for derivatives products, most notable forwards, futures, options and swaps can be traced back to the willingness of risk-averse economic agents to guard themselves against uncertainties arising out of fluctuations in asset prices. By their very nature, the financial markets can be subject to a very high degree of volatility. Through the use of derivative products, it is possible to partially or fully transfer price risks by locking-in asset prices. As instruments of risk management, derivatives products generally do not influence the fluctuations in the underlying asset prices. However, by locking-in asset prices, derivatives products minimize the impact of fluctuations in asset prices on the profitability and cash flow situation of risk-averse investors. 14 2.4.1. DEVELOPMENT OF DERIVATIVE MARKET IN INDIA The first step towards introduction of derivatives trading in India was the promulgation of the Securities Laws (Amendment) Ordinance, 1995, which withdrew the prohibition on options in securities. The market for derivatives, however, did not take off, as there was no regulatory framework to govern trading of derivatives. SEBI set up a 24–member committee under the Chairmanship of Dr.L.C.Gupta on November 18, 1996 to develop appropriate regulatory framework for derivatives trading in India. The committee submitted its report on March 17, 1998 prescribing necessary pre–conditions for introduction of derivatives trading in India. The committee recommended that derivatives should be declared as ‗securities‘ so that regulatory framework applicable to trading of ‗securities‘ could also govern trading of securities. SEBI also set up a group in June 1998 under the Chairmanship of Prof.J.R.Varma, to recommend measures for risk containment in derivatives market in India. The report, which was submitted in October 1998, worked out the operational details of margining system, methodology for charging initial margins, broker net worth, deposit requirement and real–time monitoring requirements. The Securities Contract Regulation Act (SCRA) was amended in December 1999 to include derivatives within the ambit of ‗securities‘ and the regulatory framework was developed for governing derivatives trading. The act also made it clear that derivatives shall be legal and valid only if such contracts are traded on a recognized stock exchange, thus precluding OTC derivatives. The government also rescinded in March 2000, the three– decade old notification, which prohibited forward trading in securities. Derivatives trading commenced in India in June 2000 after SEBI granted the final approval to this effect in May 2001. SEBI permitted the derivative segments of two stock exchanges, NSE and BSE, and their clearing house/corporation to commence trading and settlement in approved derivatives contracts. To begin with, SEBI approved trading in index futures contracts based on S&P CNX Nifty and BSE–30(Sensex) index. This was followed by approval for trading in options based on these two indexes and options on individual securities. 15 The trading in BSE Sensex options commenced on June 4, 2001 and the trading in options on individual securities commenced in July 2001. Futures contracts on individual stocks were launched in November 2001. The derivatives trading on NSE commenced with S&P CNX Nifty Index futures on June 12, 2000. The trading in index options commenced on June 4, 2001 and trading in options on individual securities commenced on July 2, 2001. Single stock futures were launched on November 9, 2001. The index futures and options contract on NSE are based on S&P CNX Trading and settlement in derivative contracts is done in accordance with the rules, by laws, and regulations of the respective exchanges and their clearing house/corporation duly approved by SEBI and notified in the official gazette. Foreign Institutional Investors (FIIs) are permitted to trade in all Exchange traded derivative products. The following are some observations based on the trading statistics provided in the NSE report on the futures and options (F&O): Single-stock futures continue to account for a sizable proportion of the F&O segment. It constituted 70 per cent of the total turnover during June 2002. A primary reason attributed to this phenomenon is that traders are comfortable with single-stock futures than equity options, as the former closely resembles the erstwhile badla system. Typically, options are considered more valuable when the volatility of the underlying (in this case, the index) is high. A related issue is that brokers do not earn high commissions by recommending index options to their clients, because low volatility leads to higher waiting time for round-trips. Put volumes in the index options and equity options segment have increased since January 2002. The call-put volumes in index options have decreased from 2.86 in January 2002 to 1.32 in June. The fall in call-put volumes ratio suggests that the traders are increasingly becoming pessimistic on the market. 16 Daily option price variations suggest that traders use the F&O segment as a less risky alternative (read substitute) to generate profits from the stock price movements. The fact that the option premiums tail intra-day stock prices is evidence to this. If calls and puts are not looked as just substitutes for spot trading, the intra-day stock price variations should not have a one-to-one impact on the option premiums. There are no derivatives based on interest rates in India today. However, Indian users of hedging services are allowed to buy derivatives involving other currencies on foreign markets. India has a strong dollar- rupee forward market with contracts being traded for one to six month expiration. Daily trading volume on this forward market is around $500 million a day. Hence, derivatives available in India in foreign exchange area are also highly beneficial to the users. 17 2.4.2. GROWTH OF DERIVATIVE MARKET IN INDIA : Factors Generally Attributed As The Major Driving Force Behind Growth Of Financial They are: (a) Increased Volatility in asset prices in financial markets, (b) Increased integration of national financial markets with the international markets, (c) Marked improvement in communication facilities and sharp decline in their costs, (d) Development of more sophisticated risk management tools, providing economic agents a wider choice of risk management strategies, and (e) Innovations in the derivatives markets, which optimally combine the risks and returns over a large number of financial assets, leading to higher returns, reduced risk as well as transaction costs as compared to individual financial assets. 18 Growth Of Financial Derivative Market With Respect To Cash Market Table – 2.4.1 Market Turnover of BSE & NSE in derivative and cash market (2006-2009) Market turnover (Rs. Crore) (Source : www.nseindia.com and www.bseindia.com) Market Calendar year 2005-06 2006-07 2007-08 2008-09 NSE Spot 1569558 1945287 3551038 2752023 NSE Derivatives 4824250 7356271 13090478 11010482 Total of NSE 6393808 9601558 16641516 13762505 % of NSE spot 31.15% 32.47% 21.38% 20.58% % OF NSE Derivative 68.85% 67.53% 78.62% 79.42% 19 Chart 2.4.1 Turnover of NSE in Derivative and Cash Market 14000000 12000000 Turnover(Rs. in crores) 10000000 8000000 6000000 NSE Derivatives 4000000 2000000 NSE Spot 0 2005-06 2006-07 2007-08 2008-09 Year Chart-2.4.2 Contribution of financial derivatives against cash market on NSE 100% 80% 60% NSE Derivatives 40% NSE Spot 20% 0% 2005-06 2006-07 2007-08 2008-09 20 3. RESEARCH METHODOLOGY Problem Statement The players in the derivatives market often crave to find out the direction and magnitude of interdependence of the spot and futures market. The individual have very vague idea about such relationship between two markets. There are mathematical calculations available to express such dependency between the markets. But the direction of such relationship can be precisely ascertained by studying the lead-lag relationship between the two markets. A number of studies have empirically examined the temporal relationship between the futures and spot markets. These studies seek to find the lead-lag relations between the futures and the spot market for an asset class and the differential speed of adjustments to flow of new information. The major gap in those is that the studies are mainly based on the view that the futures market is determinant of the spot market. The two way analysis showing the inter-dependence (spot dependent on futures and futures dependent on spot) fills the above gap. Literature Review There is an extensive amount of literature examining the impact of derivative trading on the return as well as on the volatility of underlying spot market, giving special emphasis on the lead- lag relationship between the spot and the derivatives, viz., futures and options market all over the world. In a world of complete market and no transaction costs, any new security can be synthesized from existing securities. Consequently, the introduction of derivatives, such as options should have no effect on underlying assets. According to Grossman (1988), the existence of transaction costs and incomplete markets suggests the possibility that futures or options can have an impact on spot market volatility. Nathan Associates (1969) makes clear that diversion of speculative interest to the option market may reduce stock trading and therefore may cause reduction in liquidity which might increase the stock‘s return variance. However, studies by Bansal et al. (1989), Skinner (1989), Damodoran et al. (1991) find significant increase in stock trading volume after the onset of derivative trading. Cox (1976) argues that futures trading can alter the available information and thus spot market volatility for two reasons. First, futures attract 21 additional traders to a market. Second, as transaction costs in the futures market is lower than those in the spot market, new information may be transmitted to the futures market more quickly. Now, as far as the temporal relationship among the spot and futures (options) market is concerned, several studies, attempted to examine the lead-lag relationship between the spot and the futures market both in terms of return and / or volatility includes Ng. (1987); Kawaller, Koch, and Koch (1987); Harris (1989); Stoll & Whaley (1990); Chin, Chan and Karolyi (1991); Chan (1992); Abhyankar (1995); Shyy (1996); Iihara (1996); Pizzi (1998); De Jong (1998); Chatrath (1998); Min (1999); Tse (1999); Frino (2000); Thenmozhi (2002); Anand babu (2003); Simpson (2004) etc. Almost all of these studies have concluded that there is a significant lead-lag relationship among the spot and the futures market, and also have tried to provide the possible explanation behind this. Most of the studies have suggested that the leading role of the futures market varies from five to forty minutes, while the spot market rarely leads the futures market beyond one minute. While explaining the causes behind such relation, Kawaller et al. (1987) attribute the stronger leading role of the futures market to the infrequent trading of component stocks. Though, at the same time, Stoll & Whaley (1990), Chan (1992) etc. proved the existence of such relation even in case of highly traded stocks or after adjusting for infrequent trading of component stocks. Chin (1991) has examined the intraday relationship among price changes and volatility of price changes in the stock index and stock index futures markets. Unlike the fact that the index futures markets served as the primary market for price discovery, as found in the previous studies, they have found the stronger interdependence in both the directions in the volatility of price changes between the cash and the futures markets than that observed in case of price changes only. Their evidence supported that the price innovations originate in one market, e.g. cash (futures) market, can predict the future volatility in the other, such as futures (cash), market. In other words, both cash and futures markets serve important role in discovering the price. Chan (1992) have investigated the intraday lead-lag relationship between MM cash index and MM and S&P futures index returns under different situations. Their results confirmed the leading role of the futures market even against all the component stocks. They have also empirically proved the leading role (to a greater degree) of the futures market for the release of any market- 22 wide information. Abhyankar (1995) have found the possibilities of the cash and the futures market playing the leading role, even in different intensities, under different situations, such as for change in transaction cost, in periods of good, moderate and bad news, for high and low trading volume in the underlying equity market etc. But as far as the conditional volatility is concerned, they could not found any clear pattern of one market leading the other neither during the periods of good or bad news nor for varying levels of market activity. By using a specially designed correlation measure that takes into account the fact that high frequency data are often observed at irregular intervals, De Jong (1998) have confirmed that even in the presence of significant contemporaneous correlation among the spot, futures and the options market, the futures price changes lead both the changes in the cash index and index option by five to ten minutes. But, among the cash and the options market, the relations are largely symmetrical and neither market consistently leads the other. Chatrath (1998) have examined the intraday behavior of the spot and futures market following the release of information and also investigate the role of such information in the volatility spillover among the two markets. Their results have supported that one market leading to greater volatility in the other is partly driven by information and therefore the leading role played by the futures market may be the result of new information efficiently reflected in the futures market. Min (1999) has investigated the possible lead-lag relationships in returns and volatilities between cash and futures markets. Their results have suggested that unlike the lead-lag relationship in the returns of spot and futures markets, there is significant but time dependent bidirectional causality between the markets, as far as the volatility interaction among the markets is concerned. Frino (2000) have examined the temporal relationship among the spot and the futures market around the release of different types of information. They have found that the lead of the futures market strengthens significantly around the release of macroeconomic information, while, the leading role of the futures market weakens around stock-specific information release. Therefore, according to them the disintegration in the relationship between the two markets is mainly driven by noise associated with trading activity around the release of different types of information. Simpson (2004) suggest that informed traders should trade in the futures market around the release of macroeconomic announcements; while, the leading role of futures market weakens 23 through the discovery of stock specific information [Grunbicher, Longstaff and Schwartz (1994)]. By looking at the Indian market, Thenmozhi (2002); Anand babu (2003) etc. have found that the futures market in India has more power in disseminating information and therefore has been found to play the leading role (for one or two days) in the matter of price discovery. The present study attempts to investigate that as the time have changed, is there any deviation in the result from the earlier work? Moreover as the market is becoming more and more efficient over a period of time, the time gap between cash and futures market in disseminating the information have decreased or not which was earlier in days. Research Question To investigate the lead-lag relationship between the NIFTY Spot and Futures market in India, in terms of return. The lead-lag relationship illustrates how well the two markets are linked, and how fast one market reflects new information from the other. If feedback between spot and futures exist, then it is possible that investor may use this information to predict the price movement or return movement. Objectives 1. To compare nifty future & spot market using intraday data on minute basis 2. To compare nifty individual stocks on daily closing price. 3. To check the efficiency of the market in processing the information. An Efficient market theory states that all market participants receive and act on all of the relevant information as soon as it is available. Research Design Descriptive Study 24 The Sample The sample population of the study comprises 1. Daily intra-day minute to minute price, for NIFTY spot index and settlement price of NIFTY futures. 2. In order to carry out the study at the stock / script level, five underlying NIFTY stocks, viz. RELIANCE (Reliance Industries Ltd.), INFOSYSTCH (Infosys Technologies Ltd.), ICICIBANK (ICICI Bank Ltd.), TATASTEEL (Tata Steel Ltd.) and DLF (DLF Ltd.). Sources of data Primary: None Secondary: The study is based on the secondary data collected from the official website of National Stock Exchange. Period of the Study 1. Nifty By using intraday data on minute basis from December-2009 to February-2010, an effort has been made to investigate the possible lead-lag relationship, in terms of return, among the NIFTY spot index and nearby contract of NIFTY futures index in India and also to explore the possible changes (if any) in such relationship around the release of different types of information. 2. Stock Daily closing price data from March-2009 to February-2010 of stock having very high trading turnover in the market have been taken into consideration. At script level 242 observation for the mentioned time period of spot market and futures market have been collected, i.e. daily closing price in spot market and daily settlement price in futures market for each script 25 Statistical Tools used in the study Augmented Dickey-Fuller test(Unit Root Test) Correlogram Cross Correlation Linear Regression (Ordinaly Least Square Method) Granger Causality Test Scope of the study This study covers only the analysis of S&P CNX NIFTY Index and Futures and five highly traded scripts of Nifty i.e. Reliance Industries Ltd, Infosys Technologies Ltd, DLF Ltd, Tata Steel Ltd and ICICI Bank Ltd based on selected time period. Benefits One of the core benefits of a market for derivative products of any asset class is the additional information content that may be extracted out of the prices evolving in this market. Thus it is said that besides the traditional role of risk sharing assigned to futures market, this market also play an important role in the aggregation of information and price discovery. The explicit determination of lead-lag relationship between the spot and the future market would help the players to increase their potential profits/returns. Limitations The assumptions of this study form the part of the limitations, too. a) Each new future contract is purchased only on the expiry of the previous contract. b) In extension to the above assumption, the trading time for the futures contract is taken from 1st day of the calendar month to the last expiry date of the same month. This limits data from being in the continuous form for subsequent months. c) Unavailability of intra-day minute to minute data of stock specific. 26 Methodology In order to get standard estimation the time series, they are converted into stationary stochastic process. A stochastic process is said to be stationary if its mean is zero and variance are constant over time and the value of the covariance between two time periods depends only on the distance or gap or lag between the two time periods and not the actual time at which the covariance is computed. In order to transform the stochastic process into stationary, the testing of stationarity is required. Therefore, the analysis is begun with the stationarity testing i.e. Graphical Analysis, Autocorrelation Function & correlogram and unit root testing. First the stationarity has been checked for the closing price of cash market and settlement price of futures market. If they are not stationary, then they are converted in logarithmic values in order to make them in a continuous form. And if yet the time series are not stationary, then daily returns are identified as the difference in the natural logarithm of the closing index value for the two consecutive trading days .It can be presented as: �������� = ������������ �������� ��������−1 (���� or �������� = ������������ �������� − log ����−1 ) Where �������� is logarithmic daily return at time t. ��������−1 and �������� are daily prices of an asset at two successive days, t-1 and t respectively. In order to do time series analysis, transformation of original series is required depending upon the type of series when the data is in the level form. The series of return was transformed by taking natural logarithm. There are two advantages of this kind of transformation of the series. First it eliminates the possible dependence of changes in stock price index on the price level of the index. Second, the change in the log of the stock price index yields continuously compounded series. In examining the lead-lag relationship between cash and futures market, the first common but important practice is to determine the maximum length of leads or lags which are assumed to be significant in the present context. Here as the market is efficient it will process the information as soon as it comes, so there may not be existence of lead-lag relationship at the higher lags. So the length of leads and lags are taken as five, as there are five trading dates in a week. In order to get 27 the lag (i.e.,����−���� ) and the lead (i.e.,����+���� ) coefficients the cross correlation function has been undertaken. Cross correlation coefficient is correlation coefficient between the current cash returns ( ��������,���� ) and past futures return ( ��������,����−���� ), and between the past cash return ( ��������,����+���� ) and current futures return ( �������� ,���� ). It is to be noted here that the asymptotic standard errors for the cross-correlation coefficients is approximated as the square root of the reciprocal of the number of observations included in the sample. After determining the lead-lag length, the next step is to examine the lead-lag behavior between the cash and futures markets by estimating the following regression equations: The model applied to investigate the lead-lag relation among the spot and the futures market in terms of returns is such that ���� ��������,���� = ���� + ���� →−���� �������� ��������,����+���� + ������������−1 + �������� Where��������,���� , and ��������,���� , are cash and futures index returns at time t which have been collected at each one minute interval. The coefficients with negative subscripts (i.e., ����−1 , ����−2 ,…, ����−���� ) are lag coefficients and those with positive subscripts (i.e., ����+1 , ����+2 , …, ����+���� ) are lead coefficients. If the lag coefficients become significant, then it can be inferred that the independent variable lags dependent variable, or in other words, dependent variable leads the independent variable. In the other way, if the lead coefficients will significant, then it can be proved that independent variable leads the dependent variable. If both the lead and lag coefficients are found to be significant, then neither market can be said to significantly lead the other and therefore both the markets (spot and futures) are proved to be informational efficient. Moreover if such relationship is not found, then Granger Causality test has been performed to check the cointegration in two series i.e. cointegration between cash series and future series. Apart from this, the efforts have been made to examine such relation between futures and individual component stocks. The analysis has been performed using MS-Excel and E-view. 28 4.1 NIFTY Table 4.1.1: Descriptive Statistics of Intra Day Price NIFTY Spot And NIFTY Futures NIFTY_FUT NIFTY_SPOT Mean 5037.881 5037.589 Median 5045.000 5049.100 Maximum 5296.100 5297.000 Minimum 4668.600 4676.550 Std. Dev. 172.1669 170.1119 Skewness -0.109025 -0.106941 Kurtosis 1.645878 1.648441 Jarque-Bera 1705.223 1697.305 Probability 0.000000 0.000000 Sum 1.10E+08 1.10E+08 Sum Sq. Dev. 6.45E+08 6.30E+08 Observations 21755 21755 Interpretation: Descriptive statistics of closing price of NIFTY spot and NIFTY futures market are presented in Table 1 above. The descriptive statistics for the series are mean, median, maximum, minimum, standard deviation, skewness, kurtosis, Jarque-Bera & probability. Here as the skewness is not zero for both the series, but negative. So both the series are negatively skewed. Moreover Kurtosis statistics are less than 3, so both the series are platykurtic. And also Jarque Bera statistics are greater than zero which rejects the hypothesis of normal distribution for both the series. 29 Figure: 4.1.1 Intra Day Price of NIFTY Spot index (Dec-2009 to Feb-2010) NIFTY_SPOT 5,400 5,300 5,200 5,100 5,000 4,900 4,800 4,700 4,600 5000 10000 15000 20000 Figure:4.1.2 Intra Day Price of NIFTY Futures (Dec-2009 to Feb-2010) NIFTY_FUT 5,400 5,300 5,200 5,100 5,000 4,900 4,800 4,700 4,600 5000 10000 15000 20000 30 Interpretation: In the above diagram, Figure 1 and Figure 2 represents the per minute closing price of NIFTY cash index and NIFTY futures.These plots gives an initial clue about the likely nature of the time series. In Figure 1 and 2, it has been seen that over the period of study closing prices of NIFTY cash and futures respectively have been increasing or decreasing, that is, showing an upward trend or downward trend, suggesting perhaps that the mean of both the series has beeen changing. This perhaps suggests that both the series are not stationary. Moreover, here both the plots are minutely observed so we can easily infer that, both the series move in the same direction and somewhat with the same magnitude. So, by establishing the lead- lag relationship we may predict the change in prices within the particular trading period in either way. 31 Autocorrelation Function And Correlogram If one plot a diagramme for autocorrelation function, then the solid vertical line in this diagramme represents the zero axis; observations above the line are positive and those below the line are nagative values. For a purely white noise process the autocorrelations at various lags hover around zero.This is the picture of a correlogram of a stationary time series. Thus, if the correlogram of an actual time series resembles the correlogram of a white noise time series, we can say that time series is probably stationary. Table 4.1.2: Correlogram of Daily Closing Price of NIFTY Cash Date: 03/14/10 Time: 17:39 Sample: 1 21755 Included observations: 21755 Autocorrelation Partial Correlation AC PAC Q-Stat Prob |******* |******* 1 1.000 1.000 21751. 0.000 |******* *| | 2 1.000 -0.076 43496. 0.000 |******* | | 3 0.999 0.006 65234. 0.000 |******* | | 4 0.999 0.035 86966. 0.000 |******* | | 5 0.999 0.020 108693 0.000 |******* | | 6 0.999 -0.002 130413 0.000 |******* | | 7 0.999 0.025 152128 0.000 |******* | | 8 0.999 0.007 173838 0.000 |******* | | 9 0.999 0.014 195542 0.000 |******* | | 10 0.998 0.005 217242 0.000 |******* | | 11 0.998 0.005 238936 0.000 |******* | | 12 0.998 -0.007 260625 0.000 |******* | | 13 0.998 0.002 282310 0.000 |******* | | 14 0.998 -0.005 303989 0.000 |******* | | 15 0.998 0.004 325662 0.000 |******* | | 16 0.998 -0.010 347331 0.000 |******* | | 17 0.997 -0.008 368994 0.000 |******* | | 18 0.997 -0.002 390652 0.000 |******* | | 19 0.997 0.007 412304 0.000 |******* | | 20 0.997 0.004 433951 0.000 |******* | | 21 0.997 -0.017 455593 0.000 |******* | | 22 0.997 -0.004 477229 0.000 32 Table 4.1.3: Correlogram of Intra Day Price of NIFTY Futures Date: 03/14/10 Time: 17:42 Sample: 1 21755 Included observations: 21755 Autocorrelation Partial Correlation AC PAC Q-Stat Prob |******* |******* 1 1.000 1.000 21751. 0.000 |******* | | 2 1.000 -0.002 43497. 0.000 |******* | | 3 1.000 -0.002 65236. 0.000 |******* | | 4 0.999 0.005 86970. 0.000 |******* | | 5 0.999 0.016 108698 0.000 |******* | | 6 0.999 -0.012 130421 0.000 |******* | | 7 0.999 0.022 152138 0.000 |******* | | 8 0.999 0.001 173849 0.000 |******* | | 9 0.999 0.010 195556 0.000 |******* | | 10 0.998 -0.002 217257 0.000 |******* | | 11 0.998 -0.001 238953 0.000 |******* | | 12 0.998 -0.003 260644 0.000 |******* | | 13 0.998 -0.001 282329 0.000 |******* | | 14 0.998 -0.013 304008 0.000 |******* | | 15 0.998 0.009 325683 0.000 |******* | | 16 0.998 -0.015 347351 0.000 |******* | | 17 0.997 -0.001 369014 0.000 |******* | | 18 0.997 -0.007 390671 0.000 |******* | | 19 0.997 -0.004 412323 0.000 |******* | | 20 0.997 0.002 433969 0.000 |******* | | 21 0.997 -0.006 455609 0.000 |******* | | 22 0.997 -0.016 477243 0.000 Interpretation: Table 2 and 3 represents the correlogram of intra day closing prices of NIFTY cash market and NIFTY futures market respectively. Here the length of lag is considered 22, as there are 22 trading days in a month. In above tables the autocorrelation coefficients starts at very high value at lag 1(1.0000 for NIFTY cash and NIFTY futures each)and declines very slowly. Thus it seems that both the time series are nonstationary. The AC statistics presented in Table 2 and 3 shows that the autocorrelation and partial autocorrelation are statistically significant as they fall outside the the asymptotic bounds 2���� −0.5 . 33 Unit root Test A unit root test is a statistical test for detecting the presence of stationarity in the series. The early and pioneering work on testing for a unit root in a time series was done by Dickey and Fuller(Dickey and Fuller 1979,1981). If the variables in the regression model are not stationary, then it can be shown that the standard assumptions for asymptotic analysis will not be valid. In other words, the usual ―t-ratios‖ will not follow a t-distribution, so we cannot validly undertake hypothesis tests about the regression parameters. The presence of the unit root in a time series is tested with the help of Augmented Dickey-Fuller Test. It tests for a unit root in the univariate representation of time series. For a return series ���� ���� , the ADF test consist of a regression of the first difference of the series against the series lagged k times as follows : ���� ∆�������� = ���� + ������������−1 + ����=1 �������� ∆��������−���� + �������� (���� ∆�������� = �������� − ��������−1 ; �������� = ln ���� ) The null hypothesis is �������� : δ=0 and ����1 : ���� < 1 . The acceptance of null hypothesis implies nonstationarity. One can transform the nonstationary time series to stationary time series either by differencing or by detrending. The transformation depends upon whether the series are difference stationary or trend stationary. 34 Table 4.1.4:Unit Root Testing of Intra Day Price of NIFTY Spot Null Hypothesis: NIFTY_SPOT has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Fixed) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -1.834484 0.6880 Test critical values: 1% level -3.958456 5% level -3.410009 10% level -3.126725 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(NIFTY_SPOT) Method: Least Squares Date: 03/15/10 Time: 19:31 Sample (adjusted): 2 21755 Included observations: 21754 after adjustments Variable Coefficient Std. Error t-Statistic Prob. NIFTY_SPOT(-1) -0.000277 0.000151 -1.834484 0.0666 C 1.454890 0.791218 1.838799 0.0660 @TREND(1) -5.99E-06 4.09E-06 -1.463099 0.1435 R-squared 0.000160 Mean dependent var -0.006415 Adjusted R-squared 0.000068 S.D. dependent var 2.861682 S.E. of regression 2.861585 Akaike info criterion 4.940766 Sum squared resid 178111.7 Schwarz criterion 4.941868 Log likelihood -53737.71 Hannan-Quinn criter. 4.941125 F-statistic 1.741985 Durbin-Watson stat 1.839837 Prob(F-statistic) 0.175197 35 Table 4.1.5: Unit Root Testing of Intra Day Price of NIFTY Futures Null Hypothesis: NIFTY_FUT has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Automatic based on SIC, MAXLAG=46) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -1.883004 0.6633 Test critical values: 1% level -3.958456 5% level -3.410009 10% level -3.126725 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(NIFTY_FUT) Method: Least Squares Date: 03/15/10 Time: 19:30 Sample (adjusted): 2 21755 Included observations: 21754 after adjustments Variable Coefficient Std. Error t-Statistic Prob. NIFTY_FUT(-1) -0.000291 0.000155 -1.883004 0.0597 C 1.530254 0.810454 1.888144 0.0590 @TREND(1) -6.31E-06 4.24E-06 -1.487228 0.1370 R-squared 0.000168 Mean dependent var -0.005519 Adjusted R-squared 0.000076 S.D. dependent var 2.961857 S.E. of regression 2.961745 Akaike info criterion 5.009572 Sum squared resid 190798.3 Schwarz criterion 5.010674 Log likelihood -54486.11 Hannan-Quinn criter. 5.009931 F-statistic 1.828074 Durbin-Watson stat 1.997068 Prob(F-statistic) 0.160748 Interpretation: Stationarity conditions of the Intra Day price of NIFTY cash and futures were tested by Augmented Dickey Fuller Test. The results of this test reported in Table 4 and 5. ADF statistics of both the series i.e. NIFTY SPOT in Table 4 and FUTURE in Table 5 shows presence of unit root in both the markets as their ���������������� exceeds the ���������������� (i.e. 1.834484 < 3.410009 for cash and 1.883004 < 3.410009 for futures) at 5% significant level. So the null hypothesis is accepted that both the series have unit root (i.e. δ=0). So both the series are non-stationary. Moreover trend coefficients of both the series are statistically insignificant as their Mackinnon‘s value do not 36 exceed the critical value at 5% level (p=0.1435> 0.05 for cash and p=0.1370 > 0.05 for futures). This suggests the absence of trend in both the markets. Table 4.1.6:Unit Root Testing of Logarithmic Series of Intra Day Price of NIFTY Spot Null Hypothesis: LN_NIFTY_SPOT has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Fixed) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -1.850756 0.6798 Test critical values: 1% level -3.958456 5% level -3.410009 10% level -3.126725 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LN_NIFTY_SPOT) Method: Least Squares Date: 03/15/10 Time: 19:36 Sample (adjusted): 2 21755 Included observations: 21754 after adjustments Variable Coefficient Std. Error t-Statistic Prob. LN_NIFTY_SPOT(-1) -0.000284 0.000154 -1.850756 0.0642 C 0.002434 0.001314 1.851402 0.0641 @TREND(1) -1.21E-09 8.28E-10 -1.463984 0.1432 R-squared 0.000162 Mean dependent var -1.28E-06 Adjusted R-squared 0.000070 S.D. dependent var 0.000576 S.E. of regression 0.000576 Akaike info criterion -12.08224 Sum squared resid 0.007206 Schwarz criterion -12.08114 Log likelihood 131421.5 Hannan-Quinn criter. -12.08188 F-statistic 1.764487 Durbin-Watson stat 1.841559 Prob(F-statistic) 0.171299 37 Table 4.1.7: Unit Root Testing of Logarithmic Series of Intra Day Price of NIFTY Futures Null Hypothesis: LN_NIFTY_FUT has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Fixed) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -1.898544 0.6552 Test critical values: 1% level -3.958456 5% level -3.410009 10% level -3.126725 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LN_NIFTY_FUT) Method: Least Squares Date: 03/15/10 Time: 19:37 Sample (adjusted): 2 21755 Included observations: 21754 after adjustments Variable Coefficient Std. Error t-Statistic Prob. LN_NIFTY_FUT(-1) -0.000298 0.000157 -1.898544 0.0576 C 0.002556 0.001346 1.899296 0.0575 @TREND(1) -1.28E-09 8.58E-10 -1.487040 0.1370 R-squared 0.000170 Mean dependent var -1.10E-06 Adjusted R-squared 0.000078 S.D. dependent var 0.000596 S.E. of regression 0.000596 Akaike info criterion -12.01280 Sum squared resid 0.007724 Schwarz criterion -12.01170 Log likelihood 130666.3 Hannan-Quinn criter. -12.01245 F-statistic 1.849968 Durbin-Watson stat 1.996934 Prob(F-statistic) 0.157267 38 Interpretation: Stationarity conditions of the logarithmic series of intra-day prices of NIFTY cash and futures were tested by Augmented Dickey Fuller Test. The results of this test reported in Table 6 and 7. ADF statistics of both the series i.e. LNIFTYCP in Table 6 and LFUTURECP in Table 7 shows presence of unit root in both the markets as their ���������������� exceeds the ���������������� (i.e. 1.850756 < 3.410009 for cash and 1.898544 < 3.410009 for futures) at 5% significant level. So the null hypothesis is accepted that both the series have unit root (i.e. δ=0). So both the series are nonstationary. Moreover trend coefficients of both the series are statistically insignificant as their Mackinnon‘s value do not exceed the critical value at 5% level (p=0.1432 > 0.05 for cash and p=0.1370 > 0.05 for futures). This suggests the absence of trend in both the markets. 39 Table 4.1.8:Unit Root Testing of Logarithmic Return Series of Intra Day Price of NIFTY Cash Null Hypothesis: DLN_NIFTY_SPOT has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Fixed) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -136.2455 0.0001 Test critical values: 1% level -3.958456 5% level -3.410009 10% level -3.126725 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(DLN_NIFTY_SPOT) Method: Least Squares Date: 03/15/10 Time: 19:40 Sample (adjusted): 2 21754 Included observations: 21753 after adjustments Variable Coefficient Std. Error t-Statistic Prob. DLN_NIFTY_SPOT(-1) -0.920935 0.006759 -136.2455 0.0000 C 9.23E-07 7.78E-06 0.118647 0.9056 @TREND(1) -1.91E-10 6.20E-10 -0.308313 0.7578 R-squared 0.460470 Mean dependent var 5.01E-08 Adjusted R-squared 0.460420 S.D. dependent var 0.000781 S.E. of regression 0.000574 Akaike info criterion -12.08835 Sum squared resid 0.007162 Schwarz criterion -12.08725 Log likelihood 131482.0 Hannan-Quinn criter. -12.08799 F-statistic 9281.414 Durbin-Watson stat 1.998230 Prob(F-statistic) 0.000000 40 Table 4.1.9: Unit Root Testing of Logarithmic Return Series of Intra Day Price of NIFTY Futures Null Hypothesis: DLN_NIFTY_FUT has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Fixed) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -147.2754 0.0001 Test critical values: 1% level -3.958456 5% level -3.410009 10% level -3.126725 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(DLN_NIFTY_FUT) Method: Least Squares Date: 03/15/10 Time: 19:42 Sample (adjusted): 2 21754 Included observations: 21753 after adjustments Variable Coefficient Std. Error t-Statistic Prob. DLN_NIFTY_FUT(-1) -0.998612 0.006781 -147.2754 0.0000 C 1.13E-06 8.08E-06 0.139688 0.8889 @TREND(1) -2.04E-10 6.43E-10 -0.316309 0.7518 R-squared 0.499310 Mean dependent var 2.70E-08 Adjusted R-squared 0.499264 S.D. dependent var 0.000842 S.E. of regression 0.000596 Akaike info criterion -12.01262 Sum squared resid 0.007725 Schwarz criterion -12.01151 Log likelihood 130658.2 Hannan-Quinn criter. -12.01226 F-statistic 10845.02 Durbin-Watson stat 1.999885 Prob(F-statistic) 0.000000 Interpretation: In Table 8 and 9, ADF statistics of both the series shows absence of unit root (i.e. δ=0) in both the series i.e. DLFUTURECP and DLNIFTYCP as their ���������������� exceeds the ���������������� ( 136.2455 & 147.2754 > 3.410009). Thus both the series are now stationary. And trend coefficients of both the series are also statistically insignificant, that shows the absence of trend in both the series. 41 Lead-Lag Relationship Analysis of Return Series of NIFTY Cash and Futures (Whole Period- From Dec 01,2010 to Feb 28,2010) Table-4.1.10: Descriptive Statistics of Intra Day Logarithmic Returns DLN_NIFTY_SPOT DLN_NIFTY_FUT Mean -0.000392 -0.000392 Median 0.000000 0.000000 Maximum 0.015491 0.013374 Minimum -8.502252 -8.504300 Std. Dev. 0.057647 0.057661 Skewness -147.4635 -147.4620 Kurtosis 21748.66 21748.35 Jarque-Bera 4.29E+11 4.29E+11 Probability 0.000000 0.000000 Sum -8.530188 -8.528331 Sum Sq. Dev. 72.29215 72.32751 Observations 21755 21755 Interpretation: Descriptive statistics on NIFTY spot and NIFTY futures market returns are presented in Table 10 above. The descriptive statistics for the return series are mean, median, maximum, minimum, standard deviation, skewness, kurtosis, Jarque-Bera & probability. If we look into the summary statistics of NIFTY Cash and NIFTY Futures index, then it can be seen that the mean returns has been found to be zero reverting. The difference between the maximum and minimum value of return is more or less same in both the market that leads to same standard deviation in both the market. Skewness and Kurtosis measure the shape of the probability distribution. Skewness measures the degree of asymmetry, with symmetry implying zero skewness. Here the returns are negatively skewed, indicating the relatively long left tail compared to the right tail, so the distribution is non-symmetric. Kurtosis indicates the extent to which probability is concentrated 42 in the centre and especially at the tail of the distribution rather than in the shoulders which are the regions between center and the tails. Every normal distribution has a Skewness equal to zero and Kurtosis of 3. Kurtosis in excess of 3 indicates the leptokurtosis. Here, it can be found that all the figures are positive and greater than 3, therefore all the return distributions are said to be leptokurtic. The more the value of the kurtosis of the return in a market, the more destabilize is the market‘s return. In statistics, the Jarque-Bera test is a goodness-of-fit measure of departure from normality, based on the sample kurtosis and skewness JB=���� 6 (���� 2 − ���� − 3 2 4), where n is the number of observations (or degrees of freedom in general); S is the sample skewness, K is the sample kurtosis. The statistic JB has an asymptotic chi-square distribution with two degrees of freedom and can be used to test the null hypothesis that the data are from a normal distribution. The null hypothesis is a joint hypothesis of the skewness being zero and the excess kurtosis being 0, since samples from a normal distribution have an expected skewness of 0 and an expected excess kurtosis of 0 (which is the same as a kurtosis of 3). As the definition of JB shows, any deviation from this increases the JB statistic. In this study, the higher value of Jarque- Bera indicates that all the return series in all the time periods are non-normal. 43 Table 4.1.11: Cross-correlation Date: 03/15/10 Time: 18:35 Sample: 1 21755 Included observations: 21754 Correlations are asymptotically consistent approximations DLN_NIFTY_FUT,DLN_NIF DLN_NIFTY_FUT,DLN_NIFT TY_SPOT(-i) Y_SPOT(+i) i lag lead |*********| |*********| 0 0.8557 0.8557 | | |* | 1 0.0349 0.1379 | | | | 2 -0.0101 0.0155 | | | | 3 -0.0163 -0.0203 | | | | 4 -0.0156 -0.0253 | | | | 5 0.0100 0.0059 | | | | 6 -0.0152 -0.0250 | | | | 7 -0.0096 -0.0042 | | | | 8 -0.0125 -0.0120 | | | | 9 -0.0069 -0.0058 | | | | 10 0.0041 -0.0037 Interpretation Using the cross-correlation function the lead and the lag coefficients have been found out in Table 11 up to 10 order. 44 Table 4.1.12: Lead-lag Relationship among the Spot and the Futures Markets Returns Panel A: Dependent Variable: DLN_NIFTY_SPOT Method: Least Squares Date: 03/15/10 Time: 18:37 Sample (adjusted): 11 21744 Included observations: 21734 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C -1.40E-06 3.86E-06 -0.361720 0.7176 DLN_NIFTY_FUT(-10) -0.004430 0.006485 -0.683098 0.4946 DLN_NIFTY_FUT(-9) -0.003292 0.006485 -0.507578 0.6118 DLN_NIFTY_FUT(-8) -0.011055 0.006485 -1.704700 0.0883 DLN_NIFTY_FUT(-7) -0.001366 0.006485 -0.210635 0.8332 DLN_NIFTY_FUT(-6) -0.026136* 0.006484 -4.030759 0.0001 DLN_NIFTY_FUT(-5) 0.008732 0.006485 1.346342 0.1782 DLN_NIFTY_FUT(-4) -0.024028* 0.006486 -3.704633 0.0002 DLN_NIFTY_FUT(-3) -0.018759* 0.006487 -2.892000 0.0038 DLN_NIFTY_FUT(-2) 0.013875* 0.006486 2.139043 0.0324 DLN_NIFTY_FUT(-1) 0.133577* 0.006487 20.59076 0.0000 DLN_NIFTY_FUT(1) 0.034351* 0.006487 5.295162 0.0000 DLN_NIFTY_FUT(2) -0.009118 0.006487 -1.405583 0.1599 DLN_NIFTY_FUT(3) -0.013710* 0.006487 -2.113455 0.0346 DLN_NIFTY_FUT(4) -0.016645* 0.006486 -2.566182 0.0103 DLN_NIFTY_FUT(5) 0.012919* 0.006486 1.991822 0.0464 DLN_NIFTY_FUT(6) -0.015230* 0.006484 -2.348781 0.0188 DLN_NIFTY_FUT(7) -0.006656 0.006485 -1.026252 0.3048 DLN_NIFTY_FUT(8) -0.012089 0.006484 -1.864409 0.0623 DLN_NIFTY_FUT(9) -0.006002 0.006484 -0.925569 0.3547 DLN_NIFTY_FUT(10) 0.002494 0.006484 0.384614 0.7005 R-squared 0.023698 Mean dependent var -1.46E-06 Adjusted R-squared 0.022799 S.D. dependent var 0.000576 S.E. of regression 0.000569 Akaike info criterion -12.10429 Sum squared resid 0.007031 Schwarz criterion -12.09657 Log likelihood 131558.3 Hannan-Quinn criter. -12.10178 F-statistic 26.35223 Durbin-Watson stat 2.146052 Prob(F-statistic) 0.000000 45 Panel B: Dependent Variable: DLN_NIFTY_FUT Method: Least Squares Date: 03/15/10 Time: 18:40 Sample (adjusted): 11 21744 Included observations: 21734 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C -1.23E-06 4.00E-06 -0.307912 0.7582 DLN_NIFTY_SPOT(-10) 0.002640 0.006978 0.378272 0.7052 DLN_NIFTY_SPOT(-9) -0.005118 0.006999 -0.731251 0.4646 DLN_NIFTY_SPOT(-8) -0.009843 0.006999 -1.406384 0.1596 DLN_NIFTY_SPOT(-7) -0.005482 0.007003 -0.782795 0.4338 DLN_NIFTY_SPOT(-6) -0.016498* 0.007002 -2.355986 0.0185 DLN_NIFTY_SPOT(-5) 0.016362* 0.007004 2.335969 0.0195 DLN_NIFTY_SPOT(-4) -0.015916* 0.007004 -2.272359 0.0231 DLN_NIFTY_SPOT(-3) -0.011858 0.007002 -1.693388 0.0904 DLN_NIFTY_SPOT(-2) -0.007855 0.007007 -1.120983 0.2623 DLN_NIFTY_SPOT(-1) 0.036698* 0.006987 5.252321 0.0000 DLN_NIFTY_SPOT(1) 0.141117* 0.006987 20.19805 0.0000 DLN_NIFTY_SPOT(2) 0.00620 0.007007 0.886091 0.3756 DLN_NIFTY_SPOT(3) -0.019386* 0.007002 -2.768424 0.0056 DLN_NIFTY_SPOT(4) -0.021094* 0.007004 -3.011604 0.0026 DLN_NIFTY_SPOT(5) 0.014323* 0.007005 2.044670 0.0409 DLN_NIFTY_SPOT(6) -0.028201* 0.007003 -4.027073 0.0001 DLN_NIFTY_SPOT(7) 0.001422 0.007003 0.203052 0.8391 DLN_NIFTY_SPOT(8) -0.010309 0.006999 -1.472996 0.1408 DLN_NIFTY_SPOT(9) -0.003149 0.006998 -0.449939 0.6528 DLN_NIFTY_SPOT(10) -0.004154 0.006978 -0.595355 0.5516 R-squared 0.023045 Mean dependent var -1.32E-06 Adjusted R-squared 0.022145 S.D. dependent var 0.000596 S.E. of regression 0.000589 Akaike info criterion -12.03484 Sum squared resid 0.007536 Schwarz criterion -12.02713 Log likelihood 130803.6 Hannan-Quinn criter. -12.03233 F-statistic 25.60866 Durbin-Watson stat 2.297313 Prob(F-statistic) 0.000000 Interpretation: Table 12 shows the lead lag relationship between the Cash and Futures market returns on minute basis. Here by using Linear Regression Equation the lead and lag coefficients have been found out up to 10th orders. In Panel A logarithmic return series of NIFTY cash DLNIFTYSPOT is taken as dependent variable and null hypothesis was set as NIFTY futures leads/lags NIFTY cash 46 and in Panel B logarithmic return series of NIFTY futures i.e. DLNNIFTYFUT is taken as dependent variable and null hypothesis was set as NIFTY cash leads/lags NIFTY futures. The t-statistics for both the hypothesis are significant between +6 to -6 at 5% confidence level. (Significant coefficients are shown using *) This suggests that both cash and futures markets would react simultaneously to much of the information. It is to be noted here that any strong generalization can‘t be made by looking in to the specific results found in this study, because such results may be restricted only for the specific time period considered in this study and therefore may be time-variant in nature. As far as the whole study period is concerned, the leads as well as lag coefficients in the futures market are found to be significant up to 6 lags. This suggests that the futures market leads or lags the cash market 4-6 minutes, while the reverse is possible up to 6 lags that cash market leads or lags the futures market for 4-6 minutes, depending on the time period. The regression results, using the cash return innovations, exhibits that neither the lead, nor the lag coefficients are found to be significant beyond 6 leads or lags. This suggests the contemporaneous bi-directional lead-lag relationship between these two market, and the flow of information is also simultaneous between cash and futures market. 47 Table 4.1.13: Pair wise Granger Causality Tests Pairwise Granger Causality Tests Date: 03/12/10 Time: 22:49 Sample: 1 21755 Lags: 10 Null Hypothesis: Obs F-Statistic Prob. DLN_NIFTY_FUT does not Granger Cause DLN_NIFTY_SPOT 21745 2.86444* 0.0014 DLN_NIFTY_SPOT does not Granger Cause DLN_NIFTY_FUT 2.36931* 0.0085 Pairwise Granger Causality Tests Date: 03/12/10 Time: 22:50 Sample: 1 21755 Lags: 9 Null Hypothesis: Obs F-Statistic Prob. DLN_NIFTY_FUT does not Granger Cause DLN_NIFTY_SPOT 21746 3.17648* 0.0008 DLN_NIFTY_SPOT does not Granger Cause DLN_NIFTY_FUT 2.64457* 0.0046 Pairwise Granger Causality Tests Date: 03/12/10 Time: 22:51 Sample: 1 21755 Lags: 8 Null Hypothesis: Obs F-Statistic Prob. DLN_NIFTY_FUT does not Granger Cause DLN_NIFTY_SPOT 21747 3.55711* 0.0004 DLN_NIFTY_SPOT does not Granger Cause DLN_NIFTY_FUT 2.77997* 0.0045 Pairwise Granger Causality Tests Date: 03/12/10 Time: 22:51 Sample: 1 21755 Lags: 7 Null Hypothesis: Obs F-Statistic Prob. DLN_NIFTY_FUT does not Granger Cause DLN_NIFTY_SPOT 21748 3.86394* 0.0003 DLN_NIFTY_SPOT does not Granger Cause DLN_NIFTY_FUT 2.99772* 0.0038 48 Pairwise Granger Causality Tests Date: 03/12/10 Time: 22:52 Sample: 1 21755 Lags: 6 Null Hypothesis: Obs F-Statistic Prob. DLN_NIFTY_FUT does not Granger Cause DLN_NIFTY_SPOT 21749 4.40578* 0.0002 DLN_NIFTY_SPOT does not Granger Cause DLN_NIFTY_FUT 3.43749* 0.0021 Pairwise Granger Causality Tests Date: 03/12/10 Time: 22:53 Sample: 1 21755 Lags: 5 Null Hypothesis: Obs F-Statistic Prob. DLN_NIFTY_FUT does not Granger Cause DLN_NIFTY_SPOT 21750 5.22613* 8.E-05 DLN_NIFTY_SPOT does not Granger Cause DLN_NIFTY_FUT 4.06200* 0.0011 Pairwise Granger Causality Tests Date: 03/12/10 Time: 22:53 Sample: 1 21755 Lags: 4 Null Hypothesis: Obs F-Statistic Prob. DLN_NIFTY_FUT does not Granger Cause DLN_NIFTY_SPOT 21751 6.48761* 3.E-05 DLN_NIFTY_SPOT does not Granger Cause DLN_NIFTY_FUT 5.05933* 0.0005 Pairwise Granger Causality Tests Date: 03/12/10 Time: 22:54 Sample: 1 21755 Lags: 3 Null Hypothesis: Obs F-Statistic Prob. DLN_NIFTY_FUT does not Granger Cause DLN_NIFTY_SPOT 21752 8.28000* 2.E-05 DLN_NIFTY_SPOT does not Granger Cause DLN_NIFTY_FUT 6.10476* 0.0004 49 Pairwise Granger Causality Tests Date: 03/12/10 Time: 22:54 Sample: 1 21755 Lags: 2 Null Hypothesis: Obs F-Statistic Prob. DLN_NIFTY_FUT does not Granger Cause DLN_NIFTY_SPOT 21753 0.71268 0.4903 DLN_NIFTY_SPOT does not Granger Cause DLN_NIFTY_FUT 1.00438 0.3663 Pairwise Granger Causality Tests Date: 03/12/10 Time: 22:54 Sample: 1 21755 Lags: 1 Null Hypothesis: Obs F-Statistic Prob. DLN_NIFTY_FUT does not Granger Cause DLN_NIFTY_SPOT 21754 1.13137 0.2875 DLN_NIFTY_SPOT does not Granger Cause DLN_NIFTY_FUT 1.22408 0.2686 Interpretation: Granger Causality Test checks the existence of relationship between two variables. In other words it checks the dependence of one variable on other variable or the direction of influence. If variable X (Granger) causes variable Y, then changes in X should precede changes in Y. Therefore, in a regression of Y on other variables (including its own lagged values) if we include past or lagged values of X and it significantly improves the prediction of Y, then we can say that X (Granger) causes Y. A similar definition applies if Y (Granger) causes X. This causality relationship between two variables can have 3 forms - (1) Unidirectional causality-if from both variables either variable significantly causes changes in other variable (2) Bilateral causality-is suggested when the sets of both time series coefficients are statistically significantly different from zero in both the regressions. (3) Independence-is suggested when the sets of both the time series coefficients are not statistically significant in both the regression. In Table 13 the dependence or causality relationship of NIFTY cash and NIFTY futures return is checked for 10 lags. From the above table, one can easily infer that the F- statistics for all 3-10 lags in both the regression, i.e. regression of NIFTY cash returns on NIFTY futures return and regression of NIFTY futures return on NIFTY cash return are statistically significant at 5% level. So it suggests both the variables are dependent and there is bilateral causality between them (Significant coefficients are shown using *). 50 4.2 DLF Preliminary Analysis Table 4.2.1: Descriptive Statistics of Daily Closing Price and Settlement Price of DLF SPOT And DLF Futures respectively DLF_FUT DLF_SPOT Mean 336.9366 338.0603 Median 365.4250 364.8000 Maximum 470.4500 471.9500 Minimum 122.4000 136.6500 Std. Dev. 81.20752 78.99383 Skewness -0.969066 -0.922891 Kurtosis 3.123610 3.036218 Jarque-Bera 38.03064 34.36624 Probability 0.000000 0.000000 Sum 81538.65 81810.60 Sum Sq. Dev. 1589313. 1503846. Observations 242 242 Interpretation Descriptive statistics on DLF spot and DLF futures closing and settlement prices respectively are presented in Table 1 above. The descriptive statistics series are mean, median, maximum, minimum, standard deviation, skewness, kurtosis, Jarque-Bera & probability. Here as the skewness is not zero for both the series, but negative. So both the series are negatively skewed. Kurtosis suggests the leptokurtic series. Moreover Jarque Bera statistics are greater than zero which rejects the hypothesis of normal distribution for both the series. 51 Graphical Analysis Figure: 4.2.1 Daily closing price of DLF SPOT index (MARCH-2009 to FEB-2010) DLF_SPOT 480 440 400 360 320 280 240 200 160 120 25 50 75 100 125 150 175 200 225 Figure:4.2.2 Daily settlement price of DLF futures (MARCH-2009 to FEB-2010) DLF_FUT 500 450 400 350 300 250 200 150 100 25 50 75 100 125 150 175 200 225 52 Interpretation In the above diagram, Figure 1 and Figure 2 represents the daily closing price of DLF cash index and daily settlement price of DLF futures.These plots gives an initial clue about the likely nature of the time series. In Figure 1 and 2, it has been seen that over the period of study closing price and the settlement price of DLF cash and futures respectively have been increasing or decreasing, that is, showing an upward trend or downward trend, suggesting perhaps that the mean of both the series has beeen changing. This perhaps suggests that both the series are not stationary. Moreover, if both the plots are minutely observed than one can easily infer that, both the series move in the same direction and somewhat with the same magnitude. So, by establishing the lead- lag relationship one may predict the change in prices within the particular trading period in either way. 53 Table 4.2.2: Correlogram of Daily Closing Price of DLF SPOT Date: 03/17/10 Time: 11:57 Sample: 1 242 Included observations: 242 Autocorrelation Partial Correlation AC PAC Q-Stat Prob .|******* .|******* 1 0.972 0.972 231.58 0.000 .|******* .|. | 2 0.942 -0.057 449.92 0.000 .|******* .|. | 3 0.911 -0.032 654.91 0.000 .|******| .|. | 4 0.880 -0.004 847.17 0.000 .|******| .|. | 5 0.849 -0.027 1026.8 0.000 .|******| .|. | 6 0.818 -0.016 1194.3 0.000 .|******| .|. | 7 0.789 0.026 1350.8 0.000 .|***** | .|. | 8 0.761 -0.010 1496.9 0.000 .|***** | .|. | 9 0.733 -0.006 1633.2 0.000 .|***** | *|. | 10 0.702 -0.082 1758.7 0.000 .|***** | .|. | 11 0.676 0.074 1875.5 0.000 .|***** | .|. | 12 0.652 0.023 1984.5 0.000 .|***** | .|. | 13 0.626 -0.052 2085.6 0.000 .|**** | .|. | 14 0.602 0.015 2179.4 0.000 .|**** | .|. | 15 0.580 0.031 2266.9 0.000 .|**** | .|. | 16 0.559 -0.008 2348.6 0.000 .|**** | *|. | 17 0.536 -0.068 2423.9 0.000 .|**** | .|. | 18 0.511 -0.019 2492.7 0.000 .|**** | .|. | 19 0.484 -0.050 2554.9 0.000 .|*** | .|. | 20 0.460 0.011 2611.1 0.000 .|*** | .|. | 21 0.438 0.047 2662.4 0.000 .|*** | .|* | 22 0.421 0.074 2710.0 0.000 54 Table 4.2.3: Correlogram of Daily Closing Price of DLF FUTURE Date: 03/17/10 Time: 11:57 Sample: 1 242 Included observations: 242 Autocorrelation Partial Correlation AC PAC Q-Stat Prob .|******* .|******* 1 0.971 0.971 230.94 0.000 .|******* .|. | 2 0.940 -0.038 448.50 0.000 .|******* .|. | 3 0.909 -0.025 652.78 0.000 .|******| .|. | 4 0.879 0.001 844.56 0.000 .|******| .|. | 5 0.849 -0.025 1024.0 0.000 .|******| .|. | 6 0.817 -0.037 1191.0 0.000 .|******| .|. | 7 0.788 0.037 1347.1 0.000 .|***** | .|. | 8 0.761 0.006 1493.2 0.000 .|***** | .|. | 9 0.735 -0.000 1630.0 0.000 .|***** | *|. | 10 0.704 -0.094 1756.1 0.000 .|***** | .|. | 11 0.678 0.067 1873.5 0.000 .|***** | .|. | 12 0.654 0.034 1983.4 0.000 .|***** | .|. | 13 0.630 -0.037 2085.8 0.000 .|**** | .|. | 14 0.607 0.002 2181.2 0.000 .|**** | .|. | 15 0.586 0.030 2270.4 0.000 .|**** | .|. | 16 0.565 -0.007 2353.9 0.000 .|**** | .|. | 17 0.543 -0.057 2431.3 0.000 .|**** | .|. | 18 0.519 -0.032 2502.2 0.000 .|**** | .|. | 19 0.492 -0.055 2566.3 0.000 .|*** | .|. | 20 0.467 0.001 2624.2 0.000 .|*** | .|. | 21 0.445 0.047 2677.1 0.000 .|*** | .|* | 22 0.428 0.085 2726.3 0.000 Interpretation Table 2 and 3 represents the correlogram of daily closing price and settlament price of DLF cash market and DLF futures market respectively. Here the length of lag is considered 22, as there are 22 trading days in a month. In above tables the autocorrelation coefficients starts at very high value at lag 1(0.972 for DLF cash and 0.971 for DLF futures)and declines gradually. Thus it seems that both the time series are nonstationary. The AC statistics presented in Table 2 and 3 shows that the autocorrelation and partial autocorrelation are statistically significant as they fall outside the the asymptotic bounds 2���� −0.5 (±0.089). 55 Table 4.2.4:Unit Root Testing of Daily Closing Price of DLF SPOT Null Hypothesis: DLF_SPOT has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Fixed) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -1.623922 0.7809 Test critical values: 1% level -3.996592 5% level -3.428581 10% level -3.137711 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(DLF_SPOT) Method: Least Squares Date: 03/17/10 Time: 11:59 Sample (adjusted): 2 242 Included observations: 241 after adjustments Variable Coefficient Std. Error t-Statistic Prob. DLF_SPOT(-1) -0.021981 0.013535 -1.623922 0.1057 C 9.237636 3.960552 2.332411 0.0205 @TREND(1) -0.009778 0.015361 -0.636553 0.5250 R-squared 0.025011 Mean dependent var 0.620124 Adjusted R-squared 0.016818 S.D. dependent var 13.87363 S.E. of regression 13.75647 Akaike info criterion 8.093266 Sum squared resid 45039.23 Schwarz criterion 8.136645 Log likelihood -972.2385 Hannan-Quinn criter. 8.110742 F-statistic 3.052706 Durbin-Watson stat 1.875349 Prob(F-statistic) 0.049085 56 Table 4.2.5:Unit Root Testing of Daily Closing Price of DLF FUT Null Hypothesis: DLF_FUT has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Fixed) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -1.721053 0.7391 Test critical values: 1% level -3.996592 5% level -3.428581 10% level -3.137711 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(DLF_FUT) Method: Least Squares Date: 03/17/10 Time: 11:59 Sample (adjusted): 2 242 Included observations: 241 after adjustments Variable Coefficient Std. Error t-Statistic Prob. DLF_FUT(-1) -0.023318 0.013548 -1.721053 0.0865 C 9.769753 3.924138 2.489656 0.0135 @TREND(1) -0.010043 0.015807 -0.635367 0.5258 R-squared 0.027832 Mean dependent var 0.694191 Adjusted R-squared 0.019662 S.D. dependent var 14.18189 S.E. of regression 14.04177 Akaike info criterion 8.134320 Sum squared resid 46926.78 Schwarz criterion 8.177699 Log likelihood -977.1856 Hannan-Quinn criter. 8.151797 F-statistic 3.406807 Durbin-Watson stat 1.930147 Prob(F-statistic) 0.034772 57 Interpretation Stationarity conditions of the daily closing price and settlement price of DLF cash and futures were tested by Augmented Dickey Fuller Test. The results of this test reported in Table 4 and 5. ADF statistics of both the series i.e. DLF SPOT in Table 4 and FUTURE in Table 5 shows presence of unit root in both the markets as their ���������������� exceeds the ���������������� (i.e. 1.623922 < 3.428581 for cash and 1.721053 < 3.428581 for futures) at 5% significant level. So the null hypothesis is accepted that both the series have unit root (i.e. δ=0). So both the series are nonstationary. Moreover trend coefficients of both the series are statistically insignificant as their Mackinnon‘s value do not exceed the critical value at 5% level (p=0.5250> 0.05 for cash and p=0.5258 > 0.05 for futures). This suggests the absence of trend in both the markets. 58 Table 4.2.6:Unit Root Testing of Logarithmic Series of Daily Closing Price of DLF SPOT Null Hypothesis: LN_DLF_SPOT has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Fixed) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -1.830141 0.6871 Test critical values: 1% level -3.996592 5% level -3.428581 10% level -3.137711 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LN_DLF_SPOT) Method: Least Squares Date: 03/17/10 Time: 12:00 Sample (adjusted): 2 242 Included observations: 241 after adjustments Variable Coefficient Std. Error t-Statistic Prob. LN_DLF_SPOT(-1) -0.022152 0.012104 -1.830141 0.0685 C 0.135655 0.066779 2.031408 0.0433 @TREND(1) -3.75E-05 4.91E-05 -0.764444 0.4454 R-squared 0.034915 Mean dependent var 0.002882 Adjusted R-squared 0.026805 S.D. dependent var 0.043298 S.E. of regression 0.042713 Akaike info criterion -3.456236 Sum squared resid 0.434216 Schwarz criterion -3.412857 Log likelihood 419.4765 Hannan-Quinn criter. -3.438760 F-statistic 4.305238 Durbin-Watson stat 1.853904 Prob(F-statistic) 0.014564 59 Table 4.2.7:Unit Root Testing of Logarithmic Series of Daily Closing Price of DLF FUT Null Hypothesis: LN_DLF_FUT has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Fixed) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -2.158723 0.5100 Test critical values: 1% level -3.996592 5% level -3.428581 10% level -3.137711 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LN_DLF_FUT) Method: Least Squares Date: 03/17/10 Time: 12:00 Sample (adjusted): 2 242 Included observations: 241 after adjustments Variable Coefficient Std. Error t-Statistic Prob. LN_DLF_FUT(-1) -0.026544 0.012296 -2.158723 0.0319 C 0.161234 0.067551 2.386865 0.0178 @TREND(1) -3.57E-05 5.24E-05 -0.680996 0.4965 R-squared 0.043233 Mean dependent var 0.003427 Adjusted R-squared 0.035193 S.D. dependent var 0.046134 S.E. of regression 0.045315 Akaike info criterion -3.337970 Sum squared resid 0.488729 Schwarz criterion -3.294591 Log likelihood 405.2254 Hannan-Quinn criter. -3.320493 F-statistic 5.377166 Durbin-Watson stat 1.950775 Prob(F-statistic) 0.005199 60 Interpretation Stationarity conditions of the intra-day price series of DLF cash and futures were tested by Augmented Dickey Fuller Test. The results of this test reported in Table 6 and 7. ADF statistics of both the series i.e. LN_DLF_SPOT in Table 6 and LN_DLF_FUT in Table 7 shows absence of unit root in both the markets as their ���������������� exceeds the ���������������� (i.e. 1.830141 < 3.428581 for cash and 2.158723 < 3.428581 for futures) at 5% significant level. So the null hypothesis is accepted that both the series have unit root (i.e. δ=0). So both the series are nonstationary. Moreover trend coefficients of both the series are statistically insignificant as their Mackinnon‘s value do not exceed the critical value at 5% level (p=0.4454 > 0.05 for cash and p=0.4965 > 0.05 for futures). This suggests the absence of trend in both the markets. 61 Table 4.2.8:Unit Root Testing of Logarithmic Return Series of Daily Closing Price of DLF SPOT Null Hypothesis: DLN_DLF_SPOT has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Fixed) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -14.42521 0.0000 Test critical values: 1% level -3.996754 5% level -3.428660 10% level -3.137757 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(DLN_DLF_SPOT) Method: Least Squares Date: 03/17/10 Time: 12:01 Sample (adjusted): 2 241 Included observations: 240 after adjustments Variable Coefficient Std. Error t-Statistic Prob. DLN_DLF_SPOT(-1) -0.936368 0.064912 -14.42521 0.0000 C 0.013170 0.005644 2.333283 0.0205 @TREND(1) -8.66E-05 4.05E-05 -2.136120 0.0337 R-squared 0.467523 Mean dependent var 0.000145 Adjusted R-squared 0.463029 S.D. dependent var 0.058681 S.E. of regression 0.043000 Akaike info criterion -3.442806 Sum squared resid 0.438216 Schwarz criterion -3.399298 Log likelihood 416.1367 Hannan-Quinn criter. -3.425275 F-statistic 104.0447 Durbin-Watson stat 1.996562 Prob(F-statistic) 0.000000 62 Table 4.2.9:Unit Root Testing of Logarithmic Return Series of Daily Closing Price of DLF FUT Null Hypothesis: DLN_DLF_FUT has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Fixed) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -15.12741 0.0000 Test critical values: 1% level -3.996754 5% level -3.428660 10% level -3.137757 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(DLN_DLF_FUT) Method: Least Squares Date: 03/17/10 Time: 12:01 Sample (adjusted): 2 241 Included observations: 240 after adjustments Variable Coefficient Std. Error t-Statistic Prob. DLN_DLF_FUT(-1) -0.983778 0.065033 -15.12741 0.0000 C 0.015756 0.006030 2.612742 0.0096 @TREND(1) -0.000103 4.33E-05 -2.376519 0.0183 R-squared 0.491245 Mean dependent var 9.09E-05 Adjusted R-squared 0.486952 S.D. dependent var 0.064002 S.E. of regression 0.045843 Akaike info criterion -3.314773 Sum squared resid 0.498072 Schwarz criterion -3.271265 Log likelihood 400.7728 Hannan-Quinn criter. -3.297242 F-statistic 114.4215 Durbin-Watson stat 1.994949 Prob(F-statistic) 0.000000 Interpretation In Table 8 and 9, ADF statistics of both the series shows absence of unit root (i.e. δ=0) in both the series i.e. DLN_DLF_SPOT and DLN_DLF_FUT as their ���������������� exceeds the ���������������� ( 14.42521 & 15.12741 > 3.410009). Thus both the series are now stationary. And trend coefficients of both the series are also statistically insignificant, that shows the absence of trend in both the series. 63 Table 4.2.10: Descriptive Statistics of Daily Logarithmic Returns DLN_DLF_SPOT DLN_DLF_FUT Mean 0.002882 0.003427 Median 0.000408 0.001674 Maximum 0.223415 0.256301 Minimum -0.111233 -0.122799 Std. Dev. 0.043298 0.046134 Skewness 0.804189 0.809027 Kurtosis 6.310293 7.107421 Jarque-Bera 136.0136 195.7021 Probability 0.000000 0.000000 Sum 0.694656 0.825911 Sum Sq. Dev. 0.449926 0.510813 Observations 241 241 Interpretation The descriptive statistics for the return of series DLF are mean, median, maximum, minimum, standard deviation, skewness, kurtosis, Jarque-Bera & probability, which are shown in Table 1. DLN_DLF_SPOT is the logarithmic return series of futures market of script DLF, where as DLN_DLF_FUT is the logarithmic return series of cash market of script DLF. The mean return of both the series are positive. There is not much difference in the std. deviation of both the series. Both the return series are positively skewed and as the kurtosis value is more than 3, both the series are leptokurtic. Moreover the Jarque-Bera statistics are also high, which rejects the hypothesis of normal distribution. 64 Figure 4.2.3: Daily Return on DLF SPOT Market DLN_DLF_SPOT .24 .20 .16 .12 .08 .04 .00 -.04 -.08 -.12 25 50 75 100 125 150 175 200 225 Figure 4.2.4: Daily Return on DLF FUTURE Market DLN_DLF_FUT .30 .25 .20 .15 .10 .05 .00 -.05 -.10 -.15 25 50 75 100 125 150 175 200 225 Interpretation From the above Figure 1 & 2, it can be seen that returns of both future series and cash series for DLF are mean reverting and close to zero. So both the series may be stationary. 65 Table 4.2.11: Unit Root Test for DLN_DLF_SPOT Null Hypothesis: DLN_DLF_SPOT has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Fixed) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -14.42521 0.0000 Test critical values: 1% level -3.996754 5% level -3.428660 10% level -3.137757 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(DLN_DLF_SPOT) Method: Least Squares Date: 03/16/10 Time: 20:42 Sample (adjusted): 2 241 Included observations: 240 after adjustments Variable Coefficient Std. Error t-Statistic Prob. DLN_DLF_SPOT(-1) -0.936368 0.064912 -14.42521 0.0000 C 0.013170 0.005644 2.333283 0.0205 @TREND(1) -8.66E-05 4.05E-05 -2.136120 0.0337 R-squared 0.467523 Mean dependent var 0.000145 Adjusted R-squared 0.463029 S.D. dependent var 0.058681 S.E. of regression 0.043000 Akaike info criterion -3.442806 Sum squared resid 0.438216 Schwarz criterion -3.399298 Log likelihood 416.1367 Hannan-Quinn criter. -3.425275 F-statistic 104.0447 Durbin-Watson stat 1.996562 Prob(F-statistic) 0.000000 66 Table 4.2.12: Unit Root Test for DLN_DLF_FUT Null Hypothesis: DLN_DLF_FUT has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Fixed) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -15.12741 0.0000 Test critical values: 1% level -3.996754 5% level -3.428660 10% level -3.137757 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(DLN_DLF_FUT) Method: Least Squares Date: 03/16/10 Time: 20:43 Sample (adjusted): 2 241 Included observations: 240 after adjustments Variable Coefficient Std. Error t-Statistic Prob. DLN_DLF_FUT(-1) -0.983778 0.065033 -15.12741 0.0000 C 0.015756 0.006030 2.612742 0.0096 @TREND(1) -0.000103 4.33E-05 -2.376519 0.0183 R-squared 0.491245 Mean dependent var 9.09E-05 Adjusted R-squared 0.486952 S.D. dependent var 0.064002 S.E. of regression 0.045843 Akaike info criterion -3.314773 Sum squared resid 0.498072 Schwarz criterion -3.271265 Log likelihood 400.7728 Hannan-Quinn criter. -3.297242 F-statistic 114.4215 Durbin-Watson stat 1.994949 Prob(F-statistic) 0.000000 Interpretation Table 2 and 3 shows that the ADF t-statistic exceeds the critical value of series DLN_DLF_SPOT in Table 2 and of DLN_DLF_FUT in Table 3 i.e. ���������������� exceeds the ���������������� (3.428660 < 14.42521 & 15.12741) significantly. So the null hypothesis of unit root has been rejected. So both the return series are stationary. 67 Table 4.2.13: Cross Correlation Date: 03/16/10 Time: 20:44 Sample: 1 242 Included observations: 241 Correlations are asymptotically consistent approximations DLN_DLF_FUT,DLN_DLF_ DLN_DLF_FUT,DLN_DLF_S SPOT(-i) POT(+i) i lag lead .|********** .|********** 0 0.9757 0.9757 .|. | .|* | 1 0.0262 0.1107 .|. | .|. | 2 0.0289 0.0162 *|. | *|. | 3 -0.0632 -0.0663 .|* | .|. | 4 0.0583 0.0280 *|. | .|. | 5 -0.0479 -0.0031 *|. | *|. | 6 -0.0650 -0.0852 .|. | .|. | 7 0.0424 0.0382 .|. | .|. | 8 0.0137 0.0196 .|* | .|** | 9 0.1431 0.1671 *|. | *|. | 10 -0.0831 -0.0755 68 Table 4.2.14: Lead-lag Relationship among the Spot and the Futures Returns on DLF on Daily basis Panel A: Dependent Variable: DLN_DLF_SPOT Method: Least Squares Date: 03/17/10 Time: 16:23 Sample (adjusted): 6 236 Included observations: 231 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 0.002681 0.002975 0.901353 0.3684 DLN_DLF_FUT(-5) -0.021103 0.064135 -0.329048 0.7424 DLN_DLF_FUT(-4) 0.055023 0.063769 0.862844 0.3892 DLN_DLF_FUT(-3) -0.075752 0.062822 -1.205833 0.2292 DLN_DLF_FUT(-2) 0.015437 0.063436 0.243341 0.8080 DLN_DLF_FUT(-1) 0.119752 0.063463 1.886953 0.0605 DLN_DLF_FUT(1) 0.039023 0.063879 0.610878 0.5419 DLN_DLF_FUT(2) 0.049079 0.065663 0.747432 0.4556 DLN_DLF_FUT(3) -0.075434 0.065337 -1.154524 0.2495 DLN_DLF_FUT(4) 0.072259 0.066524 1.086202 0.2786 DLN_DLF_FUT(5) -0.033223 0.067356 -0.493250 0.6223 R-squared 0.035397 Mean dependent var 0.003208 Adjusted R-squared -0.008448 S.D. dependent var 0.043994 S.E. of regression 0.044179 Akaike info criterion -3.354687 Sum squared resid 0.429392 Schwarz criterion -3.190762 Log likelihood 398.4663 Hannan-Quinn criter. -3.288570 F-statistic 0.807321 Durbin-Watson stat 2.147124 Prob(F-statistic) 0.621834 69 Panel B: Dependent Variable: DLN_DLF_FUT Method: Least Squares Date: 03/17/10 Time: 16:24 Sample (adjusted): 6 236 Included observations: 231 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 0.003310 0.003131 1.057104 0.2916 DLN_DLF_SPOT(-5) -0.057350 0.071635 -0.800585 0.4242 DLN_DLF_SPOT(-4) 0.088882 0.071621 1.241000 0.2159 DLN_DLF_SPOT(-3) -0.094453 0.070822 -1.333652 0.1837 DLN_DLF_SPOT(-2) 0.038690 0.071057 0.544495 0.5867 DLN_DLF_SPOT(-1) 0.032831 0.070733 0.464151 0.6430 DLN_DLF_SPOT(1) 0.121254 0.070824 1.712055 0.0883 DLN_DLF_SPOT(2) 0.043060 0.072073 0.597444 0.5508 DLN_DLF_SPOT(3) -0.080916 0.071978 -1.124178 0.2622 DLN_DLF_SPOT(4) 0.061096 0.072832 0.838865 0.4025 DLN_DLF_SPOT(5) -0.012067 0.073406 -0.164388 0.8696 R-squared 0.035625 Mean dependent var 0.003762 Adjusted R-squared -0.008210 S.D. dependent var 0.046455 S.E. of regression 0.046645 Akaike info criterion -3.246041 Sum squared resid 0.478672 Schwarz criterion -3.082117 Log likelihood 385.9178 Hannan-Quinn criter. -3.179925 F-statistic 0.812710 Durbin-Watson stat 2.173938 Prob(F-statistic) 0.616668 Interpretation In Panel A and B of Table 5, the Regression Equation has been used to find out the lead and lag relationship up to 5th orders. In Panel A DLN_DLF_SPOT is taken as dependent variable, where as in Panel B DLN_DLF_FUT is taken as dependent variable. In table if we look at the coefficient‘s values in both the Panels, then they are not significant at any lags. That means one can not predict any lead-lag relationship from this analysis. 70 4.3 INFOSYS (Infosys Technologies Ltd.) Table 4.3.1: Descriptive Statistics of Daly Returns DLN_INFY_SPOT DLN_INFY_FUT Mean 0.003146 0.003185 Median 0.001335 0.002062 Maximum 0.122349 0.089336 Minimum -0.143830 -0.108005 Std. Dev. 0.022700 0.020935 Skewness -0.161523 0.156505 Kurtosis 12.28393 7.056186 Jarque-Bera 866.5522 166.1958 Probability 0.000000 0.000000 Sum 0.758189 0.767609 Sum Sq. Dev. 0.123666 0.105182 Observations 241 241 Interpretation The descriptive statistics for the return of series INFOSYS are mean, median, maximum, minimum, standard deviation, skewness, kurtosis, Jarque-Bera & probability, which are shown in Table 1. DLN_INFY_SPOT is the logarithmic return series of cash market of script INFOSYS, where as DLN_INFY_FUT is the logarithmic return series of futures market of script INFOSYS. The mean return of both the series are negative. There is not much difference in the std. deviation of both the series. Both the return series are negatively skewed and as the kurtosis value is more than 3, both the series are leptokurtic. Moreover the Jarque-Bera statistics are also exceeds zero, which rejects the hypothesis of normal distribution. 71 Figure 4.3.1: Daily Return on INFOSYS SPOT Market DLN_INFY_SPOT .15 .10 .05 .00 -.05 -.10 -.15 25 50 75 100 125 150 175 200 225 Figure 4.3.2: Daily Return on INFOSYS FUTURE Market DLN_INFY_FUT .12 .08 .04 .00 -.04 -.08 -.12 25 50 75 100 125 150 175 200 225 Interpretation From the above Figure 1 & 2, it can be seen that returns of both future series and cash series for INFOSYS are fluctuating around zero. So both the series may be stationary. 72 Table 4.3.2: Unit Root Test for DLN_INFY_SPOT Null Hypothesis: DLN_INFY_SPOT has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Fixed) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -15.82531 0.0000 Test critical values: 1% level -3.996754 5% level -3.428660 10% level -3.137757 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(DLN_INFY_SPOT) Method: Least Squares Date: 03/16/10 Time: 22:07 Sample (adjusted): 2 241 Included observations: 240 after adjustments Variable Coefficient Std. Error t-Statistic Prob. DLN_INFY_SPOT(-1) -1.025444 0.064798 -15.82531 0.0000 C 0.006352 0.002967 2.140603 0.0333 @TREND(1) -2.52E-05 2.12E-05 -1.187833 0.2361 R-squared 0.513809 Mean dependent var 4.94E-05 Adjusted R-squared 0.509706 S.D. dependent var 0.032462 S.E. of regression 0.022730 Akaike info criterion -4.717838 Sum squared resid 0.122447 Schwarz criterion -4.674330 Log likelihood 569.1406 Hannan-Quinn criter. -4.700308 F-statistic 125.2312 Durbin-Watson stat 2.010333 Prob(F-statistic) 0.000000 73 Table 4.3.3: Unit Root Test for DLN_INFY_FUT Null Hypothesis: DLN_INFY_FUT has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Fixed) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -14.92905 0.0000 Test critical values: 1% level -3.996754 5% level -3.428660 10% level -3.137757 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(DLN_INFY_FUT) Method: Least Squares Date: 03/16/10 Time: 22:08 Sample (adjusted): 2 241 Included observations: 240 after adjustments Variable Coefficient Std. Error t-Statistic Prob. DLN_INFY_FUT(-1) -0.966816 0.064761 -14.92905 0.0000 C 0.006105 0.002739 2.229165 0.0267 @TREND(1) -2.44E-05 1.96E-05 -1.248174 0.2132 R-squared 0.484668 Mean dependent var 5.51E-05 Adjusted R-squared 0.480319 S.D. dependent var 0.029049 S.E. of regression 0.020941 Akaike info criterion -4.881816 Sum squared resid 0.103928 Schwarz criterion -4.838308 Log likelihood 588.8179 Hannan-Quinn criter. -4.864286 F-statistic 111.4489 Durbin-Watson stat 1.986657 Prob(F-statistic) 0.000000 Interpretation Table 2 and 3 shows that the ADF t-statistic exceeds the critical value of series DLN_INFY_SPOT in Table 2 and of DLN_INFY_FUT in Table 3 i.e. ���������������� exceeds the ���������������� (3.428660 < 15.82531 & 14.92905. So the null hypothesis of unit root has been rejected. So both the return series are stationary. 74 Table 4.3.4: Cross Correlation Date: 03/16/10 Time: 22:08 Sample: 1 242 Included observations: 241 Correlations are asymptotically consistent approximations DLN_INFY_FUT,DLN_INFY DLN_INFY_FUT,DLN_INFY_ _SPOT(-i) SPOT(+i) i lag lead .|********** .|********** 0 0.9863 0.9863 .|. | .|. | 1 0.0223 0.0072 **|. | **|. | 2 -0.1607 -0.1766 *|. | *|. | 3 -0.1276 -0.1181 .|* | .|* | 4 0.1090 0.1144 *|. | *|. | 5 -0.0591 -0.0793 *|. | *|. | 6 -0.0579 -0.0473 .|. | .|. | 7 0.0114 0.0073 .|. | .|. | 8 -0.0165 -0.0104 .|. | .|. | 9 0.0170 0.0113 .|* | .|* | 10 0.0542 0.0826 75 Table 4.3.5: Lead-lag Relationship among the Spot and the Futures Returns on INFOSYS on Daily basis Panel A: Dependent Variable: DLN_INFY_SPOT Method: Least Squares Date: 03/17/10 Time: 16:18 Sample (adjusted): 6 236 Included observations: 231 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 0.005158 0.001652 3.121493 0.0020 DLN_INFY_FUT(-5) -0.142703* 0.069606 -2.050164 0.0415 DLN_INFY_FUT(-4) 0.109733 0.069837 1.571279 0.1176 DLN_INFY_FUT(-3) -0.163964* 0.070255 -2.333849 0.0205 DLN_INFY_FUT(-2) -0.176553* 0.071031 -2.485577 0.0137 DLN_INFY_FUT(-1) 0.038319 0.072592 0.527865 0.5981 DLN_INFY_FUT(1) 0.044669 0.072704 0.614393 0.5396 DLN_INFY_FUT(2) -0.152693* 0.072636 -2.102180 0.0367 DLN_INFY_FUT(3) -0.188209* 0.071834 -2.620053 0.0094 DLN_INFY_FUT(4) 0.121348 0.071406 1.699404 0.0907 DLN_INFY_FUT(5) -0.114523 0.071344 -1.605232 0.1099 R-squared 0.137654 Mean dependent var 0.003226 Adjusted R-squared 0.098456 S.D. dependent var 0.022978 S.E. of regression 0.021817 Akaike info criterion -4.765788 Sum squared resid 0.104718 Schwarz criterion -4.601864 Log likelihood 561.4486 Hannan-Quinn criter. -4.699672 F-statistic 3.511791 Durbin-Watson stat 2.171756 Prob(F-statistic) 0.000256 76 Panel B: Dependent Variable: DLN_INFY_FUT Method: Least Squares Date: 03/17/10 Time: 16:19 Sample (adjusted): 6 236 Included observations: 231 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 0.005127 0.001514 3.385325 0.0008 DLN_INFY_SPOT(-5) -0.090995 0.059306 -1.534341 0.1264 DLN_INFY_SPOT(-4) 0.071394 0.059416 1.201596 0.2308 DLN_INFY_SPOT(-3) -0.149474* 0.059458 -2.513924 0.0127 DLN_INFY_SPOT(-2) -0.141427* 0.060338 -2.343904 0.0200 DLN_INFY_SPOT(-1) 0.026957 0.061722 0.436753 0.6627 DLN_INFY_SPOT(1) 0.021468 0.061797 0.347400 0.7286 DLN_INFY_SPOT(2) -0.160444* 0.061466 -2.610294 0.0097 DLN_INFY_SPOT(3) -0.157953* 0.060500 -2.610770 0.0097 DLN_INFY_SPOT(4) 0.085081 0.060494 1.406438 0.1610 DLN_INFY_SPOT(5) -0.112711 0.060553 -1.861355 0.0640 R-squared 0.136498 Mean dependent var 0.003245 Adjusted R-squared 0.097248 S.D. dependent var 0.021146 S.E. of regression 0.020092 Akaike info criterion -4.930546 Sum squared resid 0.088811 Schwarz criterion -4.766621 Log likelihood 580.4780 Hannan-Quinn criter. -4.864429 F-statistic 3.477651 Durbin-Watson stat 1.985119 Prob(F-statistic) 0.000287 Interpretation In Panel A and B of Table 5, the Regression Equation has been used to find out the lead and lag relationship up to 5th orders. In Panel A DLN_INFY_SPOT is taken as dependent variable, where as in Panel B DLN_INFY_FUT is taken as dependent variable. In table if we look at the coefficient‘s values in both the Panels, then they are significant at (-3), (-2), (2) and (3) lags. That means lead lag relationship exists in both the ways, i.e. Futures price can lead or lag the cash price by 2-3 days and cash price can also lead or lag the Futures price by 2-3 days. 77 4.4 RIL (RELIANCE INDUSTRIES LTD.) Table 4.4.1: Descriptive Statistics of Daily Returns DLN_RIL_SPOT DLN_RIL_FUT Mean -0.000933 -0.000905 Median -0.000190 -4.90E-05 Maximum 0.193667 0.197074 Minimum -0.724245 -0.724185 Std. Dev. 0.053969 0.054040 Skewness -9.845910 -9.793234 Kurtosis 135.8412 135.1591 Jarque-Bera 181096.8 179240.3 Probability 0.000000 0.000000 Sum -0.224746 -0.218070 Sum Sq. Dev. 0.699039 0.700867 Observations 241 241 Interpretation The descriptive statistics for the return of future and cash series of RELIANCE are mean, median, maximum, minimum, standard deviation, skewness, kurtosis, Jarque-Bera & probability, which are shown in Table 1. DLN_RIL_FUT is the logarithmic return series of futures market of script RELIANCE, where as DLN_RIL_SPOT is the logarithmic return series of cash market of script RELIANCE. The mean return of both the series are negative. There is not much difference in the std. deviation of both the series. Both the return series are negatively skewed and as the kurtosis value is more than 3, both the series are leptokurtic. Moreover the Jarque-Bera statistics are also high, which rejects the hypothesis of normal distribution. 78 Figure 4.4.1: Daily Return on RIL SPOT Market DLN_RIL_SPOT .4 .2 .0 -.2 -.4 -.6 -.8 25 50 75 100 125 150 175 200 225 Figure 4.4.2: Daily Return on RIL FUTURE Market DLN_RIL_FUT .4 .2 .0 -.2 -.4 -.6 -.8 25 50 75 100 125 150 175 200 225 Interpretation From the above Figure 1 & 2, it can be seen that returns of both future series and cash series for RELIANCE are mean reverting and close to zero. So both the series may be stationary. 79 Table 4.4.2: Unit Root Test for DLN_RIL_SPOT Null Hypothesis: DLN_RIL_SPOT has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Fixed) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -15.35208 0.0000 Test critical values: 1% level -3.996754 5% level -3.428660 10% level -3.137757 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(DLN_RIL_SPOT) Method: Least Squares Date: 03/16/10 Time: 22:16 Sample (adjusted): 2 241 Included observations: 240 after adjustments Variable Coefficient Std. Error t-Statistic Prob. DLN_RIL_SPOT(-1) -0.996972 0.064941 -15.35208 0.0000 C 0.009680 0.007013 1.380260 0.1688 @TREND(1) -8.73E-05 5.06E-05 -1.725201 0.0858 R-squared 0.498611 Mean dependent var 0.000167 Adjusted R-squared 0.494379 S.D. dependent var 0.075865 S.E. of regression 0.053945 Akaike info criterion -2.989281 Sum squared resid 0.689686 Schwarz criterion -2.945773 Log likelihood 361.7138 Hannan-Quinn criter. -2.971751 F-statistic 117.8432 Durbin-Watson stat 1.998503 Prob(F-statistic) 0.000000 80 Table 4.4.3: Unit Root Test for DLN_RIL_FUT Null Hypothesis: DLN_RIL_FUT has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Fixed) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -15.46799 0.0000 Test critical values: 1% level -3.996754 5% level -3.428660 10% level -3.137757 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(DLN_RIL_FUT) Method: Least Squares Date: 03/16/10 Time: 22:17 Sample (adjusted): 2 241 Included observations: 240 after adjustments Variable Coefficient Std. Error t-Statistic Prob. DLN_RIL_FUT(-1) -1.004826 0.064962 -15.46799 0.0000 C 0.009749 0.007024 1.387955 0.1665 @TREND(1) -8.78E-05 5.07E-05 -1.733517 0.0843 R-squared 0.502371 Mean dependent var 0.000162 Adjusted R-squared 0.498172 S.D. dependent var 0.076262 S.E. of regression 0.054024 Akaike info criterion -2.986351 Sum squared resid 0.691709 Schwarz criterion -2.942843 Log likelihood 361.3622 Hannan-Quinn criter. -2.968821 F-statistic 119.6294 Durbin-Watson stat 1.998720 Prob(F-statistic) 0.000000 Interpretation Table 2 and 3 shows that the ADF t-statistic exceeds the critical value of series DLN_RIL_SPOT in Table 2 and of DLF_RIL_FUT in Table 3 i.e. ���������������� exceeds the ���������������� (3.428660 < 15.35208 & 15.46799). So the null hypothesis of unit root has been rejected. So both the return series are stationary. 81 Table 4.4.4: Cross Correlation Date: 03/16/10 Time: 22:18 Sample: 1 242 Included observations: 241 Correlations are asymptotically consistent approximations DLN_RIL_SPOT,DLN_RIL_ DLN_RIL_SPOT,DLN_RIL_F FUT(-i) UT(+i) i lag lead .|********** .|********** 0 0.9990 0.9990 .|. | .|. | 1 0.0145 0.0098 .|. | .|. | 2 -0.0106 -0.0091 *|. | *|. | 3 -0.0688 -0.0724 .|. | .|. | 4 -0.0159 -0.0057 .|. | .|. | 5 -0.0076 -0.0134 .|. | .|. | 6 0.0013 0.0032 .|* | .|* | 7 0.0571 0.0550 .|. | .|. | 8 -0.0287 -0.0304 .|. | .|. | 9 0.0032 0.0068 .|. | .|. | 10 0.0152 0.0160 82 Table 4.4.5: Lead-lag Relationship among the Spot and the Futures Returns on ICICIBANK on Daily Basis Panel A: Dependent Variable: DLN_RIL_SPOT Method: Least Squares Date: 03/17/10 Time: 16:14 Sample (adjusted): 6 236 Included observations: 231 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C -0.000862 0.003684 -0.234127 0.8151 DLN_RIL_FUT(-5) -0.010493 0.067217 -0.156111 0.8761 DLN_RIL_FUT(-4) -0.010110 0.067215 -0.150407 0.8806 DLN_RIL_FUT(-3) -0.068311 0.067053 -1.018770 0.3094 DLN_RIL_FUT(-2) -0.013142 0.067481 -0.194753 0.8458 DLN_RIL_FUT(-1) 0.015489 0.067332 0.230045 0.8183 DLN_RIL_FUT(1) 0.012342 0.067406 0.183094 0.8549 DLN_RIL_FUT(2) -0.012289 0.067752 -0.181383 0.8562 DLN_RIL_FUT(3) -0.069941 0.067528 -1.035734 0.3015 DLN_RIL_FUT(4) 0.001763 0.067681 0.026048 0.9792 DLN_RIL_FUT(5) -0.012542 0.067726 -0.185184 0.8533 R-squared 0.010724 Mean dependent var -0.000691 Adjusted R-squared -0.034244 S.D. dependent var 0.054957 S.E. of regression 0.055890 Akaike info criterion -2.884423 Sum squared resid 0.687207 Schwarz criterion -2.720498 Log likelihood 344.1508 Hannan-Quinn criter. -2.818306 F-statistic 0.238475 Durbin-Watson stat 2.018955 Prob(F-statistic) 0.992060 83 Panel B: Dependent Variable: DLN_RIL_FUT Method: Least Squares Date: 03/17/10 Time: 16:15 Sample (adjusted): 6 236 Included observations: 231 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C -0.000844 0.003687 -0.228956 0.8191 DLN_RIL_SPOT(-5) -0.016712 0.067344 -0.248156 0.8042 DLN_RIL_SPOT(-4) -0.000315 0.067372 -0.004676 0.9963 DLN_RIL_SPOT(-3) -0.070763 0.067223 -1.052663 0.2937 DLN_RIL_SPOT(-2) -0.012318 0.067630 -0.182145 0.8556 DLN_RIL_SPOT(-1) 0.011375 0.067482 0.168564 0.8663 DLN_RIL_SPOT(1) 0.016125 0.067550 0.238713 0.8116 DLN_RIL_SPOT(2) -0.012629 0.067884 -0.186043 0.8526 DLN_RIL_SPOT(3) -0.066830 0.067657 -0.987783 0.3243 DLN_RIL_SPOT(4) -0.007368 0.067806 -0.108669 0.9136 DLN_RIL_SPOT(5) -0.006800 0.067853 -0.100222 0.9203 R-squared 0.010674 Mean dependent var -0.000672 Adjusted R-squared -0.034296 S.D. dependent var 0.055010 S.E. of regression 0.055945 Akaike info criterion -2.882449 Sum squared resid 0.688564 Schwarz criterion -2.718525 Log likelihood 343.9229 Hannan-Quinn criter. -2.816333 F-statistic 0.237357 Durbin-Watson stat 2.032186 Prob(F-statistic) 0.992208 Interpretation In Panel A and B of Table 5, the Regression Equation has been used to find out the lead and lag relationship up to 5th orders. In Panel A DLN_RIL_SPOT is taken as dependent variable, where as in Panel B DLN_RIL_FUT is taken as dependent variable. In table if we look at the coefficient‘s values in both the Panels, then they are not significant at any lags. This suggests lack of lead-lag relationship on daily basis. 84 4.5 TATA STEEL Table 4.5.1: Descriptive Statistics of Daily Returns DLN_TATA_STEEL_FUT DLN_TATA_STEEL_SPOT Mean 0.005355 0.005328 Median 0.007216 0.007405 Maximum 0.152051 0.157035 Minimum -0.130537 -0.128169 Std. Dev. 0.040513 0.040414 Skewness -0.018125 -0.027191 Kurtosis 3.825273 4.054963 Jarque-Bera 6.852334 11.20554 Probability 0.032511 0.003688 Sum 1.290571 1.284020 Sum Sq. Dev. 0.393921 0.391987 Observations 241 241 Interpretation The descriptive statistics for the return of series TATASTEEL are mean, median, maximum, minimum, standard deviation, skewness, kurtosis, Jarque-Bera & probability, which are shown in Table 1. DLN_TATA_STEEL_FUT is the logarithmic return series of futures market of script TATA STEEL, where as DLN_TATA_STEEL_SPOT is the logarithmic return series of cash market of script TATA STEEL. The mean return of both the series are equal and positive. There is not much difference in the std. deviation of both the series. Both the return series are negatively skewed and as the kurtosis value is more than 3, both the series are leptokurtic. Moreover the Jarque-Bera statistics are also high, which rejects the hypothesis of normal distribution. 85 Figure 4.5.1: Daily Return on TATA STEEL SPOT Market DLN_TATA_STEEL_SPOT .20 .15 .10 .05 .00 -.05 -.10 -.15 25 50 75 100 125 150 175 200 225 Figure 4.5.2: Daily Return on TATA STEEL Future Market DLN_TATA_STEEL_FUT .20 .15 .10 .05 .00 -.05 -.10 -.15 25 50 75 100 125 150 175 200 225 Interpretation From the above Figure 1 & 2, it can be seen that returns of both future series and cash series for TATA STEEL are mean reverting and close to zero. So both the series may be stationary. 86 Table 4.5.2: Unit Root Test for DLN_ICICI_SPOT Null Hypothesis: DLN_TATA_STEEL_SPOT has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Fixed) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -15.58599 0.0000 Test critical values: 1% level -3.996754 5% level -3.428660 10% level -3.137757 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(DLN_TATA_STEEL_SPOT) Method: Least Squares Date: 03/16/10 Time: 22:29 Sample (adjusted): 2 241 Included observations: 240 after adjustments Variable Coefficient Std. Error t-Statistic Prob. DLN_TATA_STEEL_SPOT(-1) -1.010645 0.064843 -15.58599 0.0000 C 0.014385 0.005295 2.716744 0.0071 @TREND(1) -7.37E-05 3.78E-05 -1.947866 0.0526 R-squared 0.506176 Mean dependent var 0.000138 Adjusted R-squared 0.502009 S.D. dependent var 0.057110 S.E. of regression 0.040302 Akaike info criterion -3.572424 Sum squared resid 0.384942 Schwarz criterion -3.528916 Log likelihood 431.6909 Hannan-Quinn criter. -3.554893 F-statistic 121.4642 Durbin-Watson stat 1.999289 Prob(F-statistic) 0.000000 87 Table 4.5.3: Unit Root Test for DLN_ICICI_FUT Null Hypothesis: DLN_TATA_STEEL_FUT has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Fixed) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -16.14162 0.0000 Test critical values: 1% level -3.996754 5% level -3.428660 10% level -3.137757 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(DLN_TATA_STEEL_FUT) Method: Least Squares Date: 03/16/10 Time: 22:30 Sample (adjusted): 2 241 Included observations: 240 after adjustments Variable Coefficient Std. Error t-Statistic Prob. DLN_TATA_STEEL_FUT(- 1) -1.045906 0.064796 -16.14162 0.0000 C 0.014978 0.005305 2.823420 0.0052 @TREND(1) -7.69E-05 3.79E-05 -2.030603 0.0434 R-squared 0.523673 Mean dependent var 9.83E-05 Adjusted R-squared 0.519654 S.D. dependent var 0.058245 S.E. of regression 0.040368 Akaike info criterion -3.569145 Sum squared resid 0.386207 Schwarz criterion -3.525637 Log likelihood 431.2973 Hannan-Quinn criter. -3.551614 F-statistic 130.2788 Durbin-Watson stat 1.994377 Prob(F-statistic) 0.000000 Interpretation Table 2 and 3 shows that the ADF t-statistic exceeds the critical value of series DLN_TATA_STEEL_SPOT in Table 2 and of DLN_TATA_STEEL_FUT in Table 3 i.e. ���������������� exceeds the ���������������� (3.428660 < 15.58599 & 16.14162) significantly. So the null hypothesis of unit root has been rejected. So both the return series are stationary. 88 Table 4.5.4: Cross Correlation Date: 03/16/10 Time: 22:28 Sample: 1 242 Included observations: 241 Correlations are asymptotically consistent approximations DLN_TATA_STEEL_FUT,D DLN_TATA_STEEL_FUT,DL LN_TATA_STEEL_SPOT(-i) N_TATA_STEEL_SPOT(+i) i lag lead .|********** .|********** 0 0.9927 0.9927 .|. | .|. | 1 -0.0141 -0.0088 .|* | .|* | 2 0.0950 0.0671 .|. | .|. | 3 -0.0122 -0.0002 .|. | *|. | 4 -0.0334 -0.0548 *|. | *|. | 5 -0.0873 -0.0905 .|. | .|. | 6 -0.0379 -0.0214 .|. | .|. | 7 0.0385 0.0283 .|* | .|* | 8 0.0843 0.0952 .|** | .|** | 9 0.1652 0.1772 *|. | *|. | 10 -0.0448 -0.0410 89 Table 4.5.5: Lead-lag Relationship among the Spot and the Futures Returns on TATA STEEL on Daily basis Panel A: Dependent Variable: DLN_TATA_STEEL_SPOT Method: Least Squares Date: 03/17/10 Time: 16:08 Sample (adjusted): 6 236 Included observations: 231 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 0.005874 0.002929 2.005477 0.0461 DLN_TATA_STEEL_FUT(-5) -0.098327 0.067983 -1.446347 0.1495 DLN_TATA_STEEL_FUT(-4) -0.051498 0.068204 -0.755047 0.4510 DLN_TATA_STEEL_FUT(-3) 0.025010 0.067545 0.370267 0.7115 DLN_TATA_STEEL_FUT(-2) 0.076291 0.066778 1.142463 0.2545 DLN_TATA_STEEL_FUT(-1) -0.006687 0.067093 -0.099666 0.9207 DLN_TATA_STEEL_FUT(1) -0.012678 0.067141 -0.188830 0.8504 DLN_TATA_STEEL_FUT(2) 0.104205 0.067248 1.549551 0.1227 DLN_TATA_STEEL_FUT(3) 0.016851 0.067885 0.248223 0.8042 DLN_TATA_STEEL_FUT(4) -0.021652 0.068555 -0.315838 0.7524 DLN_TATA_STEEL_FUT(5) -0.086376 0.068592 -1.259275 0.2093 R-squared 0.034063 Mean dependent var 0.005641 Adjusted R-squared -0.009843 S.D. dependent var 0.041031 S.E. of regression 0.041232 Akaike info criterion -3.492737 Sum squared resid 0.374024 Schwarz criterion -3.328812 Log likelihood 414.4111 Hannan-Quinn criter. -3.426620 F-statistic 0.775821 Durbin-Watson stat 1.956234 Prob(F-statistic) 0.652056 90 Panel B: Dependent Variable: DLN_TATA_STEEL_FUT Method: Least Squares Date: 03/17/10 Time: 16:10 Sample (adjusted): 6 236 Included observations: 231 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 0.005925 0.002934 2.019620 0.0446 DLN_TATA_STEEL_SPOT(-5) -0.089588 0.068278 -1.312105 0.1909 DLN_TATA_STEEL_SPOT(-4) -0.025079 0.068475 -0.366251 0.7145 DLN_TATA_STEEL_SPOT(-3) 0.013703 0.067840 0.201989 0.8401 DLN_TATA_STEEL_SPOT(-2) 0.097703 0.067045 1.457279 0.1465 DLN_TATA_STEEL_SPOT(-1) -0.017572 0.067292 -0.261130 0.7942 DLN_TATA_STEEL_SPOT(1) -0.010733 0.067259 -0.159579 0.8734 DLN_TATA_STEEL_SPOT(2) 0.076185 0.067374 1.130774 0.2594 DLN_TATA_STEEL_SPOT(3) 0.024271 0.067977 0.357048 0.7214 DLN_TATA_STEEL_SPOT(4) -0.038354 0.068629 -0.558868 0.5768 DLN_TATA_STEEL_SPOT(5) -0.092607 0.068703 -1.347932 0.1791 R-squared 0.032496 Mean dependent var 0.005665 Adjusted R-squared -0.011482 S.D. dependent var 0.041077 S.E. of regression 0.041312 Akaike info criterion -3.488871 Sum squared resid 0.375473 Schwarz criterion -3.324946 Log likelihood 413.9646 Hannan-Quinn criter. -3.422754 F-statistic 0.738922 Durbin-Watson stat 2.001448 Prob(F-statistic) 0.687314 Interpretation In Panel A and B of Table 5, the Regression Equation has been used to find out the lead and lag relationship up to 5th orders. In Panel A DLN_TATA_STEEL_SPOT is taken as dependent variable, where as in Panel B DLN_TATA_STEEL_FUT is taken as dependent variable. In table if we look at the coefficient‘s values in both the Panels, then they are not significant at any lags. It suggests the lack of lead-lag relationship on daily basis. 91 4.6 ICICI BANK (ICICI Bank Ltd.) Table 4.6.1: Descriptive Statistics of Daily Returns DLN_ICICI_SPOT DLN_ICICI_FUT Mean 0.000114 0.004378 Median 2.08E-05 0.002722 Maximum 0.159904 0.227129 Minimum -0.178257 -0.128010 Std. Dev. 0.048812 0.036384 Skewness -0.032488 0.804400 Kurtosis 4.763355 8.902096 Jarque-Bera 31.26618 375.7890 Probability 0.000000 0.000000 Sum 0.027367 1.055158 Sum Sq. Dev. 0.571830 0.317708 Observations 241 241 Interpretation The descriptive statistics for the return of series ICICIBANK are mean, median, maximum, minimum, standard deviation, skewness, kurtosis, Jarque-Bera & probability, which are shown in Table 1. DLN_ICICI_FUT is the logarithmic return series of futures market of script ICICIBANK, where as DLN_ICICI_SPOT is the logarithmic return series of cash market of script ICICIBANK. The mean return of both the series are positive. There is not much difference in the std. deviation of both the series. The DLN_ICICI_SPOT return series is negatively skewed where as DLN_ICICI_FUT series is positively skewed, and as the kurtosis value is more than 3, both the series are leptokurtic. Moreover the Jarque-Bera statistics are also high, which rejects the hypothesis of normal distribution. 92 Figure 4.6.1: Daily Return on ICICIBANK Cash Market DLN_ICICI_SPOT .20 .15 .10 .05 .00 -.05 -.10 -.15 -.20 25 50 75 100 125 150 175 200 225 Figure 4.6.2: Daily Return on ICICIBANK Futures Market DLN_ICICI_FUT .25 .20 .15 .10 .05 .00 -.05 -.10 -.15 25 50 75 100 125 150 175 200 225 Interpretation From the above Figure 1 & 2, it can be seen that returns of both future series and cash series for ICICIBANK are mean reverting and close to zero. So both the series may be stationary. 93 Table 4.6.2: Unit Root Test for DLN_ICICI_SPOT Null Hypothesis: DLN_ICICI_SPOT has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Fixed) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -23.60279 0.0000 Test critical values: 1% level -3.996754 5% level -3.428660 10% level -3.137757 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(DLN_ICICI_SPOT) Method: Least Squares Date: 03/16/10 Time: 22:42 Sample (adjusted): 2 241 Included observations: 240 after adjustments Variable Coefficient Std. Error t-Statistic Prob. DLN_ICICI_SPOT(-1) -1.403507 0.059464 -23.60279 0.0000 C 0.000871 0.005820 0.149654 0.8812 @TREND(1) -5.26E-06 4.19E-05 -0.125511 0.9002 R-squared 0.701548 Mean dependent var -6.24E-05 Adjusted R-squared 0.699030 S.D. dependent var 0.081922 S.E. of regression 0.044943 Akaike info criterion -3.354418 Sum squared resid 0.478712 Schwarz criterion -3.310910 Log likelihood 405.5302 Hannan-Quinn criter. -3.336888 F-statistic 278.5493 Durbin-Watson stat 2.253694 Prob(F-statistic) 0.000000 94 Table 4.6.3: Unit Root Test for DLN_ICICI_FUT Null Hypothesis: DLN_ICICI_FUT has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Fixed) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -14.17029 0.0000 Test critical values: 1% level -3.996754 5% level -3.428660 10% level -3.137757 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(DLN_ICICI_FUT) Method: Least Squares Date: 03/16/10 Time: 22:42 Sample (adjusted): 2 241 Included observations: 240 after adjustments Variable Coefficient Std. Error t-Statistic Prob. DLN_ICICI_FUT(-1) -0.915986 0.064641 -14.17029 0.0000 C 0.011614 0.004745 2.447650 0.0151 @TREND(1) -6.19E-05 3.39E-05 -1.825802 0.0691 R-squared 0.458655 Mean dependent var 0.000214 Adjusted R-squared 0.454087 S.D. dependent var 0.048889 S.E. of regression 0.036122 Akaike info criterion -3.791392 Sum squared resid 0.309242 Schwarz criterion -3.747884 Log likelihood 457.9670 Hannan-Quinn criter. -3.773861 F-statistic 100.3992 Durbin-Watson stat 1.985190 Prob(F-statistic) 0.000000 Interpretation Table 2 and 3 shows that the ADF t-statistic exceeds the critical value of series DLN_ICICI_SPOT in Table 2 and of DLN_ICICI_FUT in Table 3 i.e. ���������������� exceeds the ���������������� (3.428660 < 23.60279 & 14.17029) significantly. So the null hypothesis of unit root has been rejected. So both the return series are stationary. 95 Table 4.6.4: Cross Correlation Date: 03/16/10 Time: 22:39 Sample: 1 242 Included observations: 241 Correlations are asymptotically consistent approximations DLN_ICICI_FUT,DLN_ICICI DLN_ICICI_FUT,DLN_ICICI_ _SPOT(-i) SPOT(+i) i lag lead *******|. | *******|. | 0 -0.6720 -0.6720 .|******* | *|. | 1 0.6694 -0.1319 .|* | .|. | 2 0.1287 0.0031 .|. | .|* | 3 -0.0075 0.1167 *|. | *|. | 4 -0.1169 -0.1406 .|* | .|. | 5 0.1381 -0.0147 .|. | .|* | 6 0.0204 0.0709 *|. | .|. | 7 -0.0648 -0.0032 .|. | .|* | 8 0.0058 0.0923 *|. | .|. | 9 -0.0930 -0.0405 .|. | .|* | 10 0.0434 0.0528 96 Table 4.6.5: Lead-lag Relationship among the Spot and the Futures Returns on ICICIBANK on Daily Basis Panel A: Dependent Variable: DLN_ICICI_SPOT Method: Least Squares Date: 03/17/10 Time: 16:04 Sample (adjusted): 6 236 Included observations: 231 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C -0.005350 0.002544 -2.103420 0.0366 DLN_ICICI_FUT(-5) 0.142584 0.065003 2.193496 0.0293 DLN_ICICI_FUT(-4) -0.127452 0.065551 -1.944325 0.0531 DLN_ICICI_FUT(-3) 0.116326 0.065497 1.776059 0.0771 DLN_ICICI_FUT(-2) 0.071122 0.066159 1.075011 0.2835 DLN_ICICI_FUT(-1) -0.123271 0.066298 -1.859335 0.0643 DLN_ICICI_FUT(1) 0.872349* 0.067105 12.99978 0.0000 DLN_ICICI_FUT(2) 0.067914 0.067504 1.006084 0.3155 DLN_ICICI_FUT(3) 0.106393 0.067386 1.578846 0.1158 DLN_ICICI_FUT(4) -0.146561* 0.067179 -2.181645 0.0302 DLN_ICICI_FUT(5) 0.120434 0.067239 1.791140 0.0746 R-squared 0.498086 Mean dependent var -0.000338 Adjusted R-squared 0.475272 S.D. dependent var 0.049046 S.E. of regression 0.035528 Akaike info criterion -3.790536 Sum squared resid 0.277694 Schwarz criterion -3.626612 Log likelihood 448.8069 Hannan-Quinn criter. -3.724420 F-statistic 21.83221 Durbin-Watson stat 2.251252 Prob(F-statistic) 0.000000 97 Panel B: Dependent Variable: DLN_ICICI_FUT Method: Least Squares Date: 03/17/10 Time: 16:06 Sample (adjusted): 6 236 Included observations: 231 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 0.004703 0.000990 4.748465 0.0000 DLN_ICICI_SPOT(-5) 0.186930* 0.024961 7.488794 0.0000 DLN_ICICI_SPOT(-4) 0.321701* 0.030314 10.61218 0.0000 DLN_ICICI_SPOT(-3) 0.501780* 0.031488 15.93560 0.0000 DLN_ICICI_SPOT(-2) 0.673062* 0.030295 22.21683 0.0000 DLN_ICICI_SPOT(-1) 0.809408* 0.025561 31.66565 0.0000 DLN_ICICI_SPOT(1) 0.000738 0.026091 0.028292 0.9775 DLN_ICICI_SPOT(2) 0.027216 0.031447 0.865468 0.3877 DLN_ICICI_SPOT(3) 0.048550 0.032943 1.473740 0.1420 DLN_ICICI_SPOT(4) 0.028310 0.031561 0.897011 0.3707 DLN_ICICI_SPOT(5) 0.037487 0.025769 1.454734 0.1472 R-squared 0.839015 Mean dependent var 0.004984 Adjusted R-squared 0.831697 S.D. dependent var 0.036686 S.E. of regression 0.015050 Akaike info criterion -5.508393 Sum squared resid 0.049832 Schwarz criterion -5.344468 Log likelihood 647.2194 Hannan-Quinn criter. -5.442276 F-statistic 114.6586 Durbin-Watson stat 0.449083 Prob(F-statistic) 0.000000 Interpretation In Panel A and B of Table 5, the Regression Equation has been used to find out the lead and lag relationship up to 5th orders. In Panel A DLN_ICICI_SPOT is taken as dependent variable, where as in Panel B DLN_ICICI_FUT is taken as dependent variable. In table if we look at the coefficient‘s values in both the Panels, then they are significant at (-1), (-2) (-3), (-4) and (-5) lags in panel B and at (1) and (4) in panel A. That means strong leading role is played by futures market, i.e. Futures price can lead cash price by 1-5 days. 98 FINDINGS An attempt has been made to investigate lead-lag relationship, by using Linear Regression Equation and Granger Causality Test. The results for the NIFTY index and for the five scripts are as follow: 1. NIFTY The lead-lag relationship for the NIFTY cash and NIFTY futures has been found and this relationship exists which is contemporaneous and bi-directional. Here NIFTY Cash leads or lags the NIFTY Futures by 4-6 minutes. Also NIFTY Futures leads or lags the NIFTY cash by 4-6 minutes. 2. STOCK For the first script i.e. DLF, this relationship does not exists for the specific time period. For INFOSYS, this relationship exists which is contemporaneous and bi-directional. Here INFOSYS Cash/Future leads or lags the INFOSYS Futures/Cash by 2-3 days. In 3rd script i.e. RELIANCE, the lead lag relationship does not exist for the specific time period. For the TATA STEEL script, the lead lag relationship does not exist for the specific time period. And for the last script ICICIBANK, there exist lead-lag relationship which uncovers that Futures market lead the Cash market by 1-5 days. 3. For Market efficiency It can be inferred from the analysis that for the given time period as bi-directional lead-lag relationship exists between the NIFTY Index and Futures, so the market is not equally efficient in processing the information. But as the lead-lag relationship has not been found out for three scripts, one can conclude that script based market is equally efficient in processing the information. 99 CONCLUSION By using intraday (here minute-by-minute) data from December 2009 to February 2010, an effort has been made to investigate the possible lead-lag relationship among the NIFTY spot index and index futures market in India. As far as the regression results on the lead-lag relationship between spot and futures index return is concerned, it revealed that there is a strong contemporaneous and bi-directional relationship among the spot and futures market in India in disseminating information available to the market. We have got almost the same results even for some underlying NIFTY stocks that are very actively traded in the market. As far as our knowledge is concerned, the possible explanation behind such more or less symmetric lead-lag relationship among Indian spot and futures markets may be the joint efficiency of both the markets. As we know that one of the main objective of introducing derivatives product, such as index futures, in Indian market is to enhance the informational efficiency of the underlying cash market. Therefore by looking into such results, one can easily conclude that the informational efficiency of the Indian cash market has really been increased due to the onset of derivative trading, as claimed by the Indian regulators. As far as our research is concerned, it may not be feasible to make any strong generalization on the possible lead-lag relationship among the spot and futures market in India by looking at these results. Though our evidence proves that new market information disseminates (may not be equally) in both the spot and futures market and therefore serve an important role in the matter of price discovery, we can get some more strong and reliable results through investigating such relationship for a longer period of time within which the problem (if any) of any periodic effect will be disappeared. Apart from this, a comparison among the results longer (at lease one year) periods can also exhibit whether there is any change in the informational efficiency of the markets over a period of time. Therefore, a further research in those lines can strongly focus whether there is any real change in the informational efficiency of Indian cash market after the introduction of derivative trading. 100