Chapter-6 Price Discovery in NSE Nifty Index and Nifty Futures Markets
6.1 Introduction
The mechanics of price discovery arc important to both investors and regulators.
Since the trading process may introduce noise that results in inaccurate prices, it has
implications for traders interested in avoiding pricing errors and policy makers concemed
with market stability. Poor price discovcry may lead to heightened price volatility,
including bubbles or sudden market crashes, when priccs arc predominantly influenced
by short-Hill disturbanccs. A recent concern for market participants is whether the
proliferation of alternative trading venues may have adversely affectcd the price
formation process through market fragmentation.
Price discovery is the proecss of uncovering an asset's full-information or
permanent value. The unobservable permanent price reflects the fundamental value of the
stock. It is distinct from the observable price, which can bc decomposed into its
fundamental value and its transitory effects. Thc latter consists of price movements due to
the hid-ask bounce, temporary order imbalances, inventory adjustments, and rounding
effects.
Price discovery is the process of buyers and sellers arriving at a transaction price
for a given quality and quantity of a product at a given time and place. Price discovery
involves several intelTelated concepts, among them,
• Market structure (number, size, location, and competitiveness of buyers and
sellers);
• Market behavior (buyer procurement and pricing methods);
• Market information and price reporting (amount, timeliness, and reliability of
information); and
• Futures markets and risk management alternatives.
Futures trade assumes significance in a volatile ready market and pnce risk
management because of the price discovery. The price discovery is the process of
determining the price of a commodity/stock, based on supply and demand factors. The
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expectations theory hypothesizes that the current futures price is a consensus forecast of
the value of the ready (spot) price in the future.
Price discovery is the process hy which markets attempt to find equilibriulll prices
(Schreiber and Schwarz. 1986). The concept of price discovery traces back to the mid
80's when both academics and governmental authorities tried to describe the mechanisms
of different markets and how the process ends in a concct price. Fair market prices retlect
the demand of all traders and should not be affected by incomplete information. sudden
change in the depth and width of the market or the trading system as a whole.
Security markets arc more apt to consist of diversely informed traders who
collectively possess incomplete information about the assets being traded. rather than
being characterized by asymmetric information. With the individual trade. the underlying
information is made public through the trade price itself. Trading activity based on less
than full infomlation and past prices. markets may collcctively error at times or convcrge
to a new price.
Numerous factors. in addition to the underlying information change and liquidity
trading, cause the price changes to occur (Schreiber and Schwarz, 1986). Even small
orders may have huge impacts on the share price for low volumes traded of stocks. Sticky
limit order books with outstanding orders can re!lect past prices and information
situation. And the process of finding the correct price will in itself cause the actual price
to !luctuate. The advent of new information will generate a succession of trades and price
changes while traders digcst the news, including the price movement. and the markct
searches for a new equilibrium priee (Schreiber and Schwarz. 1986).
Main theme of this research is "price discovery function that measures the
information content of quotes in forecasting the next transaction". Price discovery is one
of the central functions of financial markets. In the market microstructure literature, it has
been variously interpreted as, "The search for an equilibrium price" (Schreiber and
Schwartz (1986)), "gathering and interpreting news" (Baillie et. al. (2002)), "The
incorporation of the information implicit in investor trading into market prices"
(Lehmann (2002). These interpretations suggest that price discovery is dynamic in
nature, and an efficient price discovery process is characterized by the fast adjustment of
market prices from the old equilihrium to the new equilibrium with the alTival of new
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information. In particular, Madhavan (2002) distinguishes dynamic price discovery issues
from static issues such as trading cost determination.
One notable institutional trend of financial markets is the trading of identical or
closely related assets in multiple market places. This trend has raised a number of
important questions. Does the proliferation of alternative trading venues and the resulting
market fragmentation adversely affect the price discovery process? How do the dynamics
of price discovery of an asset depend on market characteristics, such as transaction eosts
and liquidity? What institutional structures and trading protocols facilitate the
information aggregation and price discovery process? In contrast to the wide literature on
transaction costs, however, the studies on price discovery arc relatively limited. In a
recent survey of market microstructure studies, Madhavan (2002) remarks, "The studies
surveyed above can be viewed as analyzing the influence of structure on the magnitude of
the friction variable. What is presently lacking is a deep understanding of how structure
aspects return dynamics, in particular, the speed (italics as cited) of price discovery." In
this research, we propose an approach to directly characterize the speed of price
discovery in the context of NSE Nifty Index and Nifty Futures markets.
Future markets contribute in two important ways to the organization of economic
acti vity:
(i) They facilitate price discovery;
(ii) They offer means of transferring risk or hedging.
In this Research it has been focused on the first contribution. Price discovery
refers to the use of future prices for pricing cash market transactions (Working, 1948;
Wiese, 1978; and Lake 1978). In general, price discovery is the process of uncovering an
asset's full information or permanent value. The unobservable permanent priee reflects
the fundamental value of the stock or commodity. It is distinct from the observable price,
which can be decomposed into its fundamental value and its transitory effects. The latter
consists of price movements due to factors such as bid-ask bounce, temporary order
imbalances or inventory adjustments.
Price discovery and risk transfer (i.e. Hedging) have been considered as the pivot
functions of the futures market in all the economics (Telser (1981)). As we know, futures
are the standardized forward contracts, which arc traded on stock exchanges. Cost-of-
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Carry model is followed to determine the price of the futures contract. which implies that
futures represent the prospective price of the underlying asset in the cash market
(Garbade and Sibler (1983». For example; if the Nifty futures is traded at 2500 level and
the Nifty cash market Index at 2450. (if cost-of-carry model holds good) it implies that
the futures will direct the next price move in the cash market. thus the next price of the
underlying asset will be approximately 2500. Price discovery is a function of the cost-of
carry model. which implies that price discovery. will be true only if cost-of-carry model
holds good (Turkington and Walsh (1999».
In other words. if at any timc the futurcs arc mispriced thcn lead-lag relationship
between futures and cash market may be disturbed. which will result into wrong decision
for the traders to take position in the cash market on the basis of the price movement in
the futures market. In addition, if the futures are mispriced then hedging through
arbitrage positions in the cash and the futures market will not work in the interest of the
traders.
In addition. an efficient cost-of-carry relationship between the futures and cash
market results in the comovement of price series in two markets. Comovement of price
series of both markets is an evidence that price movement in both markets is
cointegrated, but evidence of cointegration docs not tell anything regarding the speed of
price discovery in the market; rather it conveys very significant information regarding the
strength of the basis (i.e. Futures Price -Cash Price) (Booth et a1.. (1999». If on the date
of the maturity of the contract. price series in two markets converges (sec Fig-6.1). it
implies that cost-of-carry model holds good and both the series have long run
relationship. If reverse holds, then it implies that the futures arc mispriced and may not be
an efficient price discovery vehicle (Garbade and Sibler (1983)). For an efficient
convergence on the maturity date the basis is required to be predictable. but predictable
basis does not necessarily imply that speedier price discovery takes place in the futures
market (Fortenbery and Zapata (1997».
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Fig -6.1 Movement of Futures and Equity price
Price
\ Equity Pric>"
I, I, Time'
Price discovery mechanism refers to absorbing the new infonnation, and
reflecting it into the market prices. P,ice discovcry in the cash market has been a serious
issue for debate for the traders, professionals, regulatory bodies and the academicians.
Thrce different schools (i.e. Fundamental Analysis. Technical Analysis and Efficient
Market Hypothesis) have emerged to analyze the reaction of the prices to new
information. Fama made significant efforts in this regard and in 1970. he came out with
formal definitions of the market efficiency. He classified the market efficiency into three
categories i.e. Weak Form Efficiency. Semi-Strong Form Efficiency and Strong Form
Efficiency.
A market is said to be weak form efficient if the cunent market price and past
price are uncorrelated (i.e. the asset price movements are random). A market is known as
semi-strong efficient, if it absorbs and reflects the market information as well as the
public information (viz; corporate actions. political announcement etc.). Strong form
efficient market is one. which neglects the chances of even insiders to make abnormal
profits on the basis of first hand information.
In the developed economies viz; U.S.A. and U.K.. markets are found to be
efficient but reverse holds in case of the emerging markets like India. Taiwan,
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Bangladesh etc. (Mobarek and Keasey (2000)). Thus in the emerging markets. relative
pricing efficiency of the futures market may work like a lantern in the dark coal mine. If
in emerging markets, futures market is able to react to the market information
immediately, when these becomes available then, it will certainly help the regulators to
control the volatil ity in the cash market and the confidence of the traders can be restored
in a market like India. where people burnt their hands in early and mid 90's due to the
overwhelming participation in the market hy one trader (i.e. Big Bull Ilarshad Mehta). If
in India, futures market acts as an efficient price discovery vehicle, traders will be getting
more confidence to trade in the cash market because they will know that futures market is
their to guide their prospcctive actions in the market and they can protect themselves
from the possible loss by tak.ing (Beta weighted) reverse positions in the futures market
(Branllen and Ulvcling (1984)).
Efficient price discovery m the futures market has many advantages for the
traders as well as for the regulators. Traders can manage their risk exposure in the cash
market by taking reverse positions in the futures market. In many stock markets it has
been observed that the volatility in the cash mark.et has reduced in the post futures trading
era as compared to the volatility in the pre futures trading era (Gulen and Mayhew
(2000)). Reductioll in the magnitude of volatility will certainly work for the benefit of all
traders (both retail as well as big traders). Reduction in volatility ensures relatively stable
price movements in the market, which will help the traders to take their decision in the
market (subject to the experience and exposure of the trader in the market) (long and
Donders (1998)). The regulatory bodies can also be benefited through efficient price
discovery in the futures market (Raju and Karande (2003)). They can simulate the
reforms through futures market and then directly implement the same in the cash market.
The reaction of the futures market to such reforms will certainly help the regulatory
bodies to evaluate the probability of success/failure of the reform in the cash market, thus
they can make appropriate modifications, if necessary.
In India, equity futures are of relatively recent origin and were introduced in the
phased manner. In the first phase index futures trading was introduced on l2'h June 2000
and in the second phase, stock futures trading was permitted on 9th Nov 2001. The trade
volume in both the markets has been increasing by leaps and bounds. These days'
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significant efforts are being taken to investigate the efficiency of Indian equity futures
market. Raju and Karande (2003) investigated the price discovery cfTiciency of the Indian
equity futures market but they could not conclude anything on the basis of short time
dimension. Gupta and Singh (2006) also made an attempt to investigate the price
discovery efficiency of the Nifty futures by considering lengthy time frame and their
results showed lead-lag relationship between the two markets.
6.2 Importance of Price Discovery
When a market experiences stress and its negative impacts persist over a period of
time, the market's liquidity declines and market conditions become unstable. Under such
stress, the price discovery function an important mechanism in markets is debilitated,
which leads to higher price volatility and lower market liquidity. At the most general
modeling perspective, each of the observable prices of an asset in multiple markets can
be decomposed into two components: one retlecting the common efficient (full
information) price shared by all these markets (Garbade and Silber (1979)); and one
retlecting the transitory frictions that arise from the trading mechanism, such as the bid
ask bounce, liquidity effects, and rounding errors. Evolving as a random walk, the
common efficient price captures the fundamental value of the financial asset and its
innovation impounds the expectation revisions of investors (thus new information) about
the asset payoff of observed prices respond to the common efficient price innovation
characterizes the dynamics of price discovery. Unfortunately, as emphasized by
Hasbrouck (2002), the common efficient price (and its innovation) is generally
unobservable. Therefore. identifying the common efficient price innovations is a
necessary step before any meaningfuimcasure of price discovery can be constructed.
How do markets arrive at prices? There is perhaps no question more central to
economics. This research focuses on price formation in financial markets, where the
question looms especially large: How, if at all. is news about macroeconomic
fundamentals incorporated into stock prices, bond prices and foreign exchange rates?
Unfortunately the process of price discovery in financial markets remains poorly
understood. Traditional "efficient markets" thinking suggests that asset prices should
completely and instantaneously retleet movements in underlying fundamentals.
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Conversely, several prominent authors have recently gone so far as to assert that asset
prices and fundamentals may be largely and routinely disconnected. Experiences such as
the late 1990s U.S. technology-driven market bubble would seem to support that view,
yet simultaneously it seems clear that financial market participants pay a great deal of
attention to data on underlying economic fundamentals. The notable difficulty of
empirically mapping the links between economic fundamentals and asset prices is indeed
striking.
The central price-discovery question has many dimensions and nuances, including
but not limited to the following. How quickly, and with what patterns, do adjustments to
news occur? Does announcement timing matter? Are the magnitudes of effects similar for
"good news" and "bad news," or, for example, do markets react more vigorously to bad
news than to good news'? Quite apart from the direct effect of news on assets prices, what
is its effect on financial market volatility? Do the effects of news on prices and volatility
vary across assets and countries. and what are the links? Are there readily identifiable
herd behavior and/or contagion effects? Do news effects vary over the business cycle?
Just as the central question of price discovery has many dimensions and nuances,
so too docs a full answer. In this research we progress by characterizing the simultaneous
response of foreign exchange markets as well as the domestic and foreign stock and bond
markets to real-time India macroeconomic news. More precisely, we seek to better
understand the links between asset prices and fundamentals by simultaneously
combining:
• High-quality and ultra-high frequency asset prIce data across markets and
countries, which allows us to study plicc movements in (near) continuous time;
• Synchronized survey data on market participants' expectations, which allow us to
infer "surprises" or "innovations" when news is announced; and
• Advances in statistical modeling of volatility. which facilitates efficient
inference.
By so doing, we can probe the workings of the marketplace in new and powerful
ways, focusing on episodes where the source of price movements is well identified,
leading to a high signal-to-noise ratio.
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6.3 Price Discovery in Different Markets
a. Price Discovery in Tick Time
A central question in market microstructure is how information about the
value of an asset is incorporated in its market price. In fragmented markets,
information about the value of an asset arrives to the market from multiple
sources. The process of how information from different sources is incorporated
into the value of an asset has become known as price discovery. An example of
such a fragmented market is the NSE India, a multiple dealer market where each
dealer contributes to the price discovery process. Interesting questions for such a
market are which dealer contributes most, how quick the discovery process
works, and how it depends on markct circumstances like liquidity, volatility and
trading intensity.
An important measure for the contribution to pnce discovery is the
information share introduced by Hasbrouck (1995). Infornlation shares are
defined as the part of the variance of the random walk component of returns that
can be attributed to a particular market or dealer. Unfortunately this variance
decomposition rs not unique when price changes are contemporaneously
correlated. As a solution, Hasbrouck (1995) suggests alternative Choleski
decompositions to establish upper and lower bounds. The Choleski
decompositions work well in many cases where the number of different markets
or market participants is small and the differences among them are large enough.
b. Price Discovery in Multiple-Dealer Markets
"Price discovery" is a dynamic process in which a diverse group of traders
and market makers gather, evaluate, and interpret disparate pieces of information;
coordinate trading demands; and generate market-clearing prices. Though it is a
principal function of securities markets, price discovery has received littIe, but
groWlllg attention from financial economists. The literature includes few
theoretical models or empirical studies, especially for multiple-dealer markets.
The classical notion of price discovery involves a Walrasian auctioneer who
observes quantities supplied and demanded at different prices and determines the
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price that clears the market. With this framework economists ask. "How do prices
work?" but not "How are prices set?" And. while tbis model yields obvious
practical advantages, it trivializes complex and economically important pricing
decisions. In reality, many individuals generate prices concurrently, and the
interactions among institutional features, preferences. and asset characteristics
imply that the quotes we observe in markets vary in their informative quality.
c. Price Discovery in Thinly Traded Markets
Price discovery is an important function performed by futures markets.
Effective futures markets should generate prices that express consciously formed
opinions on cash prices in the future, and should transmit that information
throughout the marketing system in a timely manner (Working, 1942; Tomek,
1980). Because of its importance, the effectiveness of futures markets in
performing this function has been investigated extensively in the literature. The
more recent studies have shown that futures prices playa dominant role in the
discovery and transmission of price information. In the absence of effective price
discovery. researchers have conjectured that limited trading volume associated
with thin markets has adversely affected price discovery.
Traditionally, a thin market has been understood to be a market in which
the number of transactions over a given period of time is insufficient to ensure
efficient price discovery. Peterson identifies three major concerns related to thin
markets: first, those prices may not accurately renect supply and demand
conditions in the market; second, that thinness will contribute to higher price
volatility; and third, that thinness (duc to the magnified impact of individual
transactions) increases the incentive for market manipulation.
d. Price Discovery in Informationally Linked Markets
When a security is traded in more than one market, investors have several
avenues to trade and exploit information. An investor who wants to trade the
Nikkei 225 stock index, for example, can do so in the spot market in Tokyo and,
during the same opening hours, in the futures market in Osaka or Singapore.
Where frictionless and continuous information sharing across markets exist,
trading should be considered as taking place in a single market with simultaneous
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prIce changes in the stocks, stock indices, and derivative instruments. If the
markets were not frictionless, some markets would appear to be more attractive
than others because of concerns relating to transaction costs, regulation, and
liquidity, leading to differences in price discovery across the exchanges. As the
process of globalization of trading and competition among exchanges for order
flow accelerates, it is impot1ant to determine the nature and location of price
discovery.
e, Price Discovery in Commodity Markets
Instability of commodity prices has always been a major concern of the
producers as well as the consumers in an agriculture-dominated country like
India. Farmers' direct exposure to price fluctuations, for instance, makes it too
risky for them to invest in otherwise profitahle activities. There are various ways
to cope with this problem. Apart from increasing stability of the market through
direct government intervention, various actors in the farm sector can better
manage their activities in an environment of unstable prices through derivative
markets, These markets serve a risk-shifting function, and can be used to lock-in
prices instead of relying on uncet1ain price developments. This problem can be
sorted out by making survey of the price risk management system prevailing in
agricultural commodity markcts and to empirically investigate how efficicnt is the
price discovery function of futures for ensuring bettcr hcdge against price
uncertainty in some selected commodities.
6.4 Efficient Market Hypothesis of Price Discovery
Paul Sammuelson developed Efficient Market Hypothesis (EMH) in 1965.
Eugene Fama formulated EMH later in 1970. The EMH suggests whether, at any given
time, prices fully reflect all available information on a particular stock and/or market.
Thus, according to the EMH, no investor has an advantage in predicting a return on a
stock price since no one has access to information not already available to everyone else.
In other words, the hypothesis says that capital markets are efficient and that security
prices fully rellect all available information.
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Based on EMH, there are three identified classifications of market efficiency,
which arc aimed at reflecting the degree to which it can be applied to markets.
• Strong efficiency. This is the strongest version, which states that all information
in a market, whether public or private, is accounted for in a stock price. Not even
insider information could give an investor an advantage.
• Semi·strong efficiency· This form of EMIl implies that all public information is
calculated into a stock's current share price. Neither fundamental nor technical
analysis can be used to achieve superior gains.
• Weak efficiency· This type of EMH claims that all past prices of a stock are
reflected in today's stock price. Therefore, technical analysis cannot be used to
predict and beat a market.
The EMH is an appealing description of competitive market equilibrium. An
efficient market impounds new information into prices quickly and without bias. Prices
fully reflect available information. Market participants adjust the available supply and
aggregate demand in response to publicly available information soars to generate market·
clearing prices. In major stock markets, where millions of dollars are 'voting', it seems
plausible that a rational consensus will be reached as to the share prices which best reflect
the prospects for future cash flows givcn available information.
Although the EMil may be an elegant economic concept, even a normatively
desirable condition, it may not be true. Prices in securities markets may not fully reflect
available information due to all kinds of outside factors. The early literature on market
efficiency was widely interpreted as supportive. But. by the late 1970s, the anomalous
evidence was growing and began to command attention. There is now a substantial body
of empirical research, which casts doubt upon the degree of market efficiency (Fall,
1992).
6.5 Price Discovery Processes
Prices of a financial product are discovered through trading activities among
market participants. This process by which prices adjust to incorporate new infomlation
is referred to as the price discovery (hereafter PO) process.
Analyses will be conducted according to the following framework.
IS I
i. Intraday and Intraweek patterns
Information is generated (24 X 7) 24 hours a day, 7 days a week. However, no
financial market is open for such long hours. In this sense, all market participants face
a price risk in not being able to trade at the prices, which ret1ect the generated
information when the market is closed. In addition, there may be some clustering of
important public information at certain times of the day or week, which also affects
trading activity in the market. Presumably, there are some distinct intraday and
intraweck patterns of PO, ret1ecting market participants' behaviour in coping with
these issues.
ii. PD process after arrival of public information
There must be some type of public information, which systematically affects the
PO process in government securities market. The paper analyses the effect of
statistical announcements, notification of open market operations by central banks,
and releases of policy rate changes on the PO process, as examples of such
information. Presumably, some unique patterns in trading volume, price volatility,
and bid-ask spread are observed after the arrival of this information.
iii. Inter-linkage between the cash and futures markets
If similar products are traded in more than one market, this leads to the question
of which market incorporates new information first. This question regarding PO
speed is examined, with a focus on the relationship between the cash and futures
government securities markets. This is based on the assumption that PO speed is a
proxy for market liquidity, i.e., the market is more liquid when PO speed is high,
because the degree of information content is high. Presumably, PO speed depends on
relative accessibility to the two markets.
6.6 Pricing of futures
Futures can be priced in following manner.
6.6.1 The Pricing of Futures Contracts
The price of futures is dependent on the spot price of the underlying asset
and the cost of holding (or carrying) the underlying asset until the delivery date of
the futures contract. The caITying costs refer to the costs associated with purchasing
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and carryll1g a commodity for a specified period time l9. Basically, there are four
costs associated with can'ying: storage costs, insurance costs, transportation costs,
and financing costs. For financial futures storage, transportation and insurance costs
arc almost zero; therefore, they can be ignored in calculations of financial futures
pnces.
Based on arbitrage arguments20, the theoretical futures pnce can be
determined by adding the calTying costs to the cash price of the underlying asset.
This can be expressed as follows:
F = P + P X C or F = P (1 + C) -------------------------------- (6.1)
F= Futures Price.
P= Cash Market Price.
C= Cost of can'ying, expressed as a fraction of the cash price.
According to arbitrage principles, the futures price must be equal to or less
than the cash price of the underlying commodity plus the carrying charges
necessary to hold the spot commodity forward until delivery. Mathematically, this
rule can be expressed as follows:
F:SP (1 + C) -------------------------------------------------- (6.2)
If prices do not meet this criterion, a trader can bOlTOW funds to buy the
spot commodity, sell the futures contract, and can'y the commodity to delivery
against the futures contract. This is called 'cash-and-caITy' arbitrage; it continues
until the difference between cash and futures prices n,UTOWS relevant carrying
costs.
The futures price must be equal to or greater than the cash price plus the cost of
carrying the goods to delivery. This rule can be expressed as follows:
F ~ P (1 + C) -------------------------------------------------- (6.3)
If the price of futures does not conform to this rule, there will be an
arbitrage opportunity for traders. This is called 'reverse cash-and-carry' arbitrage.
19 . EJwarJs & Ma, Op.Clt. p.7S.
2" Kolb, 1993, op.cit., p. 39 - 40; scc also: Fabozzi, & Modigliani, Op.Cil., pp.224-226.
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In order to prevent cash-and-carry arbitrage and reverse cash-and-carry
arbitrage, the requirements expressed in both equations 6.2 and 6.3 must be met.
Together these equations imply that:
F = P (I + C) ---------------------------------------------------- (6.4)
This equation holds under stable market conditions. There are no
transaction costs and no restrictions on the usc of proceeds from short sales. It is
assumed. however. that there is an unlimited ability to borrow or lend money and
that all borrowing and lending is done at the same interest rate 21. There is also an
assumption that commodities can be stored indefinitely without any change in the
characteristics of the commodity and that there arc no taxes are imposed. When
these assumptions are no longer valid, a divergence occurs between the actual
futures price and the theorctical futures price22•
Sometimes underlying assets earn a cash yield plior to the settlement date.
This cash yield must be deducted from the cost of the futures. When applying the
cash yield earned on the asset to Equation 6.1, we get the following formula23:
(Cash yield: Y)
F = P (I + C - Y) ---------------------------------------------- (6.5)
The difference between cash amI futures prices is called the 'basis'. On the
settlement date, the futures price must be equal to the cash price. As the delivery
clate approaches, therefore. the futures price must converge with the cash price.
This is illustrated in Equation 6.4 By the date of delivery. carrying costs are
approaching zero, the yield can be earned by holding investment approaches at
zero, and then the futures price will be close to the cash market price.
Basis = Cash Price - Futures Price --------------------------- (6.6)
On the settlement date, the cash price is equal to the futures price, so the
basis is zero. If futures prices are accurately retlected by the full-carry
21 The Equation 1.1 does not allow for continuous compounding of interest costs, hut captures only the simple interest financing cost.
22 Fabozzi & Modigliani, op.cit.. p.224-225.
23 Ibid .• p.225-226.
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relationship. then they arc higher than cash prices. and the basis is negative. This
circumstance is referred to as a 'contango' market. It means that the relationship
between futures prices and cash prices is determined solely by the cost of
carryIng.
When futures pnces are determined by considerations other than or in
addition to the cost of carrying factors, the market is said to be characterized by
'Backwardation'. where the futures price is less than the cash price. In this case.
the basis is positive. Backwardation is also used to refer to a market in which the
futures price is above the cash price but still below the full-eany futures priee24•
6.6.2 The cost of carry model
It uses fair value calculation of futures to decide the no-arbitrage limits on the
price of a futures contract. This is the basis for the cost-or-CatTY model where the
price of the contract is defined as:
F=S+C ----------------------------------------------- (6.7)
Where:
F Futures price
S Spot price
C Holding costs or cany costs
This can also be expressed as:
F=S (l +r)T ------------------------------------------ (6.8)
Where:
r =Cost of financing
T= Time till expiration
If F<S(l+rl or F>SO+r)T arbitrage opportunities would exist I.e.
whenever the futures price moves away from the fair value, there would be
chances for arbitrage. We know what the spot and futures prices are. but what are
the components of holding cost? The components of holding cost vary with
24 Edwards & Ma. op.cit" p.~7.
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contracts on different assets. At times the holding cost may even be ncgative. In
the case of commodity futures, the holding cost is the cost of financing plus cost
of storage and insurance purchased etc. In the case of equity futures, the holding
cost is the cost of financing minus the dividends returns.
6.6.3 Pricing equity index futures
A futures contract on the stock market index gives its owner the right and
ohligation to buy or sell the portfolio of stocks characterized by the index. Stock
index futures are cash settled; there is no delivery of the underlying stocks. In
their short history of trading, index futures have had a great impact on the world's
securities markets. Indeed, index futures trading have been accused of making the
world's stock markets more volatile than ever before. The critics claim that
individual investors have been driven out to the equity markets because the
actions of institutional traders in both the spot and futures markets cause stock
values to gyrate with no links to their fundamental values. Whether stock index
futures trading is a blessing or a curse is debatable. It is certainly true, however,
that its existence has revolutionized the art and science of institutional equity
portfolio management.
The main di fferences between commodity and equity index futures are that:
• There are no costs of storage involved in holding equity.
• Equity comes with a dividend stream, which is a negative cost if you are
long the stock and a positive cost if you are short the stock.
Therefore, Cost of carry = Financing cost - Dividends. Thus, a crucial
aspect of dealing with equity futures as opposed to commodity futures is an
accurate forecasting of dividends. The better the forecast of dividend offered by a
security, the better is the estimate of the futures price.
•
•
Pricing index futures given expected dividend amount
The pricing of index futures is also based on the cost-or-carry model, where
the carrying cost is the cost of financing the purchase of the portfolio
underlying the index, minus the present value of dividends obtained from the
stocks in the index portfolio.
Pricing index futures given expected dividend yield
156
If the dividend now throughout the year is generally uniform. i.e. if there are
few historical cases of clustering of dividends in any particular month, it is
useful to calculate the annual dividend yield.
T F=S (1 +r-q) ------------------------------------- (6.9)
Where:
F =futures price
s= spot index value
r =cost of financing
q =expected dividend yield
T =holding period
6.6.4 A Simple Model of Price Discovery
It is well known that prices of related securities like pnccs In spot and futures
markets cannot diverge without bound because they are linked by an arbitrage
relationship. The link between this arbitrage relationship (and the associated cost
of-carry pricing model) and the existence of a cointegralion relationship between
the spot and futures prices has been extensively presented in the literature (e.g.
Wahab and Lashgari [1993 J). This research suggests that inference concerning the
spot and futures price dynamics should be based on Error Correction Models
(ECM) where the elTor-correction components indicate,
• The proportion of disequilibrium from one period that IS cOITected III a
later period and
• The relative magnitude of adjustments In each market towards
·l·b· 25 equI I num .
Another important insight from this research states that the spot and
futures prices should share a common stochastic trcnd because spot and futures
markets are essentially two different places to trade the same underlying
25 See Banerjee, Dolado. Galhraith and Hendry [19931 Or Llitkepohl [19931. chap. 13 for a general analysis
of cointcgration and see Brenner and Kroner [1995] for an analysis of the link between arhitrage and
cuintcgration.
157
commodity. Based on this feature. Hasbrouck [1995] proposes a measure of price
discovery that is used in this study. In the following. the ECM and the common
trend model is presented in the context of a very simple model of price dynamics
inspired from Hasbrouck [1995J.
Suppose. first, that a claim on some future cash Ilows is traded in two
different markets, a cash market and a futures market. Obviously. it exists only
one true value for this claim and we call this value the efficient price. As standard
in the finance literature, we assume that the efficient price follows a random walk:
p, = p,-I + 11, ------------------------------------- (6.10)
Where the increments 11, are assumed to retlect new information about the
future cash tlows. The actual cash and futures price dynamics is driven by this
common random walk and it may be specified by an unobservable component
model:
P,=K+p, 1+£, -------------------------------------------- (6.11)
Where PI=(SI FI)' is a (2 x I) price vector. SI and FI are the spot and the
futures prices observed at time t, K is a (2 x I) vector of means, I is a unit vedor
and G/ is a vector of disturbances which is assumed to be a zero-mean covariance
stationary stochastic process. The process "/ allows spot and futures prices to
deviate from the efficient price due to market specific phenomenon such as a
liquidity pressure. Price discovery refers to the impounding of (new) information
into spot and futures prices and is related to the contributions to the efficient price
increments from the spot and futures markets.
Suppose, for example, that the informational content of orders and trades
(other than arbitrage-based orders and trades) in one market is larger than the
informational content of orders and trades (other than arbitrage-based orders and
trades) in the other market. These asymmetric contributions to the common
efficient price discovery create a price discrepancy between the two markets that
causes some investors to submit arbitrage orders. Therefore, arbitrage appears as
an e'Tor-correction mechanism that prevents the spot and futures prices from
diverging without bound. Furthermore, in our informational framework, the
deviation frol11 the cash and catTy relationship disappears only when all the
158
relevant information is shared by the two markets and impeded in the spot and the
futures prices. As a result, cash and futures prices ultimately renect the same
information, as suggested by the common (unobservable) efficient price model.
Inference concerning the error correction mechanism may be obtained
from an ECM for price changes and inference concerning the common
(unobservable) efficient price may be obtained from the vector moving average
(VMA) representation for the actual data. Additional motivation for these models
is that ECM and VMA arc alternative forms of a cointegrated system. In our
bivariate framework, and due to the arbitrage constraint. S, and F, are expected to
be cointegrated of order one, yielding a unique cointegrating vector. Following
Johansen [1988], the ECM for price changes is given by:
P-I
l',.Pt = L ITi l',.P'i+ U (W P'P- WK) + e, ------------------- (6.12)
i=1
Where the n, arc (2 x 2) coefficient matrices, (f. is a (2 x I) vector of
coefficients for the cointegrating vector, ~ is the (2 x I) cointegrating vector and c,
is a (2 x I) vector of serially-uncorrelated disturbances with Cov(e,) = n. Note
that in our spot-futures framework ~ should be equal to (I - I). Furthermore, the
coefficients of the vector u should indicate the proportion of the mispricing
observed in a given period that is corrected in a later period as well as the relative
magnitude of the adjustments in the spot and futures markets. The VMA
specification is directly obtaincd from the ECM and is givcn by:
l',.Pt = L \)Ii e'_i ------------------------------------------------- (6.13)
i=O Assuming that e, = 0 for I < 0, the cumulative price impact to an
innovation arriving at time I = 0 may bc obtained as:
In the present case, the matrix sum (IVO + II'I + IV2 + ... ) forms a (2 x 2) matrix
whose rows must be identical because the long term response of each price to an
159
innovation must be identical if the prices are r;ot to diverge. Denoting If! onc of
these (identical) rows, the variance of the efficient price may be obtained as:
(}2'l = 'f'Q'f" ---------------------------------------------------- (6.15)
In ordcr to measure the contribution of each market to the price discovery,
lIasbrouck [1995 J proposes to compute the quantities Si given by:
'f'2Q, I II
Sj = ------------------------------------------------- (6.16)
'f'Q'I"
Where i refers to the relevant market (i = s, f for the spot and the futures
markets, respectively), Due to the possibility of cross-colTclation in price
innovations, the matrix [2 lIlay not be diagonal and may be replaced by its
Cholesky factor. In this case, the price contribution of the market i is obtained by
the quantity:
('f' F)2 Sj = ------------------------------------------ (6,17)
('f' F) I ('f' F),
Where F is the Cholcsky factor (F is the lowcr triangular matrix such that
n = FFI) and where (J 2 q is now given by ('VF)I ('VF)'. Note that the Cholesky
decomposition forces a potential important asymmetry on the system since a
shock to the tirst variable affects the first variable initially, while a shock to the
second variable has a contemporaneous effect on both variables, Then, the
ordering of the variables matters and the price contributions will be computed for
the two different orderings of the variables. The index contribution is maximized
when index price is placed first and the futures contribution is maximized when
the futures priee is placed tirst.
6.7 Review of Literature
Futures and cash markets contribute to the discovery of a unique and common
unobservable price that is the efficient price. Besides the traditional role of risk sharing
assigned to futures markets, these markets play an important role in the aggregation of
160
information (sce, for cxample, Grossman [1977 J, Bray [19S I [ and Brannen and UI veling
[1984]), Thc case of stock index futures is analyzed in Subrahmanyam [1991] and in
Kumar and Seppi [1994]. Futures and cash markets contribute to the discovery of a
unique and common unobservable price that is the efficient pricc. The contribution of
each market to the price discovery depends, at least in part, on thc microstructure of these
markets, including the level of transparency, the liquidity supply mechanism, the rules
governing the priority of ordcrs, the constraints on short salcs and the sellielllent
mechanism.
Furthcrmore, stocks and futures are traded in different market structures, a pure
limit ordcr market for the stocks and a 1100r market for the futures. As suggcstcd by
Biais, Foucault and Salanie [1998], this difference affects the liquidity suppliers'
behavior and has an impact on the level of liquidity of the market. In paI1icular, it appcars
that the cost of liquidity is hll'ger in the 1100r market than in the limit ordcr market due to
the absence of incentive to undercut on large ask prices (overbid on low bid priccs) in the
1100r JJ];Jrket. On the contrary, limit order markets appear to entail emcient risk sharing
and competitive pricing. This may affect the order submission behavior of informed
traders in a way that is favorable to the stock market. As a conscquence, traditional
results indicating that information is first aggregated in the futures market (e.g. Stoll and
Whaley [1990]) may in fact rel1ect, at least paI1ially, differences in market
microstructure.
On the empirical ground, most of the studies emphasize some kind of causality
between futures and cash markets returns (e.g. Stoll and Whaley [1990]) and/or between
futures and cash markets return volatility (e.g. Chan, Chan and Karolyi [1991]). While
these analyses provide some evidence about the relationship between the cash and futures
markets, they do explicitly take into account neither the equilibrium relationship between
cash and futures prices nor the price discovery process. A more satisfactory specification
may be built on the observation that these two characteristics are linked to two particular
forms of the cointegration property of futures and cash prices, the en'or correction form
(hereafter, ECM) and the common trend form. Wahab and Lashgari [1993J provide an in
dcpth analysis of the relationship betwecn stock index cash and futures markets using an
ECM framework. Nevertheless, the evidence presented in their paper should be
161
interpreted with caution due to the usc of non-synchronous daily closing pnces. The
analysis of Shyy, Vijayraghavan and Scott-Quinn [1996j is more closely related to our
work because it deals with the French market and uses intraday data. Furthermore, the
empirical analysis presented in their paper suggests that traditional results concerning the
lead-lag relationship betwecn cash and futures markets may be caused by a stale price
effect due to non-synchronous trading among stocks. While this result is appealing, it
should also be considered with caution because Shyy. Vijayraghavan and Scott-Quinn
[199()j use data on the second nearest contract, which is characterized by a very low level
of activity. As far as the choice of the data is concerned, part of our work may be viewed
as an extension and analysis of the robustness of the results of Shyy, Vijayraghavan and
Scott-Quinn [1996] to the case of the first nearest contract which is characterized by a
high level of activity. Finally, Hasbrouck [1995] uses the common trends representation
of a set of cointegrated variables to measure the contribution to the efficient price
innovation from a particular market.
Investigation of causal relationship between futures and cash prices is not a new
phenomenon. At the international as well as at national level, significant efforts have
been made to evaluate the price discovery efficiency of different futures markets (viz;
commodity futures. cUITency futures. equity futures, etc.). Stensis (1983), Garbade and
Sibler (1983), Protopapadakis and Stoll (1983), French (1986), Kawaller (1987), Mohd.
Fatimah (1994), Cheung and Fung (1997), Hall (2001), Yang Jian (2001), Singh (2001),
Thomas and Karande (2001), Sahadevan (2002), Campbell and Diebold (2002), Zhong
(2004), and Isabel and Gilbert (2004) investigated the price discovcry efficiency of
commodity futures market in differcnt countries viz; America, United Kingdom,
Malaysia, India, Mexico etc. respectively. All rescarchers (except for Sahadevan (2002))
found strong lead-lag relationship between the futures and spot prices.
Granger et aI., (1998), Covrig and Melvin (2001), Anderson et aI., (2002) and
Yan and Zivot (2004) examined the price discovery efficiency of cUITency futures market
in various economies like; Hong Kong, Indonesia, Japan, South Korea, Malaysia,
Philippines. Singapore, Thailand. Taiwan, America respectively and they observed strong
bilateral causality between both markcts. Moreover. they found that futures market is
efficient for underlying currencies. in the sense that it leads the cash market.
162
Chan (1992), Hasbrouck (1995), Jong and Donders (1998), Booth (1999),
Turkington and Walsh (1999), l\lenkvcld (2003), Chuang (2003), Raju and Karande
(2003), Barclay and Hendershott (2004), Sharma and Gupta (2005), So and Tse (2005)
and Gupta and Singh (2006) evaluated the prices discovery efficiency of equity futures in
different countries namely; America, Netherlands, Germany, Australia, Taiwan, India,
Hong Kong respectively. Except for Barclay and Hendershott (2004), all researchers
observed significant evidence of efficient price discovery through equity futures market.
They all found that equity and futures prices were cointegrated and the causality from the
futures to cash market was significant as compared to the causality from reverse side.
Citing the above studies makes one thing very clear that investigating the causal
relationship between futures and cash market is not a new phenomenon, For many
markets in different economies at different time frames, price discovery efficiency of the
futures market has been investigated and the review of literature provides strong evidence
favoring the argument that futures market is an efficient price discovery vehicle.
In America, price discovery efficiency of futures market has been far investigated
for all types of futures viz; commodity futures, equity futures and cUlTency futures etc.
Stensis (1983), Garbade and Sibler (1983), French (1986), Chan (1992), Cheung and
Fung (1997), Hall et aI., (200 I), Yang J ian et aI., (200 I), Campbell and Diebold (2002)
and Isabel and Gilbert (2004) examined the causal relationship between the spot and
futures price on Chicago Board of Trade (CBOT) and they observed that spot market
significantly followed the futures market and the futures market price movements
provides a basis for predicting the prospective spot market price changes,
In addition to commodity futures, Hasbrouck (1995), Menkveld (2003) and
Barclay and Hendershott (2004) investigated the price discovery efficiency of the equity
futures market on NYSE and NASDAQ during 1993. 1997-98 and 1993-99 and except
for Barclay and Hendershott (2004), all found significant causal relationship between the
cash and futures prices, which is an essential condition for price discovery efficiency of
futurcs market. Although Barclay and Hendershott (2004) found weak lead-lag
relationship between cash and futures prices but their study does not completely reject the
hypothesis rather their results arc statistically significant and have little economic use.
Moreover, first order co integration is one of the essential features of the cash and Futures
163
prices. which reflects that both futures as well as cash prices are non-stationary as found
by different scholars in various speculative markets.
In addition to America. significant efforts have been made to investigate the price
discovery efficiency of the eljuity futures market in different economies viz. India,
Taiwan, Mexico and Hong Kong. Raju and Karande (2003) investigated the causality
relationship between eljuity futures and cash market on NSE (National Stock Exchange
of India), but found mixed results regarding the causality relationship between two
markets. The reason for the confusing results may be the short time period (i.e. Three
Years) considered for the study but when the same market was examined by considering
lengthy time frame (i.e. Five Years) by Gupta and Singh (2006), they found strong
bilateral causality between cash and futures market. Moreover by applying Impulse
Response Analysis, they found that the causality from the futures to cash market was
stronger as compared to the causality from cash market to futures market.
Chuang (2003) examined the price discovery efficiency of TAISEX (Taiwan
Stock Exchange Capitalization Weighted Index Futures) and MSCI (Morgan Stanley
Capital International Taiwan Index Futures) during 1998-99 and found strong statistical
evidence of bilateral causality and inferred that basis movement was an efficient
predictor of the prospective cash market price movements. So & Tse (2005) made an
attempt to examine the causality relationship between cash and futures market on Hang
Seng Index Market, and by considering the time frame of three years (i.e. 1999-2002),
they found significant bilateral causality between these two markets.
Booth et aI., (1999) and Upper & Werner (2002) conducted studies on German
stock markets and found strong evidence of infonnation traveling from the futures market
to the spot market and they evidently highlighted and supported the price discovery role
of the futures market. Gulen and Mayhew (2000) conducted a wonderful study
considering the behaviour of cash market prices during the post futures trading era for 25
countries. They observed that except for America and Japan, in all countries, the
magnitude of volatility during post futures trading era has gone down. Gupta (2001),
Shenbagaraman (2003) and Raju and Karnade (2003) observed the same in Indian capital
market. Kiran and Nagaraj (2003) observed that futures market could do better during the
market crash due to terrorist attack on America on 11 th Sept., 20ll! and concluded that
164
futures market provides better information during the high volatility period and the basis
looks very strong during the high volatility period, which means that both markets moves
into same direction.
Thus, the review of literature provides sufficient evidences that equity futures
market has been an efficient price discovery vehicle. Even in India, the studies conducted
by Raju and Karande (2003) and Gupta and Singh (2006) found significant causal
relationship between these two markets. The current study examines specifically the
price discovery efficiency of Indian equity futures market during high volatility periods
i.e. period around I Ilh Sept., 200 I (Terrorist attack on Amcrica), 171h May, 2004 (Ever
highest Indian stock market crash due to political uncertainty) and 14th June 2006 (Global
Sell off and Jittery effects in Indian markets). Thus, the current study will be of great
benefit for the traders and will help to fill the gap in the literature.
6.7.1 Research Contribution
Price Discovery in Derivatives market is very interesting and wide topic. Related
to this area of research as mentioned in Chapter-I, following research papers are
published to facilitate the present study.
• "Arbitrage opportunities in Intraday trading between futures, options and
cash markets - Case study on NSE India"
This research paper is mainly focused on Arbitrage opportunities being
created between Futures, Options and Cash markets over a period of time due to
number of reasons such as inside information, dividendlbonus, shorting in
markets etc. The research has mainly contributed in terms of Arbitrage
opportunities based on three approaches, (a) Transaction prices (b) Bid-ask quotes
and (c) Transaction prices that are checked for trade direction using bid-ask
prices. Overall the percentage of observations violating no-arbitrage bounds is
dramatically reduced under (b) and (c) relative to (a). Overall this research has
highlighted significant opportunities for Arbitragers between all three markets,
hence it can also help in understanding price discovery process related to this
chapter.
16S
• "Stock Index Futures & Options and Predictability of Intraday Index Price
Changc-NSE (National Stock Exchange of India) Case study."
As we know that NSE is currently forefront in the world for single stock
index futures and stock futures are having a mammoth 70'70 of share in overall
derivative segment, it becomes paramount importance to analyze price discovery
between NSE's Index price and Index futures in Intraday setting. This research
examines the impact of index futures options on the predictability of intraday
index price changes by examining the NSE futures contract. The predictor
variables examined were,
(I) Lagged cash index vailies
With regard to the lagged cash index as a predictor variable. the ratio of
significant positive to significant negative coefficients in the regression equation
remained unchanged following futures option initiation on the NSE. Although the
changes in the ratios were not consistent across all lag times, the value of lagged
index price changes as a predictor variable appears to be unaffected by NSE
futures option initiation.
(2) Lagged flltllres price changes
The impact of futures option initiation on the price discovery role of the futures
contract was evaluated through the lagged futures price change variable. The ratio
of significant positive to significant negative coefficients on the lagged futures
price change variable dropped slightly following futures option initiation. These
results indicate that the value of the lagged futures price change variable or the
price discovery role of the futures contract appears to havc diminished somewhat
following initiation of the futures option contract.
(3) Theoretical fuilires mispricings.
With respect to the theoretical futures mispricing variable there was a reduction in
the ratio of significant positive to significant negative coefficients in the post
futures option period. This relative decrease in the number of significant positive
coefficients indicates that the value of the theoretical futures mispricing variable
as a predictor of subsequent intraday index plice changes is diminished following
futures option initiation.
166
• "Short selling and Price Discovery -A Thematic Case Study on Indian Stock
Markets"
This research paper discuss the impact of the decision of the Indian
Financial authority permitting short selling to FlI (Foreign Institutional Investors)
on Derivatives market. This is a useful contribution as the SEBI parent authority
of Indian Financial Markets is really under the process to allow short selling in
Indian markets. This paper mainly highlights possible impact and behavior of
Indian capital markets after introduction of short selling and its effect in other
markets. It contributes on two issues.
o What is the effect of short-sale restrictions on skewness, volatility, the
probability of market crashes, Price discovery and liquidity?
o What is the effect on the market expected return or cost of capital?
6.8 Price Discovery between Index and Futures Markets in India- NSE Case
6.8.1 Introduction
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. 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 injol7l1alionai ejjicienc/6 of the cash
market.
26 According to Fama (1970), a market is said to be infomKltionally efficient if the prices ::llways reflect all
the information availahle to the market. Depending on availability of information, Fama suggested three
types of market efficiency- Weak form, Semi-strong form and Strong form efficiency. This proposition to
market efficiency is Icmlcd as Efficient Market Hypothesis (EMH).
167
Many emergmg 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 have 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.
Therefore the present study is being contemplated with the following specific objectives:
• Investigating the Price Discovery efficiency betwccn the Nifty Index and Nifty
Index futures market in India, both in terms of return and volatility; and
• Analyzing the possible explanations behind the variation in the prices of Index
and Futures over time. In this regard, the important propositions / hypothesis
attempted to be tested are:
o Futures market leads (if at all) the spot market not because of infreguent
trading of component stocks;
o The leading role of futures market will be greater around macroeconomic
information release; and
o The leading role of futures market weakens around the firm-specific
annOUnCCITICnts.
168
6.8.2 Methodology
Methodology deals with selection of econometric techniques, data, calculation of
returns, volatility. identification of benchmark Index and other related matters. Prices in
the cash market and futures market are expected to be inter-related. The products traded
arc similar in nature. Stock index futures value is derived from the value of the cash
market price plus interest rate. Any information; economic. political, social and other
inlluences changes in prices either in spot market or in futures market. Since futures
market has lesser trading costs, higher liquidity than spot market the information is first
expected to be retlected in the plices of futures and then it is expected to 110w to cash
market (Kawaller et.al., 1987). However, this may not be true in all circumstances.
Sometimes it can happen that the information is first discounted in the cash market and
then moves on to futures market. Alternatively, information is rel1ected simultaneously in
both the markcts. In this research what is attempted to measure is the speed of the
information tlow and its early impact on prices.
There arc some econometric techniques to measure the direction as well as the
intensity of the information now. Among others, Granger causality, Spectral Analysis
and cointegration are more appropriate techniques useful to find out speed of infonnation
tlow and its intensity on prices. In order to choose an appropriate technique between
these, the prices in their levels are tested for cointegration and found to be cointegrated.
Therefore the cointegration technique is preferred to Granger causality.
The use of cointegration analysis and error correction models explicitly takes into
account non-stationmity and enables one to distinguish between short run deviations from
equilibrium indicative of price discovery and long run deviations that account for
efficiency and stability. If two series (such as futures and spot prices) are non-stationary
but that a linear combination of the two vmiables (such as the basis) is stationary so that
both are cointegrated then a bivariate dynamic model that uses only first differences (with
lags) is misspecified because it Ignores interim short run adjustments to long run
equilibrium.
The link between cointegration and causality stems from the fact that if spot and
futures prices are cointcgrated, then causality must exist in at least one direction and
possibly in both directions. Cointegration implies that each series be represented by an
169
elTor cOlTection model that includes last period's equilibrium as well as lagged values of
the first differences of each variable, temporal causality can be assessed by examining the
statistical significance and relative magnitudes of the error cOlTection coefficients and the
coefficients on the lagged variables.
The possibility that one variable in a system of cointegrated series is exogenous
(independent) within the error correction process motivates the use of elTor cOlTection
models in evaluating price discovery. The cointegrating vectors define the long run
equilibrium while the error correction dynamics characterise the price discovery process,
the process whereby markets attempt to find equilibrium. The primary purpose in
estimating the Error Correction Model (ECM)27 is to implement price leadership tests
between futures and spot prices. Tests of causality between cointegrated variables should
be conducted in an error correction framework because standard tests of causality
overlook the reversion to equilibrium channel of causality represented by ~ (basis).
Causality tests in the ECM framework involve testing significance of the coefficients u
and B. If these coefllcients arc jointly insignificant, then there is no Granger causality and
hence there is no price discovery.
6,8.2.1 Econometric Techniques28
Price changes in one market influence price changes in the other market so as to
bring about a long run equilibrium relationship as given by the equation:
F, - ao - p J S, =e,----------------------------------- (6.18)
Where F, and S, are contemporaneous cash and futures prices at time t; ao and BJ
are parameters and e, is the classical error term (deviation from equilibrium). According
to Engle and Granger (1987), if and St are non-stationary* but the deviations, are
stationary, then S, and F, are cointcgratcd** and equilibrium exists between F, and St. For
27 The error correction component in the Error Correction Model (ECM) indicates: (i) the proportion of
disequilibrium from one period that is corrected in il later period, and (ii) the relative magnitude of
adjustments in each Il1Jrkel towards equilibrium.
2R Gujarati Damodar N (1995), Basic Econometrics, 3nJ edition. McGra\v Hill Inc.
170
F, and S, to be cointegrated, they must be integrated of the first order. Performing unit
root test on each univariate price series deten11ines the order of integration. If each series
is non-stationary in the levels, but the first dilTerenccs and deviations c" are stationary,
the prices are cointegrated of order (1.1), denoted CI(I.I) with 13 1 as the cointegrating
coefficient. An error correction model exists for each series, which is not subject to
spurious results. Ordinary least squares (OLS) is inappropriate if futures or spot prices are
non stationary because the standard enors are not consistent.
* Broadly speaking a data series is said to be stationary if its mean and variance
arc constant (non-changing) over time and the value of covariance between two
time periods depends only on the distance or lag between the two time periods
and not on the actual time at which the covariance is computed (Gujarati, 1995).
The correlation between a series and its lagged values arc assumed to depend only
on the length of the lag and not on when the series started. This property is known
as stationarity and any series obeying this is called a stationary time series. It is
also referred to as a series that is integrated of order zero or as 1(0) (Ramanathan,
2002).
** Suppose X, and Y, arc two non-stationary selies. In general we would expect
that a combination of X, and Y, is also non-stationary. However, a particular
combination may be stationary. If such a combination exists, we say that X, and
Y, are cointegrated. Two cointegrated series will thus not drift far apart overtime
ego futures and spot prices, consumption and income (Ramanathan, 2002). The
econometric technique regression assumes that mean values are stationary (do not
change much) over any study period. If the mean values of a parameter keep
changing from period to period then estimated coefficients will not provide
unbiased estimates. Therefore, it is necessary to test the stationarity of the
dependent and independent variables.
171
Cointegration29 implies that each series can be represented by an error correction
model that includes last period's equilibrium error as well as lagged values of the first
differences of each variable. lienee. temporal causality can be assessed by examining the
statistical significance and relative magnitudes of the error correction coefficients and the
coefficients on the lagged variables. In this study. the error correction model can be
written as:
Rf.t = aor+ alr(FI. I - SI.I) + ~Ir Rf.I-1 + ~2r Rs.II + En ------------- (6.19)
Rs.l = Uos + a l.s (FI-I - SI.I) + ~"Rs.lI + ~2s Rf.I-1 + Esl ------------ (6.20)
Where Rf.1 is Nifty futures returns and Rs.l is Nifty Index returns. air and al s are
the error correction terms and I3s represent short run effects.
Each of the above two equations is interpreted as having two parts. The first part
IS the equilibrium error. This measures how the left hand side variable adjusts to the
previous period's deviation from long run equilibrium. The remaining portions of the
equations are the lagged first differences. which represent short run effects of the
previous period's change in price. If air is statistically insignificant the current period
change in the futures price to period's deviation from long run equilibrium. If both and B2f
are statistically insignificant then the spot markct price does not Granger cause futures
market price.
Both the dependent and explanatory variables behavior varies over time. If both
dependent and independent variables are non-stationary then the estimates of simple
regressIOn arc incorrect and the results will mislead. Therefore, it is necessary to test
whether the variables are stationary or not. Some of the most widely used techniques to
test stationarity are Dickey Fuller test and Augmented Dickey Fuller test and Phillip
Perron test. In this study both Phillip Perron Dickey Fuller test Augmented Dickey Fuller
test has been used to test for the unit root in variables. The results are presented in Table-
6.2 & 6.3.The hypothesis of unit root has becn rejectcd at one per cent significant level.
A non-stationary timc series is said to be integrated in order one. often denoted by
1(1). if the series is stationary aftcr the first-order differencing. An (n x I) vector time
2'J Co-intergration and error correction; Repre:.;cntation, estimating and testing- By RobcI1 Eagle and
W.J.Granger, Econometric<l, Vol 55, No.2 (March 19~7), 251-276.
172
series Yl is said to be cointegrated if each of the series taken individually is 1(1) while
some linear combination of the series A' Y, is stationary for some nonzero vector A
(Hamilton, 1994). The theory of cointegration relates to the study of the efficiency of a
futures market in the following way. Let S, be the cash price at time t and Fl . i be futures
price taken at i periods before the contract matures at time t, where i is the number of
periods ahead, then some linear combination of S, and F,.i is expected to be stationary
that is there exist a and b such that Z, is stationary with mean 0:
Zl = Sl - a - bFli (I) --------------------------------- (6.21)
If both S, and F,.i are I (I), a condition that usually holds for prices, the vector
process (S, and Fl.i) is cointegrated. This cointegration between Sl and Fl.i is a necessary
condition for market efficiency (Lai and Lai (1991)). Cointegration ensures that there
exists a long-run equilibrium relationship between the two series. If Sl and Fl.i are not
cointegrated, they will drift apart without bound, so that the futures price provides little
information about the movement of the cash price.
In addition to cointcgration, market efficiency also requires an unbiased forecast
of futures price on cash price i.e. a = 0 and b =1 in equation (6.21). Therefore, the market
efficiency should be tested in two steps: first to examine the cointegration relationship
between the two price series Sl and Fl. I. if cointegration exists then parameters restriction
a = 0 and b = I is tested. The second step may consist of multiple tests: a = 0 and b = I
jointly or each individually. The constraint b = I is a more important indicator of market
efficiency, because "a" is non-zero under the existence of risk premium and/or
transportation costs even when the market is efficient. That is why we also test them
separately through a = 0 and b = I are often tested jointly. The cointegration relationship
and the parameter restrictions can be tested using Johansen's approach as outlined below.
6.8.2.2 Cointegration Tests
Before testing for cointegration. each individual price series should be examined
for I (I) /irst. Phillips-Perron unit root test is the common method (Booth et. al .. (1999)).
If both the futures and cash price series are I (I), Johansen's cointegration tests can be
conducted. Consider a general k'" order V AR model:
173
K-J
;\.. Y, = D + n Y'I + ~ r j ;\.. Y" + L, -------------------------- (6.22)
i - J Where Y, is an (n x I) vector to be tested for cointegration, and 6 Y, = Y, - Y,.,: 0
is the deterministic term which may take different forms such as a vector of zeros or non
zero constants depending on properties of the data to be tested nand f: and are matrices
of coefficients; and k is chosen so that £, is a multivariate normal white noise process
with mean () and finite covariance matrix.
The cointegration relationship can be detected by examllung the rank of the
coefficient matrix n, because the number of cointegration vectors equals the rank of n. In
particular, the 0 rank i.e. n = () implies no eointcgration. In a bivariable case, i.e. n = 2,
the two variables are cointegrated only if the rank of n equals I (Johansen and Juselius
(1990)).
Johansen (1998) suggcsted two test statistics to test the null hypothesis that there
are at most r cointegration vectors. The null hypothesis can be equivalently statcd as the
rank of n is at most r, for r = O. I, ... n-1. The two test statistics are based on trace and
maximum eignvalues, respectively,
I.Trace = -T 1: III( \- I.i) i~r-I -------------------------- (6.23)
j.'lax = -T 111(1- I.r-l) ____________________________ (6.24)
Where A, ...... A, are the r largest squared canonical correlations between the
residuals obtained by regressing 6 Y, and Y,.,on 6 Y,." 6 Y,.2 , ..... , fI. Y,.k.' and
respectively. The critical values have been taken from Johansen and Juselius (1990).
In our test for efficiency of futures market, Y, = (S" F,.,), n = 2, and the null
hypothesis should be tested for r = 0 and r = I. If r = () cannot be rejecled, we will
conclude that there is no cointegration vector, and therefore, no cointegration. On the
other hand, if r = () is rejected, and r = I cannot be rejected. we will conclude that there is
a cointegration relationship.
174
6.8.3 Data Source and Time Period
Index futures on S&P CNX Nifty and BSE Sensex started trading on National
Stock Exchange (NSE) and on The Stock Exchange. l'vlumbai (ESE) respectively in June
2000. Volumes traded on BSE arc negligible and they account for less than one per cent
of the total number of contracts traded on NSE. Therefore, for the purpose of the research
study of price discovery only Index futures on S&P CNX Nifty are considered. Daily
closing values of NSE Nifty Index futures and NSE Nifty Index arc considered from June
20()() till December 2006 (i.e. 1644 observations) refer Appendix-I, Trading activity
slowly picked up in Index futures and peaked in September 200 I. Thereafter with some
!luctuations the activity has been very high. Number of contracts traded varied between
1.00,00 to 7,00,00 per month during September 200 I to December 2006. The study
period is divided into two sub periods on the basis of low volumes (June 2000 to
December 2003) and high volumes (January 2003 to December 2(06). The distinction is
made to assess the impact of volume (liquidity) on long run price equilibrium. Returns
are calculatcd as log of ratio of present day's price to previous day's price.
In order to examine the Price Discovery between the underlying spot market and
the futures market, the basic data used in this study consist of intraday price histories for
the nearby contract of nifty index futures, nifty cash index recorded Daily closing values
of Index futures and S&P CNX Nifty have been taken from June 2000 to December 2006
(i.e. 1644 observations), Returns (Rll have been calculated as log of ratio of present day's
price to previous day's price (i.e. RI = In (PI /PI.1))30. Data relating to the price series have
been obtained from website of NSE (www.nseindia.com).
6.8.4 Results and Analysis
Prior to discussing the lead-lag relationship between the futures and cash markets,
Table- 6.1 discusses the descriptive statistics of the NSE eash as well as the futures
market and the spread between futures and the cash prices (i.e. Basis). The results of
Table- 6.1 clearly show that the futures and cash market returns are asymmetric and
3D Ibrahim e{ "I. [J 9991 and Kar cLal. [20IN)/. p.1252
175
highly volatile. Asymmctry in the cash market and futures market returns is not a new
phenomenon. Risk averse nature of the traders in the market may be the prominent cause
for the asymmetric returns (Moolman (2004)). Asymmetric behavior has been observed
in basis as well, which implies that the comovcmcnt of both series does not havc constant
variance.
Significance of the Jarque-Bcra (JB) test statistics does not only imply that the
returns are asymmetric, but it also means that the returns are not normally distributed,
which is the precondition for any market to be efficient in the weak form (Fama (1965),
Stevenson and Bear (1970), Reddy (1997) and Kamath (1998).
Coefficient of Box-Ljung (LB) statistic provides very interesting and useful
information. Basis is predictable for full period as well as for all sub periods. Basis are
serially correlated at 1 % signiticance level, which means for full period as well as for all
sub periods there is strong comovemcnt between futures markct and the cash market.
Figure-6.2 provides same information through the plot of futures and cash prices and the
spread between these two. Both futures and cash market shows upward co movement
trend and more or less basis scems to be stationary during the whole period (see table
6.2). In Figure-6.2 comovcment between cash and the futures market is so strong that it is
very diflieult to see the curve of cash and futures market separately.
Figure- 6.2 Spread betwecn the Nifty Futures and Cash priccs
NM FUTURES NIfTY bluis
.----.----... -----~."
-.------~.,~~-.----- .~~,--. -"",--~-- ----.. .-----..... -___________________________ J'5L4
176
ARIABLE N I\IEAN VARIANCE SKEW KURT J-B LB(I)
NES." OSIS FULL FUTURES 1644 4.753E-04 2. I 52E-04 -U50 14.262 7807.06 4.615**
CASH 1644 4.854E-04 1.9X7E-04 -0.976 7.774 1548.42 19.106
BASIS 1644 -1.9116 58.80S -1.219 2.735 }50.07* 842.110'
00-01 FUTURES 154 -1.l7E-OJ 3.007E-04 -0.90 I 3.H26 32.91 * 0.501
CASH 154 -1.13E-03 2.998E-04 -0.444 1.440 26.99* 1.469
BASIS 154 2.1787 47.137 -2.327 9.536 539.17* 76.606*
01-02 FUTURES 247 3.464E-05 1.971 E-04 -0.597 }.OSI 14.68* 2.640
CASH 247 -3.07E-05 1.979E-04 - 0.576 2.428 16.96* 7.175*
BASIS 247 -3.8506 57.211 -0.922 0.899 80.10* 159.699*
02-03 FUTURES 25} -6.04E-04 8.339E-05 0149 0.230 80.85* 0.392
CASH 253 -6.09E-04 9.852E-05 0.101 0.757 52.83* 0.310
BASIS 253 1.0859 13.368 - 0.263 1.282 33.6.,* 109.726*
03-04 .·UTURES 252 2.3 I SE·03 2. I 66E·04 ·0.215 ·0.244 112.88* 1.477
CASH 252 2.324E-03 2.061 E-04 -0.347 0.135 91.61 * 5.177**
BASIS 252 0.7010 31.484 0.159 0.348 75.21 * 121.703*
04-05 FUTURES 253 4.590E·04 3.427E·04 ·2.693 27.306 6507.80 0.004
CASH 253 4.451 E-04 2.679E-04 -2.290 20.022 3262.61 17.465*
BASIS 253 -4.1866 66.822 -1.627 4.781 144.49* 148.207*
05-06 FUTURES 240 1.661 E-03 1.434E-04 -0.562 0.731 50.49* 0.057
CASH 240 1.673E-03 I. I 65E-04 - 0.696 0.866 51.12* 2.337
BASIS 240 -8.1629 70.736 -3.22 ·OA63 421.04* 92.343*
06-07 FUTURES 245 3.661 E-05 2.784E-02 -1.745 8.523 89.53* 0.015
CASH 245 3.493E·05 2.425E·02 - 1.599 7.569 78.19* 5.209
BASIS 245 -5.9869 67.568 -2.146 2.578 289.09* 119.587*
One Year FUTURES 250 -1.09E·03 2.370E·04 ·0.836 4.470 51. 63* 2.637
11 'h Sept CASH 250 -1.09E-03 2.469E-04 - 0.398 1.830 20.86* 5.404**
WOI(Pre) BASIS 250 -0.1248 66.732 -1.624 3.593 113.55* 179.981*
~ne Year FUTURES 255 1.279E-03 2.526E-04 ·0.769 2.865 25.33* 0.094
II 'h Sept CASH 255 1.260E·03 2.276E-04 ·0.832 2.825 29.74* 0.763
)0 I( Post)) BASIS 255 -3.9508 39.033 - 0.373 -0.759 156.05* 63.967*
Jne Year FUTURES 253 1.910E-03 2.572E-04 -0.659 1.550 40.48* 1.\45
lth l\lay, CASH 253 1.922E-03 2.445E-04 -0.863 2.748 32.07* 3.275***
!OO4(Pre) BASIS 253 -5.83E-02 42.150 -0.353 0.858 53.62* 145.059*
)ne Year FUTURES 252 2.640E-03 2.673E-04 0.848 10.158 568.19* 0.178 l7th .May, CASH 252 2.337E-03 2.036E-04 0.837 7.198 214.47* 1.\08
004(Post) BASIS 252 252 -6.7853 81.425 - 1.651 4.185 129.23* 68.195*
)ne Year FUTURES 249 1.43E·08 1.570E-03 ·0.566 3.620 73.63* 3.925
22 nd ~lay, CASH 249 I.32E·06 1.499E-09 -0.426 3.130 69.79* 3.569**
2006(Pre) BASIS 249 -0.1548 70.526 -I. 985 3.641 121.52* 186.981 *
One Year FUTURE 251 2.310E-07 2.38E·09 0.799 9.264 489.29* 0.159 ~2n{) :\Iay, CASH 251 2.137E-05 2.011 E·02 0.726 7.032 199.36* 1.020
W06(1'ost) BASIS 251 242 ·5.3486 79.566 - 1.214 3.8189 117 .45* 63.258*
177
Table 6.1 Descril}tive Statistics
*Significant at I % level of significance, ** Significant at 5% level of significance
and ***Significant at 10% level of significance.
Comovemcnt of two series is one of the pre-condition for the relatively speedier
price discovery in one market. Comovement of futures and cash market price series
implies that long run relationship exists between both the markets. 10hansens
cointegration has been applied and Table-6.4 discusses the cointegration results.
Table 6.2 Unit Root Test Results (Philips Perron)
Philips Perron Test Results Variables At Levels First Difference
With Drift With Drift and With Drift With Drift and
Trend Trend Full Period (Close to Close)
Futures 2.40 -3.27 -1370.28* -1307.36* Niftv 2.52 -2.98 -1241.67* -1182.50* Basis -570.68* -610.13*
2000-01 Futures -6.03 -9.87 -75.cJ2* -75.14*
Nifty -6.18 -9.94 -83.97* -84.21 * Basis -98.41 * -92.06*
2001-02 Futures -6.31 -6.05 -220.03* -215.84*
Nifty -6.65 - -6.31 -192.37* -88.19* Basis -54.34* -59.97*
2002-03 Futures -6.24 -6.31 -266.80* -264.19*
Nifty -6.74 - -6.88 -251.08* -248.85* Basis -119.10* -119.63*
2003-04 Futures -0.99 -8.08 -228.91 * -224.51 *
Nifty -0.94 -8.31 200.82* -197.04* Basis -116.34* -120.11*
2004-05 Futures -1.82 -7.77 -216.59* -207.72*
Nifty -UO -7.42 -199.57* -190.08* Basis -92.80* -116.22*
2005-06 Futures -0.12 -19.53** -178.56* -176.77*
Nifty -0.25 -17.85 -160.62 * -158.85* Basis -82.15* -85.53*
178
2006-07 Futures -0.96 -11.74** -199.69* -193.11*
Nifty -0.87 -10.99 -187.23* -181.55*
Basis -102.34* -109.69* One Year Pre 11th Sept, 2001
Futures -3.70 -15.35 -268.72* -269.02*
Nifty -3.67 -15.77 -241.91* -242.24*
Basis -108.59* -119.95* One Year p()st 11th Sept, 2001
Futures -1.39 -27.24* -230.24* -212.37* Nifty -1.60 -23.75* -223.04* -206.20* Basis - 108.59* -119.95*
One Year Pre 17th May, 2004
Futures -2.69 1.46 -250.05* -213.80* Nifty -2.65 1.41 -227.05* -193.79* Basis -83.27* -83.32*
One Year Post 17th May, 2004
Futures -4.06 -35.65* -199.11* -195.71* Nifty -2.83 -23.99* -94.03* -100.65* Basis -199.11 * -195.71*
One Year Pre 22"" MaL 2006 Futures -3.91 -28.35 -215.72* -221.02*
Nifty -3.77 -26.62 -204.51* -209.24* Basis -178.59* -185.95*
One Year Post 22nd May, 2006 Futures -4.70 -39.35 -302.72* -321.02*
Nifty -4.67 -38.62 -284.51 * -302.24* Basis -201.59* -211.95*
... ... . - .. * SignIfIcant at 5'70 Slgnlhcance level. ** SlgnIhcant at 10 % SignIficance level.
Table 6.3 Unit root test results (Augmented Dickey- Fuller test statistic)
Variable Augmented Significance level Optimal number ()f Nifty futures -2.85 0.18 7 Nifty Index -2.81 D.19 7
Nifty futures -13.30** 0.01 2 Nifty Index returns - 8.84** 0.01 6
** - Significant at I per cent level
The results of the unit root tests for Nifty futures and Nifty Index are given in
Table-6.3, which indicates that Nifty futures and Nifty Index arc not stationary at their
levels but their returns are stationary. From table-6.4 it is clear that both nIarkets have
179
stable long run relationship, though in the sh0l1 run they may be in the disequilibrium.
Presence of the cointegration bctween two price series implies that both the series are
integrated of onler I, which has already been shown with the help of unit root testing in
Table-6.2.
Presence of long run relationship implies that if both the price series contribute to
same nature of information the there may exist causality relationship between these two.
For this purpose Grange Causality testll has been applied. Table-6.6 discusses the results
of Granger causality. The results of Granger causality as presented in Table-6.6 are very
interesting. Bi-directional causality has been observed, which implies that both futures
and cash market contributes to the price movement in other series. In order to study the
extent of causality between both the markets V AR methodology has been applied, the
results of which have been attached in the appendix.
Table 6.4 Johansens Cointegration Test ResuIts<
Vector (r) A max A Trace
Full Period (Close to 0 71.30· 76.10· I 4.90 4.90
2000-01 0 49.70· 52.40-I 2.70 2.70
2001-02 0 29.70 33.00 1 3.30 3.30
2002-03 0 44.00· 48.50-I 4.50 4.50
2004-05 0 22.20· 22.90, 1 0.70 0.70
2005-06 0 40.60· 46.00-I 5.40 5.40
2006-07 0 39.80· 44.50· 1 3.50 4.80
31 The Granger Callsality tesl on the spot and futures index return has heell applied through a ncar-V AR approach.
180
One Year Pre II th Sept.,
2001
1 23.50, 26.60· 0 3.10 3.10
One Year Post 11 th Sept.,
2001 I 24.30, 31.20· 0 6.90 6.90
One Year Pre 17th May,
2004 1 22.00· 27.70· 0 5.70 5.70
One Year Post 17th May,
2004 I 20.80· 24.20· 0 3.50 3.50
One Year Pre 22nd May, 2006 I 25.60· 30.80· 0 8.70 8.50
One Year Post 22nd May,
2006 1 22.90· 26.60· 0 6.40 6.70
. .. .. * SlgIllhcant at 5% level of slgIllflcance.
c Critical values for the Johansens cointegration test have been taken from
Johansen S. and K. Juselius (1990).
The results of the cointegration tests for Nifty futures and Nifty Index are tabulated
below.
Table 6.5 Cointegration test results
Cointcgration Cointegrating vector -1.02
Engle Granger 5.72** p-valne 0.01
Optimal number of lags 4 ** - SIgnIficant at I per cent level
The above results indicate that Nifty futures and Index are cointegratcd of order I.
181
Table 6.6 Granger Causality Results
Dependent I Futures Cash Full Period (Close to Close)
Futures ---------- 10.00-Cash 17.04- ---------
2000-01 Futures ---- 13.80-
Cash 13.38- ----
2001-02 Futures ---- 11.00-
Cash 10.56' ----
2002-03 Futures ---- 13.28-
Cash 13.90- ----
2003-04 Futures ---- 25.50-
Cash 24.90' ----
2004-05 Futures ---- 37.78-
Cash 34.96- ----
2005-06 Futures ---- 20.7?'
Cash IS.IS- ----2006-07
Futures ---- 27.22-Cash 31.SI- ----
One Year Pre 11 th Sept.,
2001
Futures ---- 11.23-Cash II.OS- ----
One Year Post 11 th Sept.,
2001 Futures ---- 14.05*
Cash 13.S4* ----
One Year Pre 17th May,
2004 Futures ---- 29.45*
Cash 29.73* ----
One Year Post 17th May,
2004 Futures ---- 26.42*
Cash 25.41 * ----
IS2
One Year Pre 22",1 May,
2006 Futures ---- 32.45*
Cash 32.73* ----
One Year Post 22"" May,
2006 Futures ---- 29.81 *
Cash 29.99* ----. .. ... * Slgl1lt!cant at 1'70 level of slglllficance .
The results of the price discovery regression are tabulated below.
Table 6.7: Price discovery results (June 2000 - Dec 2006)
Coefficient Value t-statistic Significance
aor -0.0007 -1.26 0.21
au -0.2109* -2.22 0.03
PH -0.0732 -0.51 0.61
P2f 0.1496 1.06 0.29
30s -0.0006 -0.99 0.32
al s -0.0062 -0.06 0.95
Pis 0.0197 0.14 0.89
PZs 0.0938 0.65 0.52 . -* - Slgl1lt!cant at 5 per cent level
Table 6.8: Price discovery results (June 2000 - Dec 2003)
Coefficient Value t-statistic Significance
aor -0.0009 -1.12 0.26
aH -0.0549 -0.45 0.65
PH -0.3789 -1.16 0.25
P2f 0.4809 1.69 0.09
30s -0.0009 -1.05 0.29
al s 0.1604 1.22 0.22
Pis 0.4101 1.28 0.20
PZs -0.2894 -0.76 0.45
183
From the Table-6.7 above it is clear that for the entire period (June 2000 to
December 2006) there is no causality from either futures to spot or vice versa. Also, only
the futures market (and not the spot market) responds to a deviation from equilibrium.
From the Table-6.8 above it is clear that for the period (June 2000 to December
2003) there is no causality from either futures to spot or vice versa. Also, neither the
futures market nor the spot market responds to a deviation from equilibrium.
Table 6.9 Price discovery results (Jan 2004 - Dec 2006)
Coefficient Value t-statistic Signifkance
aUf -0.0008 -1.05 0.29
alf -0.4788** -3.65 0.01
IlH 0.4314* 1.96 0.05
Illf -0.4140* -2.19 0.03
aos -0.0005 -0.71 0.47
als -0.2838* -2.17 0.03
Ills -0.6324** -3.42 0.01
Ills 0.7140** 3.27 0.0 I
* Significant at 5 per cent level ** Significant at I per cent level
From the Table-6.9 above it is clear that for the period (January 2004 to
December 2006) there is causality from both futures to spot and vice versa. Also, both the
futures market and the spot market respond to a deviation from equilibrium.
Tables-6.2 to 6.9 present results of co-integration and Price discovery results
(equations 6.18, 6.19 and 6.20). Table-6.5 gives information flow from one market to
another. Engle and Granger methodology has been used to find out co- integration of
futures and cash market. Null hypothesis is that both the markets are independent (not co
integrated).
Tables-6.7, 6.8 and 6.9 present the results of pnce discovery. Excepting
coefficient af all other coefficients are found statistically insignificant even at 5 per cent
level. This indicates information gets reflected first in the futures market. From the
results it is very difficult to say how much time it takes to go to cash market. One of the
184
constraints of the data is that daily close values are used whereas the information might
get transmitted much fastcr. This particular aspect can be stated more authoritatively only
if high frequency data is used for this purpose. High frequency data is currently not
available for spot market Index in India; therefore they could not be employed in the
equation.
)<'igure- 6.3(a) Shock in futures market destabilized the cash market
Response of DlFl[LN[NIFTYll to a unit shock in DlFl[LN[N:\l FUTURES])
Figure-6.3(b) Shock in the cash market and its effect to the futures market
Response of DlFl[LN[NM FUTURES]] to a unit shock in DlFl[LN[NIFTY]) ~ . -"-~ _____ ' __ '_r~_~".~. ____ ... -- .. - '.-~~------"_51)(£-002
I
.-'-...L'-j-....l....L.L...LLL...L'-.L....LLL..'-.-JLL-'....J-'--'....J-'-"---,--'--L-l--'--.Ll-LLJ.--'-L.l....L'--1.....LLl....LLl.--'-,d,'B no'[ ·(1(12
V AR results for the aggregate period (i.e. 2000-2(06) clearly shows that both
markets affect each other up to 4 lags (see figure 6.3(a) and 6.3(b», which implies that
there is no preferable market for the traders and they cannot rely upon the price
movement of the futures market. In figure 6.3(a) shows that a unit shock in futures
market destabilized the cash market up to 4 lags and thereafter the cash market price
curve established. Similar observation can be made from a unit shock to price series in
the cash market and its effect to the futures market, as shown through figure 6.3(b). The
185
notable consideration is that cash market reacted instantaneously from very upward point
to a unit shock in the futures market whereas, reverse seems to be the case of shock to the
cash market and its reaction to the futures market.
However, when disaggregatc price series were evaluated then significant price
discovery behaviour has been found in few sub periods viz; in 2000-0 I futures market
\cad the cash market by 4 days (sec figure 6.6(a) and 6.6(b», in 2001-02 by 6 days (see
figure 6.7(a) and 6.7(b», in 2002-03 by 2 day (see figure 6.8(a) and 6.S(b», in 2003-04
hy I day (see figure 6.9(a) and 6.9(b)) and in 2004-05 hy II days (see figure 6.10(a) and
6.10(b», whereas in 2005-06 (see figure 6.II(a) and 6.II(b» there is no preferable
market available to the traders. These results are very significant from the trader's
viewpoint because 2001-02 and 2004-05 witnessed highest volatility in the capital
market. In 2001-02 stock markets crashed due to the terTorist attack on WTC (World
Trade Center) in America on 11 Ih Sept, 2001, in 2004-05 Indian economy observed Black
Monday on nIh May, 2004 when Indian markets had to be closed due to the ever highest
selling pressure because of unexpected election results and in 2005-06 Indian markets
tumbled on 22"" May, 2006 due to Global Meltdown because of huge sell-off in Chinese
market.
In order to eonfim1 the impact of these abnormalities in the market and to verify
whether during this period futures market was actually able to provide significant
information regarding the prospective price movements in the cash market, we studied
the causality relationship between the futures and cash market by taking sub periods as
one year pre abnormal event and one year post abnormal event.
Fig-6.4(a) One-Year Pre 11th September 2001
Response ofDIFl[LN[NIFTYll to a unit shock in DIFI[LN[NM FUTURESll
I .,.1...1 ..LI .-JILL I *~.-JI_..LI-'I-,-I ..LI -'-'--L-'-'---'-LL-'.I...JILLI -'.1-'--.1...1 -'.1-'--Ll.I-'L~"l I I I I I I I I I .11 SS9:(,[ 002
186
Response of DIFl[LN[NM FUTURESll to a unit shock in DIFl[LN[NIFTYll
~~. ~----------------------------------------------,
.,-'-1 -'-I ~ILIl--'-I-1I--'-I-1I--'---'------'--1 -,-I ~I--,--I --11--,--1 -,-I --,1--,--1 -,-I --,I_ILL I --,I~ILLI --,I~ILLI -,-I~ILLI -,-I ~I-,-I -,-1--,1_-,---,--,--1 -'-1-11--,---,-I--'I';~ll !aS11r 007
Fig·6.4(b) One· Year Post Illh September 2001
Response of DIFl[LN[NIFTYll to a unit shock in DIFI[LN[NM FUTURES]] --------------~--- .. ----- --.~--"-,. --;1.11£.1[-002 ,---------.---~----- ---<---,
\
1
~~:~~~: ~I ~I~~----------------------------------~! .. . I
~i -,-I --'.1-,--1 -,-I --'.I--"ILL' --'.I--!I,-'-I --'.1 ~LI ..'-1--"1-,--1 --,1-,--1 -,-I --'.'_ILLI --'.I--"ILLI --'.1-,1-,--1 ..'-1 -,1-,--1 ..LI --'.1_1LLI --,-I--"ILL1 ..LI ~.LI ..L1 -,1-,--1 ..LI -'-.,-1 "-"I 1, m" .. , U ') .~
Response of DIFI [LN[NM FUTURES II to a unit shock in DIFI [LN[NIFTY]) _ I • A-_-"'--____ ~~_~ ___ • ____________ _
l"~~
I --,-1-,-,--1-,-1-,1-,-1 +--,1--'--1 LI-1I_LI--,I--,--1 LI~LI ,-I J.I_ILLI-,-I~ILLI-,-I~ILLI ..L'~I--,--I -,-1--,1--,--1 -'-I--'I_ILL~'--~LL~LL-'---'I"l11J]o£'DII] . ~
Fig·6.S (a) One· Year Pre 17th May, 2004
Response of DIFI [LN[NIFTYII to a unit shock in DIFI [LN[NM FUTURESll -----_ •. _---
~~, ---~----------·-------~:1.'5715£_{l():1
, •• -,-1 --'.I-,---'--.\'_ILL--,-I--"ILLI --'.1_,--1 --,-1--'--"-...LLL...LLL-'-.LLI ...11--,---,-' -,-1...L-,--,-I-,I--,---,---,I-,-1 -,---,_-,---,--,--I -,-I --,1--,---,---,1 "J11 5115[ 011]
187
Responsc of D1FI [LN[NM FUTURES)] to a unit shock in DIFl[LN[NIFTY]J
i ~~I----------------------------------------------------------~I . . I
i
. .--l-' ~I~I ~l ~'~I ~I_ILLI ~I __ .L· ~'_'LL' --"'LLI -'.I..JILLI -'.I..JILL' -'.I..JI~' -,-I..JI~' -,-,-",~, l'-"'_'LL'-"..J'---"..J'LL' -"--.LL-'.I..JI~L U:?5f DO] o ~ ~
Fig-6.S (b) Onc-Year Post 17th May, 2004
Rcsponse ofDIFl[LN[NIFTYll to a unit shock in D1FI[LN[NM FUTURES)]
\' ..
··-----~~---·~1'.051Q[ 001
I " .' ~'.('!"'"=:,..' c.......,...... : "7 . , S::;. : '7'" , !' • I 1 I I
. It -"'LL I II -"'LLI --"'LLI -'.' _IL---~I_ILLI -'.'--.lol -"'~' -,-I -"'LL I -,-I -"ILL I -'.I-"ILLI -'.I-"ILL' ~I..JILLI ~I..JILL' -"t..JIL----"'~1 -,-I ..JILL~---'--.:I L;} .051 0£-002 ~ l' ~
Responsc of DIFI [LN[NM FUTURES]] to a unit shock in DIFl[LN[NIFTYll . ----- --- --------- -- .... - •.....
111I -{)87
.~
•• \-ll-"--. "LL'~ "_L.L"~ "_L'~ "_'Ll ''\', '.-"--...J.L-'...J'LL-'--"--. "Ll'~ 'LL-'-...LJ 'LL-,--" II_LI.L:.I' ..Jt--'--ll...LJ "..JLIJ. '-"--.ILc.I-'-J"",.Il2Jf.OO2
From Figure 6.4 and 6.5 it is clear that during one year prior to the II th September
attack on America, futures market could lead the cash market by I day but during one
year after the attack Indian futures market was leading the cash market by 2 days. Similar
evidence has been observed during 2004-05 when Indian capital market observed biggest
ever market crash on 17'h May 2004.
One year prior to 17'h May 2004, futures market was leading the cash market by
one day, whereas one year after the date of abnormality, futures market lead the cash
market by 2 days, which supports the evidences available in the literate, that if efficient
188
cost-of carry exists between futures and cash markets then futures market plays key role
to stahilize the cash market and traders prefer to take hedging positions through futures
market. Existence of cointegration relationship clearly indicates that cost-of-carry
relationship bctwcen both markets is efficient and further evidences from the periods of
abnormalities implies that when Indian cash market is volatile then futures market is
more preferahle for the traders to take hedging and arbitrage positions.
6.9 Summaries and Conclusion
Introduction of derivatives in the Indian capital market had been a very well
planned decision. Prior to introducing derivatives in the Indian capital market, its
prospective impacts on the market were thoroughly evaluated; L. C. Gupta Committee
Report and J. R. VemJa Committee Reports are one of the significant evidences in this
regard. After thorough review and serious debate on the issue the derivatives were
introduced in live phases viz. in the first phase index futures were introduced, followed
by index options, stock options. and Stock futures respectively and in the last interest rate
futures.
Shenbagaraman (2003), Raju and Karande (2003) and Bandivadekar and Ghosh
(2005) observed significant decline in the spot market volatility during the post futures
treading era. The current study provides significant support to the decline in volatility
hypothesis by evaluating the price discovery performance of Indian equity futures market
during the period of high volatility. The results of the study are bcnclieial for the traders
as well as the regulators. The above results assures the traders that in the event of high
fluctuations in the market they can rely upon the direction of the futures market because
it would provide them significant information regarding the prospective move in the cash
market. Thus the retail as well as Indian institutional traders can design their portfolio
and can take positions in the futures market to safeguard themselves from the t1uctuations
in the cash market. In addition, the regulators will in advance come to know regarding the
prospective price movement in the cash market and when they feel market ovclTcacting
to the information. they can take appropriate action in the interest of the common
investor. Moreover from the price movements in the futures market they can adjudge the
expected volatility in the cash market.
189
Thus on the basis of above observations, it can be concluded that Indian futures
market is an cfficient price discovery vehicle and it will certainly help the traders to take
hedging and arbitrage positions to secure maximum returns at minimum risk exposure. In
addition. the contribution of the futures market to minimize the volatility of the cash
market is an important implication of the efficient price discovery. Though futures
market has been found relatively efficient price discovery vehicle but investigation of the
behaviour of spread between the futures and cash market (i.c. Basis) will provide
significant information regarding the exact extent of price discovery of the Indian equity
futurcs market.
Figure 6.6 (a) Year 2000-01 Nifty Cash Index
Response ofDIFl[LN[NIFTYll to a unit shock in DIFl[LN[NM FUTURESll
Figure 6.6 (b) Year 2000-01 Nifty Future Index
Response of DIFl[LN[NM FUTURESll to a unit shock in DIF1[LN[NIFTY]] ------------,I'I])7'I:...{l()2
~~~.~~~~~------------------------------------------~
190
Figure 6.7 (a) Year 2001-()2 Nifty Cash Index
Response of DIF1[LN[NIFTYll to a unit shock in DIFl[LNINM FUTURES]]
Figure 6.7 (b) Year 2001-02 Nifty Future Index
Response of DIFI [LN[NM FUTURES II to a unit shock in DIFI [LN[NIFTY])
Figure 6.8 (a) Year 2002-03 Nifty Cash Index
Response ofDIFI[LN[NIFTY]) to a unit shock in DIF1[LN[NM FUTURES]) ~------------~--- 1026E-003
.. <- •
191
Figure 6.8 (b) Year 2002-03 Nifty Future Index
Response of DIFl[LN[Nl\I FUTURES]] to a unit shock in DIFl[LN[NIFTY]] ... ~~~~ .. ~.~ .. ~ _. - -~.~~~ .. ~----~ - ·--"-·~~---·--~-~-~.1492[.OO)
! ~------, ~------;I
u I I -'-".tj-"I-'-~~~I-'-I---JL.---.l---.Lli I I I I I I I LLLj,-,--,--,-,---,--,-I_,IL.L-'--'-"-' '-.;;1 19 J.4a}[ _0111 50
Figure 6.9 (a) Year 2003-04 Nifty Cash Index
Response of DIFl[LN[NIFTY]] to a unit shock in DIFI [LN[Nl\I FUTURES]]
•---,--1 LI -,-I~ILL-,--,~ILLI m'-'-'~--'-' -,-I-,---,-I-,-I-'-LI LI -,-I~I-,-I -,--,-1--,1-,-1 -'--'--'-LI LI -'-1~1--,---,--,-I-,-I-'--'--'--'-LL.LJLL,jI. 1.(12'8[-0112 I til ~
Figure 6.9(b) Year 2003-04 Nifty Future Index
Response of DIFl[LN[Nl\I FUTURES]] to a unit shock in DIFl[LN[NIFTY]]
: , .
192
Figure 6.10 (a) Year 2004-05 Nifty Cash Index
Rcsponse of DIFI[LN[NIFTYJj to a unit shock in DIF1[LN[NM FUTURESJj
-"-~-r'-
I .--'-,--'--"-, .LI """--"''---'-'--''_'L.L' ~-LI -,-I--,---,~-,-,--,--I .LI """--"'-L' -,-I ",',,-"''-'--'---'--'---'-'.-'-L' -,-I--'--LL----''--'---'-'--'--.LI --'I--"I--.;il, 4311£ 002 D SI)
Figure 6.IO(b) Year 2004-05 Nifty Future Index
Response of DIFI[LN[NM FUTURESll to a unit shock in DIFl[LN[NIFTYll -~-.~.-----,,-...... " ...... _ ... __ ._._-_._--_._ ..• -----.~-~-.------,
r-"-r-'~~~~~~~~~~~~------------------------~
r LI -'-'--'--.L..l~L..L--'--'--..L1 --"'-L' i\;' _. -L"--,--,I_IL.L..L-'-LI -,-I ..... I--,I'-'--'-'--'--.LI -,-I -,'--,--I -'-'-'-.--L-'--"--,---,--"LL..LI-.[J"l '.''':'802 8 U ~
Figurc 6.11 (a) Year 2005-06 Nifty Cash Index
Response of DIF 1 [LN[NIFTYll to a unit shock in DIFI [LN[NM FUTURESll ------,1.0941£.002
193
Figure 6.11 (b) Y car 2005-06Nifty Future Index
Response of D1Fl[LN[NM f'UTURES]l to a unit shock in D1Fl[LN[NIFTYll
1 • I 1 I ) ! I I
j 1
I I I I I L_J-,I~I'-LI -'-11-,--1 LI -"--,1-,--1 -'--J.I-"I_-,--,-,--I LI -,-I U--L l, 1mr 00' . 'ill
194