RESEARCH
includes research articles that
focus on the analysis and
resolution of managerial and
academic issues based on
analytical and empirical or
case research
Price Discovery Process and Volatility
Spillover in Spot and Futures Markets:
Evidences of Individual Stocks
T Mallikarjunappa and Afsal E M
Executive
Summary
This paper analyses information-based superiority of markets mainly with an objective
of exploring arbitrage opportunities. It attempts to determine the lead-lag relationship
between spot and futures markets in the Indian context by using high frequency price
data of twelve individual stocks, observed at one-minute interval. The study applies the
concept of co-integration and establishes the spot-futures relationship using Vector Error Correction Mechanism (VECM) represented by EGARCH framework. To study the
price discovery process in the two markets, five lags each of one-minute resolution for
nine individual stocks and four lags for the remaining three stocks are chosen.
The key results of the study are given below:
• There is a contemporaneous and bi-directional lead-lag relationship between the spot
and futures markets.
• A feedback mechanism of short life is functional between the two markets.
• Price discovery occurs in both the markets simultaneously.
• There exists short-term disequilibrium that could be corrected in the next period.
• Volatility spillover from spot market to futures market is present in such a way that
a decrease in spot volatility leads to a decrease in futures volatility.
• Volatility shocks are asymmetric and persistent in both the markets.
• Spillover from futures market to spot market is not significant.
• Neither spot nor futures assume a considerable leading role and neither of the markets is supreme in price discovery.
• In the case of 33.33 per cent of spot values and 33.33 per cent of futures values, there
exists short-term disequilibrium that could be corrected in the next period by decreasing the prices.
KEY WORDS
Lead-Lag Relationship
Spot Market
Futures Market
VECM
EGARCH
Volatility Spillover
• Spot market volatility spills over to futures market in most of the cases (66.66 %) and
a decrease in spot volatility brings about a decrease in futures volatility in 50 per cent
of the cases.
• Spillover effect from futures to spot market is present and significant in 91.66 per
cent of stocks and is more than the spillover effect from spot to futures (50% valid
cases).
• The markets are highly integrated.
• Asymmetric behaviour of volatility shocks is mixed in both the markets. Asymmetric
volatility is detected in 50 per cent of the cases of spot market and 58.33 per cent cases
of futures market.
• Stocks exhibiting asymmetric volatility show more sensitivity to negative shocks.
• There are no cases of market becoming more volatile in response to good news.
VIKALPA • VOLUME 35 • NO 2 • APRIL - JUNE 2010
49
F
utures market is expected to serve as a price discovery vehicle for investors in spot market. As
Fleming, Ostdiek and Whaley (1996) suggested,
the trading cost advantage of futures market makes it
more responsive to new information than other markets.
As a result, prices are first updated in the futures market, which thus serves as a price discovery vehicle for
investors. There are other explanations also for one market leading the other (Infrequent trading hypothesis of
Tan and Lim, 2001; liquidity factor identified by Daigler,
1990, etc.). In short, a lead-lag relationship would be
eventually established between spot and derivatives
markets. The success of a specific futures contract in
providing price risk protection, however, is dependent
on the ability of a potential hedger to accurately anticipate the future relationship between cash and futures
prices. Attempts to quantify and forecast futures-cash
price relationships have received considerable attention
in the futures market literature.
Karmakar (2009) studied the Indian market, using daily
data of S&P CNX Nifty and Nifty futures and found that
Nifty futures dominate the cash market in price discovery process. He also found that although persistent volatility spills over from one market to another market
bi-directionally, past innovations originating in the futures market have unidirectional significant influence
on the present volatility of spot market. Therefore, he
concludes that Nifty futures is informationally more efficient than the underlying cash market. However, there
are reported evidences to support spot market’s dominance to discover prices (Ching-Chung et al., 2002 and
Frino, Walter and West, 2000)), and no significant leadlag relationship between the markets (Grandson,
Fernandez and Muoz, 1998 and Abdul, Khairuddin and
Obiyathulla 1999). Wang and Wang (2001), in a study
on the British, German, French, and Canadian currencies against the US dollar, find a bi-directional price discovery in both markets.
From an empirical perspective, a substantial academic
and professional literature explores the dynamics of
stock index and index futures prices in developed economies with the aim of determining which market is dominant. The methodologies of these studies vary widely,
but the major finding is that the dominant influence runs
from the futures market to the cash and weaker effects
(though still measurable) occur in the reverse direction
(Joel, 2003). Chan (1992), using intra-day data, reports a
strong evidence to show that the futures leads the cash
index and a weak evidence that the cash index leads the
futures. He concludes that the futures market is the main
source of market-wide information. Frino, Walter and
West (2000) document a strengthening in the lead of
stock index futures returns over stock index returns
around macroeconomic information releases. They also
document evidence of a strengthening in feedback from
the equities market to the futures market and weakening in the lead of the futures market around major stockspecific information releases. They argue that their
findings are consistent with the hypothesis that investors with better market-wide information prefer to trade
in stock index futures while investors with stock-specific information prefer to trade in underlying stocks.
Tse (2006) examines the lead-lag relationship between
the spot index and futures price of the Nikkei Stock Average. Using daily data, he found that lagged changes
in the futures price affect the short-term adjustment in
the spot index, but not vice versa.
Mukherjee and Mishra (2006) use intra-day data for Nifty
and five underlying Nifty stocks for the period AprilSeptember 2004 to investigate the possible lead-lag relationship, both in terms of return and volatility, among
the Nifty spot index and index futures market in India.
Their results suggest that though there is a strong contemporaneous and bi-directional relationship among the
spot and futures market in India, the spot market has
been found to play comparatively stronger leading role
in disseminating information available to the market.
They have got almost the same results even for some
underlying NIFTY stocks. They conclude that the informational efficiency of the Indian cash market has really
been increased due to the onset of derivative trading.
Their results on the volatility spillover among the spot
and futures market in India reveal that there is an interdependence (in both direction) and therefore a symmetric spillover among the stock return volatility in the
Indian spot and futures market, though the spillover
from the spot to the futures market is found to be little
stronger than the same in the opposite direction. We find
that the results are mixed for both the foreign and the
Indian market. In the light of mixed results that are more
market-specific, the issue of lead-lag relation continues
to be a debatable one among academic and practical circles.
50
In this paper, we attempt to determine the lead-lag relationship between spot and futures markets in the Indian
PRICE DISCOVERY PROCESS AND VOLATILITY SPILLOVER IN SPOT AND FUTURES MARKETS
context. As an emerging economy, Indian market attracts
attention of both investors and researchers alike. However, most of the previous studies on Indian market are
based on daily price data. Given a fully automated,
screen-based trading system on National Stock Exchange
of India Limited (NSE), which supports an anonymous
order-driven market, trading, release of information, and
its transmission happen instantaneously. The frequency
is much more in the case of spot market where on an
average three million transactions take place in a day.
This fact limits the utility of daily data to determine leadlag relationship between spot and derivatives markets.
Unlike most of the other Indian studies, the present
study uses tick-by-tick price data of individual stocks
that makes it a distinct one. It uses relatively more
number of futures on individual stocks taken at high
frequency settings than any other Indian study. The
present study uses high frequency price data of twelve
individual stocks, observed at one-minute interval. In
addition, when the data for the two markets are modelled through time series, problems of auto correlation,
stationarity, heteroscedasticity and co-integration are to
be recognized and accounted for. To do this, we use
appropriate econometric tools balancing these features
and reducing the error to a minimum level. Finding the
data properties and following the best practices among
the researchers, we use the idea of co-integration and
model the spot-futures relationship using Johansen’s
Vector Error Correction Mechanism (VECM) represented by Nelson’s EGARCH framework. Thus, the
present work becomes a value addition to the derivatives literature as well as market insights.
ECONOMETRIC METHODOLOGY
Given the nature of the problem and the quantum of
data, we first study the data properties from an econometric perspective and find that co-integration and error correction models are required to establish the
equilibrium relationship between the markets. Further,
to quantify the short-run relationship and to study
volatility spillover, we use the VECM represented by
EGARCH framework. A brief account of the methodology follows.
Unit Root Test
The regression analysis would yield efficient and time
invariant estimates provided that the variables are stationary over time. However, many financial and macroVIKALPA • VOLUME 35 • NO 2 • APRIL - JUNE 2010
economic time series behave like random walks. We first
test whether or not the spot and futures price series are
co-integrated. The concept of co-integration becomes
relevant when the time series being analysed are nonstationary. In particular, two time series χt and Yt are
both integrated of order one, denoted as I(1), if they are
both non-stationary in levels but their first differences
are stationary. Then, χt and Yt are co-integrated if there
exists a linear combination zt = Yt — Axt, which is stationary, denoted as I(0). Therefore, before analysing cointegration between prices of each symbol of the sample
data, we first check if the two price series for each stock
is I(1). In order to check for the presence of a unit root in
the series, we use Dickey-Fuller test. Table 1 shows that
the spot and futures price series of all the symbols are
non-stationary and they attain stationarity only after
differencing. It is important to establish the number of
unit roots that a series contains while testing for co-integration. For two non-stationary series to be co-integrated, they must be integrated of the same order. For
each series, the test indicates the presence of one unit
root; each price series may therefore be regarded as difference stationary. Given that each stock’s spot and futures prices are integrated of the same order, (1),
co-integration techniques may be used to determine the
existence of a stable long-run relationship between the
price pairs. Also, as reported in the Table, we check for
the presence of auto correlation in the spot and futures
price series and find significant auto correlation effects
for all the price series. It is tested using Ljung-Box (LB)
statistics.
Co-integration and Dynamic Effect between
Spot and Futures Prices
A regression containing non-stationary variables, which
can be made stationary only by appropriate differencing,
generally leads to the problem of a spurious regression.
If spot and futures prices are both non-stationary and
require first differencing to render each series stationary, then, in general most linear combinations of the two
series will also be non-stationary. A co-integrating vector may, however, exist that makes a specific linear combination of the two series stationary (McKenzie and Holt,
2002). Previous research has attempted to circumvent
the stationarity problem by differencing the series so that
the new series would be stationary (Hansen and
Hodrick, 1980; Hakkio, 1981; Baillie, Liens and McMahon
1983). Following this idea, we employ first log differ-
51
ence, defined as Rx = ln xt — ln xt–1, with χt taking the
value of spot/futures price at time t.
Subjecting the spot and futures price series individually
to unit root analysis, we find that they are I(1); that is,
they contain a unit root. However, despite being individually non-stationary, a linear combination of two or
more time series can be stationary. Then one can say
that the variables are co-integrated. In econometric
terms, two variables will be co-integrated if they have a
long-term or equilibrium relationship between them
(Gujarati, 2005). Though the co-integrated variables
share a long-term or equilibrium relationship, in the
short-run there may be disequilibrium. Therefore, one
can treat the error term in the regression model as the
“equilibrium error” and this can be used to tie the shortrun behaviour of the dependent variable to its long-run
value. The error correction mechanism (ECM) first used
by Sargan (1984) and later popularized by Engle and
Granger (1987) corrects for disequilibrium. An important theorem, known as the Granger representation theorem, states that if two variables X and Y are co-integrated,
then the relationship between the two can be expressed
as ECM (Gujarati, 2005).
We apply the Johansen (1988) model, which was expanded by Johansen and Juselius (1990) and Johansen
(1991). This method features the maximum likelihood
procedure, facilitates treatment of multivariate analysis, and is considered to be powerful and efficient. The
causal relationship between spot and futures prices is
investigated by estimating the following VECM
(Johansen, (1988)). In this method, a p th order
autoregressive process, xt = α 1 xt −1 + α 2 xt −2 + .... + α p xt − p + ε t
is rewritten as
. . . (1)
where, ∆ is the first-difference lag operator, χt is a (n x
1) vector of I(1) time-series variables, εt is a zero mean
n-dimensional white noise vector, Γ are n x n matrices
of parameters, and Π is an n x n matrix of parameters
whose rank is equal to the number of independent cointegrating relations.
The Johansen procedure estimates equation (1) subject
to the hypothesis that Π has a reduced rank ‘r’ less than
the number of variables used. This hypothesis can be
written as H(r) = αβ′. The matrices, α and β′ are of di-
52
mension n X r, α depicts the speed of adjustment, and β′
represents the co-integrating vectors. Johansen and
Juselius (1990) show that, under certain circumstances,
the reduced rank condition implies that the processes,
∆ χt and β′ χt are stationary even though χt itself is nonstationary. The stationary relations β′ χt are referred to
as co-integrating relations (Kim, 1998).
Johansen (1988) suggests two test statistics to determine
the co-integration rank. The first is the trace statistic,
which is the relevant test statistic for the null hypothesis: r ≤ r0 against the alternative r ≥ r0 + 1. The second
test statistic is the maximum eigen value test known as
λ max with the alternative r = r0 + 1.
They are defined as:
. . . (2)
and ,
. . . (3)
with T being the number of usable observations and λ t
being the estimated value of the characteristic root (Eigen
value) obtained from the estimated ∏ matrix. In the
present study, the number of variables (k) is two, corresponding to the spot and futures price series. Both
λ trace (r) and λ max (r,r + 1) statistics follow non-standard
distributions. Their critical values are provided in
Johansen and Juselius (1990). The Johansen co-integration model has several variations to accommodate specific characteristics of time series. The model type used
in this paper is the one with no deterministic terms. We
determine the number of lags in the model by using the
multivariate version of the Schwarz Bayesian criterion
(Schwarz(1978)).
Test of Lead-Lag Relationship:
An Application of EGARCH
Lead-lag relationship is based on the hypothesis that
changes in one market (either spot or futures) influences
the other. This hypothesis can now be tested by using a
technique developed by Granger (1969). Although the
VECM outlined above provides a useful means of testing for short-run market efficiency and unbiasedness,
the approach is limiting in several ways. First, the model
does not address the possibility that volatility may be
time varying in nature. Secondly, the VECM framework,
at least in its current form, can only account for linear
price dynamics in the conditional mean of price changes.
PRICE DISCOVERY PROCESS AND VOLATILITY SPILLOVER IN SPOT AND FUTURES MARKETS
Finally, VECM estimation that relies on ordinary least
squares (OLS) assumes that the distribution of price
changes is characterized by a constant variance. GARCH
effects characterized by volatility clustering imply that
models that allow for time variation in the conditional
second moment may better represent the data-generating process. As noted by Gao and Wang (1999), omitting GARCH effects in estimation may result in incorrect
inferences regarding the existence of an autoregressive
process in the conditional mean of price changes. In the
present case, modelling spot/futures price changes by
using a VECM without accounting for identified
GARCH effects could lead to spurious conclusions.
In light of the above discussion, ARCH/GARCH models are used to test lead-lag relationship, volatility spillover, and short-run market efficiency. As we are interested in knowing how volatility responds to good and bad
news, we apply EGARCH specification popularized by
Nelson (1991). To test the causality between spot and
futures prices, the following expanded VECM may be
estimated using EGARCH representation for each symbol.
. . . (4)
error correction coefficients δs+δf≠ 0, ensures that
lagged disequilibrium ξ t-1, occurs in at least one of the
equations (Patterson, 2002). The specification of ε i,t allows for the possibility that they are serially correlated
and hence the use of ARCH/GARCH class of models.
Moreover, the causality models are very sensitive to the
lag length used in the model. The number of lags used
in (4) and (5) are determined using the Schwarz Information Criterion (SIC) because of its superiority over
other criterions as reported in Reimers (1992).
Equations (6) and (7) are the conditional variance equations for spot and futures values respectively and reflect the EGARCH (1,1) representations of the variances
of ε s,t and ε f,t. ln(h s,t) and ln(h f,t) are the conditional
(time varying) variances of spot and futures values. Conditional on Ωt−1, ε s,t and ε f,t are assumed to be normally
distributed with zero mean and variance of (h s,t) and
(h f,t). The persistence of volatility is measured by φs for
spot values and φf for futures values. The coefficients
γ s and γ f measure the ARCH effects or spillover effects and θ s and θ f capture the asymmetric behaviour.
The lag truncation length (p and q) is determined using
Likelihood Ratio (LR) tests and we choose EGARCH
(1,1).
DATA
. . . (5)
. . . (6)
(7)
In equations (4) and (5), ∆St and ∆ft are the first log difference of spot and futures price, ξ s,t-1 and ξ f,t-1 are the
error correction terms obtained from lagged residuals
of co-integrating regression of first log difference of spot
on futures price and first log difference of futures on
spot prices respectively. The error correction terms capture the dynamic linkages between spot price and futures price changes. ε s,t and ε f,t are the stochastic error
terms and α, β and δ are the coefficients to be estimated.
Ωt-1 is the information set at time, t-1. A condition on the
VIKALPA • VOLUME 35 • NO 2 • APRIL - JUNE 2010
The data comprises intraday minute-by-minute spot and
futures prices for a period from July 3, 2006 to December 28, 2006. The high frequency historical data is provided by NSE. NSE observes and records each and every
trade taking place in fast intervals. As we take the most
eligible minute-wise data, a time length of six months is
manageable and appropriate for addressing the question of price discovery. Also the data belongs to a normal period when the market did not experience any
extraordinary events either politically or economically.
This is a period of flourishing and buoyant stock market with good liquidity. For each derivatives contract,
there are three expiration cycles. But only the near month
futures contract is used in this study because others are
not very liquid. In order to standardize the length of
interval and to overcome the problem of non-trading in
futures market, we limit the number of stocks based on
certain criteria stated below.
• The stock should be traded on both the segments
throughout the sample period.
53
• There should be at least one observation of price in
every one-minute interval so that the trading frequency would be high in both the markets.
• Non-trading probability of the stock should be closest to zero.
Adhering to these criteria, we consider twelve most liquid individual stock contracts for further analysis. The
trading day was divided into 325 one-minute intervals,
starting from 10.00 a.m. and ending at 3.25 p.m. omitting the first and the last five minutes of transaction to
remove any perceived abnormalities. We use the price
recorded first after each time interval. The futures price,
Fit on day i at time t (t corresponding to each of the 325
time slots) is defined as the first transaction price recorded at or after t. Thus, synchronous pairs of transaction prices for spot and futures (Pit, Fit) for each trading
day i are first formed and then combined to form a comprehensive data sheet for processing.
Trading Frequency and Non-trading Probability
Table 2 records summary statistics of futures and spot
price data. Trading frequency is the average number of
trades in the one-minute interval. Non-trading probability is the proportion of intervals in which no trade takes
place. Futures frequency is to be interpreted as the
number of contracts traded per minute and one contract
comprises a prescribed number of shares as per the lot
size assigned to each contract symbol. It is clear that all
the stocks are heavily and frequently traded in the spot
as well as futures segments.
CO-INTEGRATION
Maximal Eigen value and trace test statistics presented
in Table 3 indicate that the null hypothesis of no co-integration when r=0, is rejected at the 1 per cent level and
it is not rejected when r=1 for each symbol of twelve
stocks. This means that there exists one co-integrating
vector for each symbol. Overall, Johansen’s test results
support the hypothesis that spot and futures prices for
each symbol are co-integrated and there exists at most
one co-integrating relationship between spot and futures
prices. In other words, spot and futures prices share common long-run information.
RESEARCH FINDINGS AND DISCUSSIONS
We now present the results of lead-lag relationship and
volatility spillover between spot and futures markets
54
using VECM-EGARCH model. Table 4 offers the test
results of spot to futures of twelve symbols examined.
These are the estimates of equations (4) and (6). Similarly the estimates of equations (5) and (7) giving the
test results of futures to spot prices of all the symbols
are presented in Table 5.
First, we consider the price discovery process in the two
markets. As reported earlier, we choose five lags each
of one-minute resolution for nine individual stocks,
namely, Century Textiles, India Cements, Infosys, IVR
Infra, Reliance Capital, SBI, Sterlite, Tata Steel, and
Wipro; and four lags for the remaining three stocks,
namely, Hindalco, PunjLloyd, and RIL. For convenience
of analysis, we club the results of symbols showing similar behaviour and thus present the analysis in three
groups.
The results indicate that three individual stocks, namely,
Century Textiles, IVR Infra, and SBI spot market values
depend on the lagged futures values up to five minutes
and the serial dependence is also significant up to five
minutes in these cases. On the other hand, the futures
market values lag spot values up to five minutes for
Century Textiles and SBI, and up to two minutes for IVR
Infra. This leads us to infer that neither spot nor futures
assume a considerable leading role and neither of the
markets is supreme in price discovery. The error correction term (ECT) is found statistically different from zero
and negative for the spot to futures and statistically zero
for the futures to spot in the case of Century Textiles.
This informs that in the event of spot market being above
its long-run relationship with futures, it will decrease to
restore the equilibrium level whereas futures adjusts to
changes in spot in the same period. One can draw the
conclusion about the relative efficiency of futures market in this particular stock during the study period. But
other two stocks report just the opposite, with zero for
the spot to futures and significant negative value for the
futures to spot. This further strengthens our conclusion
of contemporary and bi-directional lead-lag relationship
between the spot and futures markets with regard to
the three stocks.
There exist significant volatility spillover effects from
spot market to futures market in the case of Century
Textiles and SBI, at one per cent level. The spillover coefficients are negative, suggesting a decrease in futures
volatility for a given decrease in spot volatility. The vola-
PRICE DISCOVERY PROCESS AND VOLATILITY SPILLOVER IN SPOT AND FUTURES MARKETS
tility spillover from futures market to spot market is
more than that of spot to futures market except in the
case of Century Textiles. Also, the volatility spillovers
are asymmetric and ‘bad news’ effect is more than ‘good
news’ effect for spot to futures of Century Textiles and
SBI, and for futures to spot values of all the three stocks.
For the three stocks, spot market volatility is persistent
over time. Futures market volatility is found unrelenting at the chosen level of significance for Century Textiles.
The estimates of two other stocks, Punj Lloyd and Reliance Capital, reveal that spot values lag futures values
up to four minutes and the futures values lag spot market up to one minute for Punj Lloyd and five minutes
for Reliance Capital. Significant serial dependence is also
reported for spot as well as futures up to four lags for
spot, and one and five lags for futures of Punj Lloyd
and Reliance Capital respectively. It can be concluded
that Punj Lloyd futures market seems to behave more
efficiently reducing the degree of serial dependence but
not the spot market. The coefficient of ECT is significant
and negative at ten per cent and five per cent levels for
spot and futures respectively in this case. This means
that both the markets are out of equilibrium and will
fall to achieve the equilibrium in the next period. A
higher value of ECT for futures reflects its slowness to
adjust to the other market (i.e., spot) and thus invalidates its perceived relative efficiency. Even in the case
of Reliance Capital, error correction term is significant
and negative, suggesting that equilibrium will be attained in both the markets when any of them is above
its long-run relationship with the other. But the information flow is found in both the ways and that information sustains for a relatively long time, not making
any of the markets leading the other. The logical conclusion will be in line with the earlier cases that price
discovery is not achieved in any of the markets and spot
and futures markets almost move in tandem.
For the above two stocks, volatility spills over from one
market to another, offering a reduction of volatility for
a given decrease in volatility in the other market. This is
clear from significant negative coefficients for the ARCH
term in the model. Significant spillover from one market to the other is a sign of high integration between
spot and futures markets. Spillover effect from spot to
futures is more than that of futures to spot in the case of
Punj Lloyd, whereas the spillover from futures to spot
VIKALPA • VOLUME 35 • NO 2 • APRIL - JUNE 2010
is higher than the other for Reliance Capital. The asymmetric volatility spillover coefficients show that spillover
effects are asymmetric for futures of both stocks and for
spot value of Reliance Capital. The negative values again
imply that market volatility is more sensitive to negative innovations than to positive ones. The degree of
volatility persistence is found significant in both the
markets.
The model parameters of the remaining seven stocks
present different behaviour. The spot values of Hindalco
and RIL depend on the lagged values of futures up to
two minutes and India Cements up to one lag of futures.
In the case of Infosys, Sterlite, Tata Steel, and Wipro, the
spot’s dependence on lagged futures is absolutely nil.
On the other hand, in the case of five stocks (Hindalco,
India Cements, Infosys, Sterlite, and Tata Steel), the
lagged spot values do not influence the futures values
at any of the select lags. Two exceptions are RIL and
Wipro futures which lag spot by one minute and five
minutes respectively. It is worth noting that serial dependence of spot prices of these stocks is also weak as
observed by significant values up to three lags for
Hindalco, two lags for RIL and Sterlite, one lag for Tata
Steel and India Cements, and zero lag for Infosys and
Wipro. And in the case of futures market, no serial dependence is observed in the case of four stocks namely
Hindalco, India Cements, Sterlite, and Tata Steel. Infosys
and RIL report serial dependence up to one lag and
Wipro futures up to five lags. The reported serial correlation is generally found steadily decreasing over time.
From this, we understand that both the markets are information-efficient and it is more correct for futures
market. In such a situation, the market reacts very
promptly to new information so that the current price
reflects all the available information. The implication of
this phenomenon would be lack of arbitrage opportunities. Since our results show that one market (spot or futures) fails to supply information to the other, we may
have to conclude that neither of the markets leads or
lags the other.
The coefficient of error correction term that measures
the speed of adjustments in the markets is not statistically different from zero for the spot values of five stocks,
Hindalco, Infosys, Sterlite, Tata Steel, and Wipro; and
for the futures values of India Cements, Infosys, RIL,
Sterlite, and Wipro. This suggests that one market adjusts to changes in the other in the same period to main-
55
tain short-run equilibrium. Hindalco and Tata Steel futures show significant positive value for ECT that suggests that futures market is slow to adjust to spot to
restore equilibrium level. This also supports the relative advantage of spot market in the case of these two
stocks as their spot values achieve equilibrium instantly.
India Cements and RIL spot values report significant
negative values for error correction term at one per cent
level, but their futures values have statistically zero ECT.
This finding supports an argument that futures market
behaves more efficiently in these cases. However,
Infosys, Sterlite, and Wipro are found to show a fast
equilibrium process in both the markets and this may
have contributed to non-existence of lead-lag relationship. Though both the markets seemingly move very
closely, the flow of information from one market to other
(especially from futures to spot as reported by a fast
equilibrium process) is extremely fast leaving little scope
for arbitrage opportunities. The ability of both the markets to discover prices is evidently identical and therefore shares a weak lead-lag relationship between the spot
and futures markets. The overall finding is in line with
that of the other stocks examined.
Examining the volatility behaviour, it is found that the
spot to futures market spillover effect is present in four
stocks, namely, Hindalco, RIL, Tata Steel, and Wipro and
the spillover effect is absent in India Cements, Infosys,
and Sterlite. The coefficients of volatility spillover from
futures to spot market are statistically significant at one
per cent level for Hindalco, at five per cent level for Tata
Steel and Wipro, and at ten per cent level for India Cements, RIL, and Sterlite. Hindalco and Wipro show positive values for volatility spillover in spot as well as
futures and this implies that volatility of the two markets is not necessarily in the same direction. The spillover
effect from futures to spot is more than that of spot to
futures in the case of Hindalco, India Cements, and
Sterlite while RIL, Tata Steel, and Wipro show more
spillover from spot to futures. Notably, the coefficients
of spillovers for RIL and Tata Steel are of negative sign
for both spot and futures, and because of this, one can
predict a decrease in volatility in one market for a given
fall in volatility in other market for these two stocks. It
is a clear evidence of high integration between spot and
futures markets. Moreover, it is to be noted that the two
stocks, RIL and Tata Steel, are the most liquid stocks in
both spot and futures segments. We can now conclude
56
that both the markets interact closely in the case of heavily traded stocks and the hedgers in fractions of minute
may have economically exploited this interaction so that
an observable lead-lag is absent. But given the relative
low intraday volume in the futures market , this conclusion generally may not hold good.
Examining the asymmetric volatility behaviour, we find
that it is mixed. Spot and futures of Hindalco, Infosys,
Sterlite, and Wipro show symmetric volatility behaviour.
It is asymmetric and more sensitive to negative shocks
as identified by significant negative values for the leverage coefficients in the case of spot and futures values
of two stocks, India Cements and RIL. In case of Tata
Steel, the spot value is asymmetric whereas its futures
value shows symmetric volatility. However, in no case,
do we find market becoming more volatile in response
to good news, with significant positive asymmetric coefficients. Finally, spot volatility is persistent over time
for the stocks except India Cements and Infosys; but significant volatility persistence in futures market is present
in India Cements, Infosys, RIL, Tata Steel, and Wipro.
One may interpret the presence of persistence of volatility relaxing our earlier argument of relatively better
information efficiency of these stocks, but we understand
that the persistence may be due to similar contents in
various information releases as one cannot expect an all
changing information set on a normal trading day.
CONCLUSIONS
We find no significant leading or lagging effects in either spot or futures markets with respect to top twelve
individual stocks. There exists a contemporaneous and
bi-directional lead-lag relationship between the spot and
the futures markets. As against the widely accepted
hypothesis of futures market, with its cost and hedging
advantages, leading the spot market, Indian futures
market fails to supply early information to spot market.
Our results are similar to those reported by Grandson,
Fernandez and Muoz, (1998), Abdul, Khairuddin and
Obiyathulla,(1999), and Wang and Wang (2001) who
found no significant lead-lag relationship between the
markets. The findings almost support Mukherjee and
Mishra (2006), who report contemporaneous and bi-directional relationship between the two markets. However, they have found that the spot market plays
comparatively stronger leading role in disseminating
information available to the market. Our results support
PRICE DISCOVERY PROCESS AND VOLATILITY SPILLOVER IN SPOT AND FUTURES MARKETS
this only in case of two stocks and not in all other cases.
For majority of the stocks, our results also contradict
those of Chan (1992), Tse (2006), Frino, Walter and West
(2000), and Karmakar (2009), who found that Index futures market is more efficient than the underlying Index cash market. Although our results indicate that both
futures and spot markets are information-efficient, it is
more correct for futures market than for spot market.
This is because the notion that some of the spot values
depend on lagged futures value and vice versa is true
only in exceptional cases, which lends some support to
the findings of Karmakar (2009). In two cases, our results are similar to those of Frino, Walter and West (2000)
who found that, in stock-specific investigations, there is
strengthening of leading role of spot market and weakening role of futures market. The results can be interpreted in two ways: first, futures market is not capable
of capturing any piece of information inaccessible to spot
market. This does not discount the information efficiency
of the futures market, but instead conveys that both the
markets are identical in the process of information assimilation and price discovery. Secondly, it describes
pricing efficiency of the markets, as correctly priced securities leave little scope for arbitragers. On the other
hand, the short-term disequilibrium is corrected simultaneously or in the very next period. The presence of
substantial volatility spillover between the markets suggests high level of market integration and hence is a further proof of our conclusion that both the markets share
similar information capacity. We take care to caution that
the stocks examined in our study are highly liquid with
high trading frequency even on intra-day basis and
therefore, more studies are required for Indian markets
in other data settings like daily data or less frequency
than one-minute interval examined in this study.
Table 1: Dickey- Fuller Test for Unit Root
Symbol
Century Tex
Hindalco
India Cements
Infosys
IVRCL Infra
Punj Lloyd
Reliance Cap
Coefficients$
Futures Price
Spot Price
Futures Log
Difference
Spot Log
Difference
Auto Corre. #
Value &
LB Stat.
B1
3.635
(-0.41)
3.036
(-0.353)
0.006
(-2.413)
0.006
(-2.441)
Spot (AR16)
0.53
(1031.09)
δ
-0.001
(-0.049)
0
(-0.02)
-1.049*
(-10.650)
-1.031*
(-10.457)
Futures (AR16)
0.53
(1033.)
B1
14.501
(-2.301)
14.846
(-2.337)
0
(-0.009)
0
(-0.049)
Spot (AR16)
0.18
(667.63)
δ
-0.083
(-2.304)
-0.086
(-2.342)
-0.960*
(-10.567)
-0.926*
(-10.214)
Futures (AR16)
0.21
(643.97)
B1
10.935
(-2.364)
10.583
(-2.326)
0.003
(-1.188)
0.003
(-1.212)
Spot (AR16)
0.55
(1077.90)
δ
-0.05
(-2.248)
-0.048
(-2.207)
-0.913*
(-10.062)
-0.898*
(-9.912)
Futures (AR16)
0.55
(1082.71)
β1
13.434
(0.645)
15.149
(0.674)
0.003
(2.240)
0.003
(2.215)
Spot (AR16)
0.74
(1024.91)
δ
-0.004
(-0.409)
-0.005
(-0.460)
-0.984*
(-10.590)
-0.956*
(-10.258)
Futures (AR16)
0.74
(1025.71)
β1
1.98
(-0.648)
2.06
(-0.655)
0.003
(-1.207)
0.003
(-1.178)
Spot (AR16)
0.62
(1454.29)
δ
-0.003
(-0.268)
-0.003
(-0.286)
-0.781*
(-8.785)
-0.779*
(-8.760)
Futures (AR16)
0.62
(1457.59)
β1
7.919
(-0.539)
7.22
(-0.5)
0.002
(-0.792)
0.002
(-0.814)
Spot (AR16)
0.09
(674.55)
δ
-0.007
(-0.369)
-0.006
(-0.323)
-0.837*
(-8.601)
-0.837*
(-8.600)
Futures (AR16)
0.09
(673.78)
β1
11.921
(-0.87)
11.045
(-0.828)
0.003
(-0.767)
0.003
(-0.788)
Spot (AR16)
0.55
(1290.40)
δ
-0.02
(-0.785)
-0.019
(-0.737)
-1.033*
(-9.464)
-1.026*
(-9.387)
Futures (AR16)
0.55
(1291.46)
VIKALPA • VOLUME 35 • NO 2 • APRIL - JUNE 2010
57
Table 1 ...
Symbol
RIL
SBI
Sterlite
Tata Steel
Wipro
Notes:
Coefficients$
Futures Price
Spot Price
Futures Log
Difference
Spot Log
Difference
Auto Corre. #
Value &
LB Stat.
β1
16.501
(-0.893)
15.981
(-0.865)
0.001
(-0.956)
0.001
(-0.914)
Spot (AR16)
0.63
1469.50
δ
-0.013
(-0.808)
-0.012
(-0.779)
-1.004*
(-10.992)
-0.966*
(-10.591)
Futures (AR16)
0.64
(1480.75)
β1
12.466
(-1.211)
12.514
(-1.231)
0.004
(-2.038)
0.004
(-2.054)
Spot( AR16)
0.60
(1434.67)
δ
-0.008
(-0.841)
-0.008
(-0.854)
-0.940*
(-10.339)
-0.919*
(-10.136)
Futures (AR16)
0.60
(1440.93)
β1
10.096
(-1.166)
9.474
(-1.117)
0.003
(-0.982)
0.002
(-0.947)
Spot( AR16)
0.63
(1428.78)
δ
-0.02
(-1.060)
-0.018
(-1.007)
-1.061*
(-11.758)
-1.035*
(-11.415)
Futures (AR16)
0.63
(1428.92)
β1
70.782
(-2.746)
63.789
(-2.6)
-0.001
(-0.753)
-0.001
(-0.761)
Spot (AR16)
-0.11
(211.85)
δ
-0.141
(-2.776)
-0.127
(-2.631)
-1.109*
(-11.235)
-1.050*
(-10.574)
Futures (AR16)
-0.12
(211.15)
β1
11.977
(0.897)
12.317
(0.917)
0.002
(1.076)
0.002
(1.043)
Spot (AR16)
0.58
(1290.40)
δ
-0.021
(-0.835)
-0.022
(-0.855)
-1.146*
(-12.765)
-1.122*
(12.435)
Futures (AR16)
0.59
(1291.41)
$ the coefficients are from Dickey- Fuller test equation ∆ y t = β 1 + δ yt-1 + εt, where ∆ yt = yt- yt-1 yt takes values of futures price, spot price,
futures first log difference and spot first log difference of each symbol. Dickey- Fuller statistic (τ ≈ t) at 1% = -3.34 and at 5 %=-2.86.
* indicates significance at 1% level.
# Auto correlation at lag 16 (16th minute) is reported, corresponding LB statistic is given in the parenthesis below the values and p value
not included in the Table is zero for all the cases.
Table 2: Trading Frequency and Non-trading probability of Futures and Spot Market
Symbol
Century Tex
Futures
Permitted
Lot size
Futures
NonTrading
trading
Frequency* Prob. %)
Average
Closing
Average
Daily
Trades
Spot
Trading
Frequency
NonAverage
trading Closing
Prob. %)
Average
Daily
Trades
425
28.256
0
507.7524
9324
5490.639
0
505.76
1811910
Hindalco
1595
21.776
0
173.8804
7186
11468.528
0
173.41
3784614
India Cements
1450
24.802
0
207.822
8185
12608.726
0
207.44
4160879
Infosys
100
21.168
0
1944.346
6986
3631.851
0
1944.141
1199171
IVRCL Infra
500
24.544
0
286.2956
8100
8082.376
0
285.7
2667184
Punj Lloyd
1500
12.385
0
812.2107
4775
1176.388
0
803.06
388208
Reliance Cap
550
27.922
0
521.2965
9214
5531.327
0
526.98
1825337
RIL
150
87.209
0
1156.174
28779
10414.724
0
1152.63
3436858
SBI
250
30.528
0
1012.3824
10074
3804.245
0
1009.81
1255400
Sterlite
438
28.747
0
465.0716
9486
6584.744
0
463.61
2172965
Tata Steel
675
50.117
0
507.3660
16539
9872.184
0
500.07
3257820
Wipro
600
9.366
0
530.141
3091
3246.643
0
530.848
1071392
Notes:*Futures trading is given in terms of number of contracts traded per minute and one contract comprises shares equal to the permitted lot
size. The sample period is July 2006 to December 2006.
58
PRICE DISCOVERY PROCESS AND VOLATILITY SPILLOVER IN SPOT AND FUTURES MARKETS
Table 3: Johansen’s Co-integration Test
λ trace (r = 0)
λtrace (r ≤ 1)
λ max (r = 0)
λmax (r ≤ 1)
Century Tex (4)
43.89**
(23.76)
5.76
(6.01)
41.21**
(22.74)
5.76
(6.01)
Hindalco (3)
123.67**
(24.54)
7.85
(4.25)
120.89**
(22.89)
7.85
(4.25)
India Cements (4)
56.98**
(17.89)
8.41
(4.78)
55.73**
(16.84)
8.41
(4.78)
Infosys (4)
122.01**
(23.50)
4.15
(4.45)
120.77**
(22.19)
4.15
(4.45)
IVRCL Infra (4)
67.83**
(45.35)
6.49
(3.97)
58.43**
(37.01)
6.49
(3.97)
Punj Lloyd (3)
54.07**
(34.77)
7.14
(5.79)
52.37**
(33.91)
7.14
(5.79)
Reliance Cap (4)
125.96**
(54.93)
4.84
(6.14)
120.47**
(52.87)
4.84
(6.14)
RIL (3)
24.78**
(23.65)
3.92
(4.07)
22.64**
(20.47)
3.92
(4.07)
SBI (5)
57.9**
(86.42)
7.9
(5.79)
55.89**
(77.28)
7.9
(5.79)
Sterlite (4)
34.09**
(56.07)
4.83
(4.58)
31.83**
(48.56)
4.83
(4.58)
Tata Steel (3)
43.97**
(35.89)
5.08
(6.45)
41.52**
(30.47)
5.08
(6.45)
Wipro (5)
21.74**
(22.45)
4.90
(4.01)
20.63**
(20.87)
4.90
(4.01)
Symbols
Notes: The values of Trace and Maximal Eigen value tests are reported; t values are shown in parentheses. **Indicates that the null hypothesis is
rejected at 1% level. The critical values at the 1% level are taken from table provided by Johansen and Juselius (1990), and the values for r=0
and r=1 are 16.31 and 6.51 respectively for trace test and, 15.69 and 6.51 respectively for Maximal Eigen value test. The lag length chosen
by the SIC criteria is shown in parentheses after the relevant symbol.
Table 4: Lead-Lag Analysis and Volatility Spillover using VECM- EGARCH Model: Spot to Futures
Parameter
Century Hindalco India
Tex
Cements
IVR
Infra
Infosys
Punj
Lloyd
Rel
Cap
RIL
SBI
Sterlite
Tata
Steel
Wipro
αs,0
0.00#
(-1.93)
0.00
(-1.33)
0.00
(-3.08)
0.00
(-0.37)
0.00
(1.50)
1.18
(-0.10)
0.00
(-0.27)
0.00
(-0.07)
0.01
(-3.13)
0.01
(-1.12)
0.00
(-0.74)
0.00
(0.99)
αs,1
0.71
(-1.41)
-1.49
(-2.51)
2.35
(-3.21)
1.37
(-1.11)
0.53
(0.62)
-3.55
(-5.23)
1.01
(-1.21)
2.95
(-3.56)
0.96
(-2.15)
-1.99
(-0.97)
1.10
(-2.29)
-0.25
(-0.30)
αs,2
0.51
(-1.17)
-1.12#
(-1.87)
0.25
(-0.28)
0.62
(-0.62)
0.85
(1.01)
-1.72
(-2.28)
1.98
(-2.28)
1.75#
(-1.88)
1.45
(-2.43)
-0.31
(-3.29)
0.52
(-0.19)
-0.02
(-0.03)
αs,3
-0.71
(-1.53)
-0.95#
(-1.87)
0.46
(-0.50)
-0.20
(-0.19)
0.16
(0.19)
-0.86#
(-1.68)
2.65
(-2.56)
-0.69
(-1.06)
2.05
(-5.70)
-0.67
(-0.37)
-0.03
(-0.08)
0.49
(0.63)
αs,4
0.63
(-1.17)
-0.56
(-1.39)
0.09
(-0.10)
1.36
(-1.50)
0.41
(0.59)
-0.74
(-2.22)
2.77
(-2.88 )
-0.42
(-1.12)
1.03#
(-1.92)
0.07
(-0.05)
0.26
(-0.99)
0.33
(0.40)
αs,5
0.97
(-2.32)
—
0.86
(-1.06)
2.10
(-2.91)
0.07
(0.14)
—
0.79
(-1.01)
—
-0.79
(-1.98)
-1.07
(-1.00)
-0.42
(-0.69)
0.43
(0.80)
βf,1
-0.41
(-0.96)
0.95
(-1.84)
-1.51
(-2.19)
-0.49
(-0.42)
-0.91
(-1.15)
3.36
(-5.05)
-1.37#
(-1.67)
-3.63
(-4.34)
-1.27
(-3.10)
1.72
(-0.87)
-1.07
(-0.98)
-0.16
(-0.21)
βf,2
-0.69
(-1.57)
1.23
(-2.04)
-0.39
(-0.46)
-0.75
(-0.75)
-0.83
(-0.93)
1.85
(-2.44)
-1.92#
(-1.84)
-1.61
(-2.22)
-1.58
(-3.67)
0.23
(-0.14)
-0.43
(-0.46)
-0.01
(-0.01)
βf,3
0.43
(-0.97)
0.64
(-1.23)
-0.58
(-0.62)
0.19
(-0.18)
-0.29
(-0.34)
0.73
(-1.45)
-2.63
(-2.61)
0.66
(-1.06)
-1.97
(-5.45)
0.51
(-0.28)
0.15
(-0.39)
-0.45
(-0.58)
VIKALPA • VOLUME 35 • NO 2 • APRIL - JUNE 2010
59
Table 4 ...
Parameter
Century Hindalco India
Tex
Cements
IVR
Infra
Infosys
Punj
Lloyd
Rel
Cap
RIL
SBI
Sterlite
Tata
Steel
Wipro
βf,4
-0.90#
(-1.79)
0.32
(-0.76)
0.11
(-0.13)
-1.44
(-1.59)
-0.30
(-0.43)
1.02
(-2.99)
-2.60
(-2.86)
0.26
(-0.72)
-0.92#
(-1.81)
-0.21
(-0.14)
-0.26
(-0.81)
-0.29
(-0.59)
βf,5
-1.09
(-2.63)
—
-0.93
(-1.19)
-2.04
(-2.88)
0.00
(0.01)
—
-0.86
(-1.13)
—
0.76
(-2.00)
0.87
(-0.82)
0.39
(-0.65)
-0.47
(-0.57)
∆s
-0.002
(-3.01)
-0.001
(-0.55)
-0.001
(-3.99)
-0.003
(-0.81)
-0.001
(-1.11)
-0.002#
(-1.68)
-0.005
(-3.60)
-0.003
(-3.43)
0.000
(-0.93)
0.004
(0.95)
0.003
(-1.37)
0.000
(-0.28)
Ωs
-5.00
(-7.06)
-3.47
(-2.09)
-5.00
(-2.73)
-2.32
(-0.99)
-5.00
(-0.32)
-3.75
(-4.14)
-2.87
(-5.36)
-4.75
(-5.44)
-2.47
(-5.82)
-3.57
(-1.98)
-5.00
(-6.35)
-1.19
(-1.14)
Φs
0.35
(-4.02)
0.58
(-2.84)
0.37
(-1.58)
0.68
(-2.10)
0.43
(0.24)
0.48
(-3.85)
0.64
(-8.41)
0.43
(-4.18)
0.70
(-13.63)
0.51
(-2.06)
0.41
(-4.48)
0.86
(6.75)
Γs
-1.68
(-5.98)
1.21
(-3.35)
0.03
(-0.12)
0.49
(-1.35)
0.00
(-0.01)
-1.26
(-4.27)
-0.87
(-3.36)
-1.42
(-4.42)
-0.98
(-5.64)
0.49
(-1.48)
-1.58
(-5.19)
0.68
(1.98)
Θs
-1.52
(-5.16)
0.03
(-0.15)
-0.52
(-2.69)
-0.14
(-0.81)
-0.08
(-0.42)
0.01
(-0.07)
-1.76
(-9.09)
-0.37
(-2.39)
-0.65
(-5.36)
-0.10
(-0.66)
-0.99
(-4.10)
0.08
(0.42)
Notes: The Table reports the estimated coefficients from the VECM-EGARCH model; t values are given in parentheses. # denotes statistically
significant at 10 % level, at 5 % level and at 1 % level. Critical t values are 1.65 (10% level), 1.98 (5%level) and 2.58 (1% level).
Table 5: Lead-Lag Analysis and Volatility Spillover using VECM- EGARCH Model: Futures to Spot
Parameter
Century Hindalco India
Tex
Cements
IVR
Infra
Infosys
Punj
Lloyd
Rel
Cap
RIL
SBI
Sterlite
Tata
Steel
Wipro
αf,0
0.01
(-3.65)
0.00
(-0.44)
0.00
(-0.51)
-0.01
(-1.39)
0.00
(2.16)
0.00
(-1.38)
0.00
(-0.72)
0.00
(-0.44)
0.01
(-2.48)
0.01
(-1.26)
0.00
(-0.77)
0.00
(0.00)
αf,1
-0.39
(-0.39)
0.11
(-0.20)
-0.58
(-0.44)
-2.31
(-4.18)
-1.38
(-2.11)
1.01#
(-1.78)
1.22#
(-1.77)
-1.96
(-3.37)
-1.97
(-16.99)
-0.55
(-0.54)
-0.98
(-1.34)
-0.38
(-0.56)
αf,2
-0.21
(-0.20)
0.10
(-0.27)
-1.55
(-1.38)
-1.31#
(-1.82)
-1.08
(-1.48)
-0.87
(-1.00)
0.04
(-0.04)
-0.76
(-0.86)
-1.71
(-9.53)
-1.88
(-1.10)
-0.60
(-0.78)
-0.18
(-0.27)
αf,3
0.17
(-0.24)
-0.38
(-1.09)
-1.32
(-0.78)
-0.79
(-1.28)
-0.34
(-0.47)
-1.26
(-1.58)
0.91#
(-1.74)
0.97
(-1.05)
-1.46
(-9.39)
-2.16
(-1.22)
-0.18
(-0.21)
-0.91
(-1.46)
αf,4
-1.35
(-1.44)
-0.17
(-0.46)
-0.62
(-0.39)
-0.24
(-0.46)
-0.28
(-0.46)
-0.02
(-0.03)
-1.46
(-1.36)
0.59
(-1.02)
0.12
(-0.74)
-1.61
(-0.98)
-0.29
(-0.31)
-0.63
(-0.93)
αf,5
-2.97
(-3.94)
—
0.70
(-0.63)
-0.26
(-1.05)
-0.16
(-0.44)
—
-2.24
(-4.07)
—
0.83
(-7.97)
-0.39
(-0.39)
-0.31
(-0.47)
-0.88
(-2.11)
βs,1
0.21
(-0.20)
0.27
(-0.43)
0.66
(-0.67)
1.88
(-3.74)
0.86
(1.27)
-1.29
(-2.05)
-1.35
(-1.54)
1.28
(-2.34)
1.27
(-10.68)
-0.23
-0.21
0.67
(-0.61)
0.37
(0.54)
βs,2
-0.15
(-0.14)
-0.11
(-0.28)
1.50
(-1.28)
1.66
(-2.40)
1.01
(1.47)
1.13
(-1.28)
-0.02
(-0.02)
0.93
(-1.10)
1.59
(-8.48)
1.93
(-1.12)
0.61
(-0.79)
0.17
(0.24)
βs,3
-0.34
(-0.48)
0.07
(-0.20)
1.16
(-0.70)
0.76
(-1.28)
0.16
(0.24)
1.09
(-1.35)
-0.99#
(-1.87)
-1.00
(-1.10)
1.38
(-8.49)
2.10
(-1.19)
0.26
(-0.30)
0.89
(1.39)
βs,4
1.04
(-1.08)
0.17
(-0.44)
0.62
(-0.41)
0.25
(-0.51)
0.31
(0.53)
0.24
(-0.45)
1.54
(-1.38)
-0.70
(-1.21)
0.08
(-0.54)
1.50
(-0.90)
0.21
(-0.22)
0.59
(0.85)
βs,5
2.88
(-3.59)
—
-0.63
(-0.57)
0.27
(-1.07)
0.21
(0.58)
—
2.23
(-3.93)
—
-0.85
(-7.77)
0.29
(-0.28)
0.25
(-0.37)
0.84
(2.08)
δf
0.003
(-1.45)
0.003#
(1.65)
0.000
(-0.14)
-0.010
(-11.38)
0.000
(0.07)
-0.002
(-2.52)
-0.003
(-2.75)
0.000
(-0.31)
-0.001
(-5.73)
0.001
(0.66)
0.004
(4.51)
-0.001
(-0.54)
ωf
-5.00
(-3.18)
-5.00
(-2.09)
-2.83#
(-1.85)
-5.00
(-8.37)
-216
(-0.57)
-2.58
(-3.79)
-2.70
(-3.65)
-5.00
(-2.71)
-3.68
(-11.38)
-5.00#
(-1.92)
-2.26#
(-1.83)
-1.17
(-1.17)
ϕf
0.34
(-1.64)
0.39
(-1.33)
0.63
(-3.14)
0.31
(-3.95)
0.76#
(1.83)
0.64
(-6.84)
0.66
(-6.83)
0.41#
(-1.90)
0.56
(-13.05)
0.32
(-0.92)
0.72
(-4.90)
0.86
(6.97)
60
PRICE DISCOVERY PROCESS AND VOLATILITY SPILLOVER IN SPOT AND FUTURES MARKETS
Table 5 ...
Parameter
Century Hindalco India
Tex
Cements
IVR
Infra
Infosys
Punj
Lloyd
Rel
Cap
RIL
SBI
Sterlite
Tata
Steel
Wipro
Υf
1.14
(-3.68)
1.27
(-3.48)
0.40#
(-1.79)
-1.08
(-4.13)
0.24
(0.78)
-1.05
(-3.57)
-1.20
(-5.36)
-0.56#
(-1.97)
-1.34
(-6.39)
0.60#
(-1.90)
-0.83
(-2.40)
0.62
(2.28)
θf
-0.44#
(-1.94)
0.00
(-0.01)
-0.29#
(-1.90)
-1.18
(-5.46)
-0.07
(-0.55)
-0.31
(-2.32)
-0.38
(-2.48)
-0.41
(-2.35)
-1.20
(-9.48)
-0.09
(-0.52)
-0.03
(-0.34)
0.03
(0.18)
Notes: The Table reports the estimated coefficients from the VECM-EGARCH model; t values are given in parentheses. # denotes statistically
significant at 10 % level, at 5 % level and at 1 % level. Critical t values are 1.65 (10% level), 1.98 (5%level) and 2.58 (1% level).
REFERENCES
Abdul, J I; Khairuddin, O and Obiyathulla, I B (1999). “Issues
in Stock Index Futures Introduction and Trading: Evidence from the Malaysian Index Futures Market,” Capital Markets Review, 7(1 and 2), 1-37.
Baillie, R T; Liens, R E and McMahon, P C (1983). “Testing
Rational Expectations and Efficiency in the Foreign Exchange Market,” Econometrica, 51(3), 553-563.
Chan, Kalok (1992). “A Further Analysis of the Lead-Lag Relationship Between the Cash Market and Stock Index
Futures Market,” The Review of Financial Studies, 5(1), 123152.
Ching-Chung, L C; Shen-Yuan, H; Dar-Yeh and Chien-Fu, L
(2002). “Does Index Futures Dominate Index Spot? Evidence from Taiwan Market,” Review of Pacific Basin Financial Markets and Policies, 5(2), 255-275.
Daigler, R T (1990). “Intraday Stock Index Futures Arbitrage
with Time Lag Effects,” Working Paper, Florida International University, http://www.fiu.edu/~daiglerr/pdf/
intraday_SIF_arbitrage.pdf, downloaded on 25/09/2005.
Engle, R F and Granger, C W J (1987). “Co-integration and
Error Correction: Representation, Estimation, and Testing,” Econometrica, 55 (2), 251-276.
Fleming, J; Ostdiek, B and Whaley, R E (1996). “Trading Costs
and the Relative Rates of Price Discovery in Stock, Futures, and Option Markets,” Journal of Futures Markets,
16(4), 353-87.
Frino, Alex; Walter, Terry and West, Andrew (2000). “The
Lead-lag Relationship between Equities and Stock Index
Futures Markets around Information Releases,” Journal
of Futures Market, 20(5), 467-487.
Gao, A H and Wang, G H K (1999). “Modelling Nonlinear
Dynamics of Daily Future Price Changes,” Journal of Futures Markets, 19(3), 325-351.
Grandson, L; Fernandez, A and Muoz, M J (1998). “Market
Efficiency in the Spanish Derivatives Markets: An Empirical Analysis,” International Advances in Economic Research, 4(4), 349-355.
Granger, C W J (1969). “Investigating Casual Relations by
Econometric Models and Cross-Spectral Methods,”
Econometrica, 37(3), 424-438.
Gujarati, N Damodar (2005). Basic Econometrics, New Delhi:Tata
McGraw-Hill.
Hakkio, C S (1981). “Expectations and the Forward Exchange
Rate,” International Economic Review, 22(3), 663-678.
Hansen, L P and Hodrick, R J (1980), “Forward Exchange Rates
VIKALPA • VOLUME 35 • NO 2 • APRIL - JUNE 2010
as Optimal Predictors of Future Spot Rates: An Econometric Analysis,” Journal of Political Economy, 88(5), 829853.
Joel, H (2003), “Intraday Price Formation in U.S. Equity Index
Markets,” The Journal of Finance, 58(6), 2375-2399.
Johansen, S (1988). “Statistical Analysis of Co-integration Vectors,” Journal of Economic Dynamics and Control, 12(2-3),
231-254.
Johansen, S (1991). “Estimation and Hypothesis Testing of Cointegrating Vectors in Gaussian Vector Autoregressive
Models,” Econometrica, 59(6), 1551-1580.
Johansen, S and Juselius, K (1990). “Maximum Likelihood Estimation and Inference on Co-integration with Allocation
to the Demand for Money,” Oxford Bulletin of Economics
and Statistics, 52(2), 169-209.
Karmakar, M (2009). “Price Discoveries and Volatility
Spillovers in S&P CNX Nifty Future and its Underlying
Index CNX Nifty,” Vikalpa, 34(2), 41-56.
Kim, K (1998). “US Inflation and the Dollar Exchange Rate: A
Vector Error Correction Model,” Applied Economics, 30(5),
613-619.
Mckenzie, M A and Holt, T M (2002). “Market Efficiency in
Agricultural Futures Markets,” Applied Economics, 34(12),
1519-1532.
Mukherjee, Kedarnath and Mishra, R K (2006). “Lead-Lag Relationship between Equities and Stock Index Futures
Market and Its Variation around Information Release:
Empirical Evidence from India,” NSE Working Paper No.
39, July, http://nseindia.com/content/research/
comppaper155.pdf, downloaded on 30-9-2009.
Nelson, D (1991). “Conditional Heteroscedasticity in Asset
Returns: A New Approach,” Econometrica, 59(2), 347-370.
Patterson, K (2002). An Introduction to Applied Econometrics - A
Time Series Approach, New York: Palgrave.
Reimers, H E (1992). “Comparisons for Tests for Multivariate
Co-integration,” Statistical Papers, 33(1), 335-375.
Sargan, J D (1984). “Wages and Prices in the United Kingdom:
A Study in Econometric Methodology,” in Wallis, K F
and Hendry, D F (Eds.), Quantitative Economics and Econometric Analysis, Oxford: Basil Blackwell, 112-116.
Schwarz, G (1978). “Estimating the Dimension of a Model,”
Annals of Statistics, 6(2), 461-464.
Tan, H B and Lim, C S ( 2001). “Intraday Price Discovery in
the Malaysian Stock Index Futures and Cash Markets,”
61
Banker’s Journal Malaysia, 4(1), 117-130.
Tse, Y K (2006). “Lead-lag Relationship between Spot Index
and Futures Price of the Nikkei Stock Average,” Journal
of Forecasting, 14(7), 553-563.
T Mallikarjunappa is a Professor in the Department of Business Administration, Mangalore University, Karnataka. He has
26 years of Post-graduate teaching and research experience.
He has an MBA and a Ph.D. from the University of Mysore
and an AICWA from the ICWA of India. He is on the Editorial
Board of AIMS International Journal of Management and has published 51 papers. His papers are published in AIMS International Journal of Management, ICFAI Journal of Applied Finance,
Decision, Asian Academy of Management Journal of Accounting
and Finance, etc. His area of specialization is Accounting and
Finance.
Wang, P and Wang, P (2001). “Equilibrium Adjustment, Basis
Risk and Risk Transmission in Spot and Forward Foreign Exchange Markets,” Applied Financial Economics,
11(2), 127-136.
Afsal E M is an Assistant Professor of Management in the
School of Management and Business Studies, Mahatma Gandhi
University, Kottayam, Kerala. He has received his MBA with
gold medal from Kannur University, Kerala and a Ph.D in Business Administration from Mangalore University. His papers
are published in ICFAI Journal of Applied Finance, Decision, Asian
Academy of Management Journal of Accounting and Finance. He
specializes in Finance and Marketing Management.
e-mail:[email protected]
e-mail: [email protected]
When you get rid of the volatility factor the stock
option expense creates, the earnings growth was
actually very good.
— John Aiken
62
PRICE DISCOVERY PROCESS AND VOLATILITY SPILLOVER IN SPOT AND FUTURES MARKETS