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THE LEAD-LAG RELATIONSHIP BETWEEN FUTURES
PRICES AND SPOT PRICES: EMPIRICAL EVIDENCE BASED
ON THAI DATA
By
WARITTHA LASORN
An Independent Study
Submitted in partial fulfillment of the requirements
for the Degree of
MASTER OF SCIENCE IN FINANCE AND ECONOMICS
MARTIN DE TOURS SCHOOL OF MANAGEMENT AND ECONOMICS
Assumption University
Bangkok, Thailand
November 2013
ABSTRACT
The aims of this paper are to investigate the existence of long-run relationship
between spot and futures prices and to detect the short-run dynamic relationship
between spot and futures prices in context of Thailand. The Unit Root tests,
Cointegration tests, and Vector Error Correction Model (VECM) tests are applied in
this paper. The two products that were selected to study are RSS3 and SET50 index.
The daily spot and futures prices of RSS3 and SET50 index were gathered since the
first day of trading, on May 28, 2004 for RSS3 and on April 28, 2006 for SET50
Index, until May 31, 2013 to investigate the long-run and short-run relationships
between the spot and futures prices.
By applying Unit Root tests, all data series are found to be stationary at first
difference. The Cointegration tests by both Engle-Granger and Johansen methods
were applied, the results are the same which prove that there are long-run
relationships between RSS3 spot prices and RSS3 futures prices and between SET50
index spot prices and SET50 index futures prices. The VECM tests were applied, and
found that the relationship between RSS3 spot and futures prices is bidirectional.
However, in case of SET50 index, the result shows that SET50 index spot return lead
SET50 index futures return.
The results of this paper provide benefits to both Thai and foreign investors and
speculators who participate in the trading of RSS3 and SET50 index; they can hedge
their exposure or speculate their returns more properly. Moreover, the rubber tree
planters will also get the benefit from the results of this paper in designing their
hedging strategy to prevent themselves from unfavorable price movement in the time
of harvesting. Additionally, the corporations that sell or export rubbers and its related
products and also the corporations that use rubbers as their main raw material can also
use the result of this paper to properly construct their hedging program. In term of
academic contribution, the result of this study will add more updated empirical
evidence on the studies regarding Thailand’s futures market, which are considered to
be limited at the present time.
TABLE OF CONTENTS
Page
ABSTRACT ................................................................................................... i
TABLE OF CONTENTS ................................................................................ ii
LIST OF TABLES ......................................................................................... iii
CHAPTER I: GENERALITIES OF THE STUDY
1.1 Background of the Study ............................................................................ 1
1.2 Statement of the Problem .......................................................................... 4
1.3 Research Objectives .................................................................................. 5
1.4 Research Questions ................................................................................... 5
1.5 Scope of the Research ............................................................................... 5
1.6 Limitations of the Research....................................................................... 6
1.7 Significance of the Study .......................................................................... 6
1.8 Definition of Terms .................................................................................. 7
CHAPTER II: REVIEW OF RELATED LITERATURE AND STUDIES
2.1 Theories Related to the Study ................................................................... 10
2.2 Variables .................................................................................................. 13
2.3 Empirical Evidences from the Prior Studies .............................................. 21
CHAPTER III: RESEARCH METHODOLOGY
3.1 Data Collection ......................................................................................... 24
3.2 Methodology ............................................................................................ 25
3.3 Research Hypotheses ................................................................................ 31
CHAPTER IV: PRESENTATION AND CRITICAL DISCUSSION OF
RESULTS
4.1 Unit Root Tests ......................................................................................... 33
4.2 Cointegration Tests ................................................................................... 34
4.3 Vector Error Correction Model Tests ........................................................ 35
CHAPTER V: CONCLUSION, IMPLICATION AND FURTHER STUDY
5.1 Conclusion ................................................................................................ 38
5.2 Implications .............................................................................................. 39
5.3 Further Study ............................................................................................ 40
BIBLIOGRAPHY ....................................................................................... 41
APPENDICES .............................................................................................. 53
Appendix A: Futures Contract Specifications.................................................. 54
Appendix B: Tests Results .............................................................................. 57
LIST OF TABLES
TABLE Page
1 Availability of Futures Products in Thailand ................................... 3
2 Summary of the Empirical Evidences from the Prior Studies .......... 19
3 Results from Unit Root Tests .......................................................... 33
4 Results from Johansen Cointegration Rank Test (Trace) ................. 34
5 Results from VECM Test for RSS3 ................................................ 36
6 Results from VECM Test for SET50 Index..................................... 37
1
CHAPTER I
GENERALITIES OF THE STUDY
1.1 Background of the Study
The importance of futures market is discussed by many economists. In early
school of thought, Kaldor (1940a, b) suggested that the futures markets exist because
it can offer price insurance. This idea views the futures contracts as instruments that
businesses can utilize to avoid the risk of unfavorable movement in price. Working
(1962) proposed another explanation by relying on the assumption that there must be
the compensation for speculators to bear the hedgers’ price risks. Hence, futures
markets exist since they offer speculators the chance to get positive returns. However,
some may opposed that this price risk can also be hedged by using forward contracts,
Telser (1981) argues that the futures markets exist since they offer cheaper transaction
costs than forward markets. Futures contracts are traded in organized exchanges, the
futures contract is more standardized than forward contract, and the clearinghouse
acts as the counter-party, so it has lower default risk. These characteristics reduce the
transaction costs and make futures contract more favorable than forward contracts.
Presently, the futures products are considered to be the alternative financial
products available to investors for the purpose of hedging, speculating, and
arbitraging. Futures and spot prices present an interesting case for application of
relationships testing (Peck, 1985). As the predictive relationship may exist between
these two prices, it is interesting to investigate the relationship between both price
series, in order to ascertain which series provides an indication of the other in the
future.
There is an intense investigation towards the relationships and interactions
between the price of particular product in spot market and its price in futures market.
The studies by Kenourgios and Samitas (2004), Thongthip (2010), Zakaria and
2
Shamsuddin (2012), Choudhary and Bajaj (2012), and Songyoo (2013) have been
conducted in the area of investigating the lead-lag relationship. Generally, the main
focus of these investigations is to clarify whether futures price leads spot price,
whether spot price leads futures price or whether there is a bi-directional feedback
effect between these two markets. If the investors could understand the lead-lag
relationship between these two markets, they would know how well these two
markets are linked, and also how fast one market could react to the new information
from another market. This information would help the investors in the process of
decision making. Hence, the participants in spot market could use the futures position
as a tool to minimize risk (Jackline & Deo, 2011).
In Thailand, the Stock Exchange of Thailand has been introduced since April
1975; however the trading on futures products is considered to be relatively new to
Thai investors. Thailand has two futures markets, namely Agricultural Futures
Exchange of Thailand (AFET) and Thailand Futures Exchange (TFEX). The first
day of trading of the product was on May 28, 2004 in AFET and April 28, 2006 in
TFEX. The futures products offered by these two markets are presented in Table 1.
3
Table 1: Availability of Futures Products in Agricultural Futures Exchange of
Thailand (AFET) and Thailand Futures Exchange (TFEX)
No.
Futures Products in
AFET
First Day of
Trading
Futures Products
in TFEX
First Day of
Trading
1 Ribbed Smoked
Rubber Sheet No.3 May 28, 2004
SET50 Index April 28, 2006
2
Thai Hom Mali
100% Grade B
Both Options
July 14, 2008
Single Stock November 24,
2008
3 Tapioca Chip Both
Options July 13, 2009
50 Baht Gold February 2,
2009
4 White Rice 5%
FOB April 29, 2011
10 Baht Gold August 2,
2010
5 Block Rubber
STR20
October 28,
2011
5Y Gov Bond October 18,
2010
6 Canned Pineapple September 28,
2012
3M BIBOR November 29,
2010
7
6M THBFIX November 29,
2010
8
Silver June 20, 2011
9
Brent Crude Oil October 17,
2011
10
USD June 5, 2012
11
Sector Index October 29,
2012
Sources: Agricultural Futures Exchange of Thailand (2013); Thailand Futures
Exchange (2013)
4
1.2 Statement of the Problem
The different relationships across different markets and countries were reported,
that may be because of the differences in the level of economic development and
particular market development. For commodities, Liu and Zhang (2006) found that
the relationship between Chinese spot and futures markets is bidirectional (bilateral
causality), while Iyer and Pillai (2010) found that the futures prices of most
commodities in Indian market play their price discovery role by leading the spot
prices. For stock indices, Fassas (2010) found that the bilateral causality running
between Greece spot and futures stock indices; on the other hand, Zakaria and
Shamsuddin (2012) found that spot price of Malaysian stock index leads its futures
price.
In the context of Thailand, there are some studies that investigated this
relationship. Nittayagasetwat and Nittayagasetwat (2010) study the lead-lag
relationship between the spot and futures price of Ribbed Smoked Rubber Sheet No.3
(RSS3) during May 2004 to August 2009 and found that future prices lead spot prices.
Thongthip (2010) studied the lead-lag relationship and mispricing between SET50
index cash and futures market by using both 5-minute prices and daily SET50 Index
and SET50 Index futures in the trading period from October 1, 2008 to September 29,
2009. Songyoo (2013) studied technical trading strategy in spot and futures markets
by using 10-minute prices of SET50 Index and SET50 Index futures in the trading
period from September 12, 2011 to November 11, 2011. Both of them found that
futures prices lead spot prices. However, these studies on SET50 Index emphasized
on investigating the arbitrage opportunity between these two markets by using the
intraday data (5-minute and 10-minute data), since these intraday data are available
only in the past 1 year, so it would limit their studies to be able to be conducted by
using only the short-term period data (no more than 1 year).
Therefore, this paper intends to add more updated empirical evidence on the
study of commodity product and fill the gap on the study of financial product by using
the long-term period data; in other words, this paper intends to investigate the long-
5
run and short-run dynamics in relationship between spot and futures prices of
commodity product and financial product in Thailand by using the data in long-term
period.
1.3 Research Objectives
There are two main objectives of this paper:-
1) To investigate the existence of long-run relationship between spot and futures
prices in context of Thailand.
2) To detect the short-run dynamic relationship between spot and futures prices in
context of Thailand.
1.4 Research Questions
1) Does the long-run relationship exist between spot and futures prices in context
of Thailand?
2) Does the short-run relationship exist between spot and futures prices in context
of Thailand?
1.5 Scope of the Research
As this paper intends to use the long range period data, only products that have
trading data available more than 5 years would be selected to be studied in this paper.
According to the information provided in Table 1, there are only two products in both
futures markets that were traded more than 5 years, which are Ribbed Smoked Rubber
Sheet No.3 (RSS3) on AFET and SET50 Index futures on TFEX. Hence, only these
two products were selected to be studied.
Consequently, there are four variables or two pairs of relationship, which are spot
and futures prices of RSS3 and spot and futures prices of SET50 Index. The daily data
would be gathered since the first day of trading on May 28, 2004 for RSS3 and on
6
April 28, 2006 for SET50 Index, until May 31, 2013. All data would be gathered from
SETSMART database, AFET’s website, and Office of The Rubber Replanting Aid
fund’s website.
1.6 Limitations of the Research
1) Only two products in Thailand’s futures market will be selected to study.
Since this paper intends to conduct the study by using the long period (more than
5 years) of historical prices data in spot and futures markets, so only two products,
RSS3 and SET50 index, will be selected. Hence, the result of this paper could not be
the representative for the relationship between the futures price of all types of futures
products in Thailand and their spot price.
2) Spot price of Ribbed Smoked Rubber Sheet No. 3 comes only from one
central market.
In Thailand, there are three central rubber markets for RSS3, which are Hat Yai
central rubber market, Surat Thani central rubber market, and Nakhon Si Thammarat
central rubber market. The spot prices of RSS3 in each market are slightly different
depending on the demand and supply in the particular market. However, this paper
will use only the price from Hat Yai central rubber market, the first central rubber
market in Thailand, as a proxy for spot price of RSS3 in Thailand, due to the limited
availability of data in the other two markets.
1.7 Significance of the Study
The empirical result of this paper will be the statistical evidences that may benefit
both Thai and foreign investors and speculators who participate in the trading of
RSS3 and SET50 index. They can hedge their exposure or speculate their returns by
investing in RSS3 futures and SET50 index futures more accurately. Moreover, the
rubber tree planters will also get the benefit from the result of this paper in designing
their hedging strategy to prevent themselves from unfavorable price movement in the
7
time of harvesting. Additionally, the corporations that sell/export rubbers and related
products and corporations that use rubbers as their main raw material can also use the
result of this paper to construct their hedging program more accurately. In term of
academic contribution, the result of this study will add more updated empirical
evidence on the studies regarding Thailand’s futures market, which are considered to
be limited at the present time.
1.8 Definition of Terms
AFET AFET standing for Agricultural Futures Exchange
of Thailand, which has been established since 1999.
It is under the supervision of Agricultural Futures
Trading Commission (Agricultural Futures
Exchange of Thailand, 2013).
Futures price The price that the two parties in futures market
agree to trade at on the expiration date of futures
contract (Investorwords, 2013).
Lead-lag effect The situation when the values of one variable
(leading variable) is correlated with the values of
another variable (lagging variable) at later times (Lo
& MacKinlay, 1990)
Mean-reverting When prices are forced back to their long-run
equilibrium after deviation. The rate of mean-
reversion is negative if the spot price is higher than
the mean- reversion level and positive if lower
(Higgs & Worthington, 2008).
8
Price discovery In futures market, price discovery is usually defined
as the situation when the futures prices could be
used as a tool to determine the expected (future)
spot prices (Yang, Bessler, & Leatham, 2001).
RSS3 RSS3, standing for Ribbed smoked rubber sheet
No.3, is most of Thai rubber production, because it
is easy to transport and store and is globally
accepted. RSS3 is the first product that is available
in futures market in Thailand. It has been listed on
AFET since May 28, 2004 (Agricultural Futures
Exchange of Thailand, 2013).
Semi-strong form efficiency A market is semi-strong efficient when stock prices
instantaneously reflect any new publicly available
information (both historical prices and fundamental
data) (Poshakwale, 1996).
SET50 index The first Thailand’s large-cap index that is
calculated from the stock prices of the companies
that are in top 50 listed on SET in terms of their
large market capitalization, high liquidity and also
compliance with the requirements regarding the
distribution of shares to minor shareholder. SET50
index provides a benchmark of investment in The
Stock Exchange of Thailand. SET50 Index Futures
is the first product traded on TFEX. It has been
launched since April 28, 2006 (Stock Exchange of
Thailand, 2013; Thailand Futures Exchange, 2013).
9
Spot price The price of an immediate delivery products that
are traded on the spot market. It could be called
as cash price also (Investorwords, 2013).
Strong form efficiency A market is strong form efficient when all types of
information whether available publicly or privately
are reflected in stock prices (Poshakwale, 1996).
TFEX TFEX stands for Thailand Futures Exchange. It was
established on May 17, 2004 as a subsidiary of the
Stock Exchange of Thailand (SET) to facilitate a
derivatives exchange. TFEX is regulated by the
Securities and Exchange Commission (SEC)
(Thailand Futures Exchange, 2013).
Weak form efficiency A market is considered weak form efficient when
all information contained in historical prices are
fully reflected in the current prices, which implies
that no investor can earn abnormal returns by using
only past price patterns in their trading strategy
(Poshakwale, 1996).
10
CHAPTER II
REVIEW OF RELATED LITERATURE AND STUDIES
This section presents theories related to the relationship of futures and spot
market. It also explains about the RSS3 and SET50 index which are the variables in
this study. Additionally, some empirical evidences from the prior studies are
discussed.
2.1 Theories Related to the Study
1) Law of One Price
This theory states that in a competitive market, if two assets have the same risk
and return, they should be sold at the same price (Bodie, Kane & Marcus, 2008).
However, if the same assets are traded in two markets with different prices, there will
be operators who will buy in the market where the asset is sold at the cheap price and
sell in the market where the price is more expensive. This activity called as arbitrage,
which involves the simultaneously purchase and sale of the same or essentially similar
asset in two different markets to gain riskless profit from different prices (Sharpe &
Alexander 1990). This activity will continue until the price gap in the two markets is
closed, in other words, the price is reached equilibrium.
In the real world, some market microstructure factors may cause a temporary
deviation of prices from their no-arbitrage or equilibrium values. For example, if there
are extreme order imbalances in a spot market, these may create inventory problems
for market makers and could lead to temporary deviations of spot prices from the
corresponding no-arbitrage prices implied by futures markets (Roll, Schwartz, &
Subrahmanyam, 2007).
11
2) Market Efficiency
The Efficient Markets Hypothesis (EMH) indicates that all available information
is already reflected in the market prices. This idea was developed by Samuelson and
Fama in the 1960s (Samuelson, 1963; Fama, 1963, 1965a, b) and after that it has been
applied widely through empirical studies and theoretical models of financial securities
prices. This theory generates the considerable controversy against the price-discovery
process (Lo, 2007). According to Samuelson and Eugene F. Fama in the 1960s, the
EMH suggests that no one can achieve the abnormal returns consistently on a risk-
adjusted basis. There are three major versions of this hypothesis, which are weak,
semi-strong and strong form efficiency. In futures market, market efficiency theory
indicates that the futures price would equal to the expected future spot price plus or
minus a time-varying risk premium. Hence, if markets are both efficient and have no
risk premium, the futures price could be an unbiased predictor of future spot prices. In
other word, the hypothesis that futures prices represent as an unbiased predictors of
spot prices in the future is a joint hypothesis of risk neutrality and market efficiency
(Holt & Mckenzie, 1998).
Fama (1970) suggested that if all relevant information is reflected in the prices, a
futures market will be efficient. Grossman and Stiglitz (1980) extend this definition
more by indicating that if there is a cost to access the information, informational
efficient markets would be impossible.
3) Cost of Carry
According to Lin and Stevenson (2001), the futures price is the spot price plus
the cost of carry of the underlying asset to delivery date. In other words, the futures
price is in effect a price in the future (the price at maturity) that takes into account the
cost of carry. The cost of carry is the cost of storing the underlying asset until the
maturity time that was specified in futures contract. It could include the cost for
physical storage, as in commodity futures like rubber contracts, interest paid to
finance the asset less the income earned on the asset, and also include the
opportunity cost of selling the underlying asset in the future rather than the present; if
12
the owner sold the underlying asset now, they could invest the proceeds or use the
space in other ways. If the futures price does not correspond with the spot price
adjusted for cost of carry, the arbitrage opportunity would be incurred and then
market forces will bring the two back into balance (Brenner & Kroner, 1995).
According to Cornell and French (1983), the cost of carry model implies that a pair of
spot price and futures price should be cointegrated in the long-run. They assumed that
the capital markets are perfect, that means there is no transaction costs and also taxes,
which means that there is no short selling restrictions, and the assets can be divided
infinitely. However, according to Lim (1992), index futures price does not conform to
the cost of carry benchmark all the time. Definitely, when the arbitrage profit is
smaller than transaction costs, the arbitrager would not step into the market.
Consequently, it proves that the arbitrage opportunity is not always continuous.
4) Risk Premium
As commodity futures are introduced and became more popular over the last
decade, there is intense debate over the existence and also the source of a commodity
futures risk premium. According to Melolinna (2011), the risk premium is defined by
the actions of hedgers and speculators in the market. Hedgers would like to pay for
the protection against the risk that the futures provide, while the speculators also need
the compensation for the risk they are taking. Hence, if positions of hedgers are net
short, while speculators are net long, the price of futures would be lower than the
expected future spot price, since the speculators who hold net long in the markets
need compensation which came in form of a lower futures price to enter the market.
Conversely, if hedgers hold net long and speculators hold net short positions, the price
of futures would be higher than the expected future spot price.
There are two hypotheses based on the source of a commodity futures risk
premium. The first hypothesis mentioned that it comes from the risk transfer or
hedging pressure hypothesis which is introduced by Keynes (1930) and Hicks (1939).
This hypothesis stated that the risk premium would be accrued to the speculators as a
reward for facing the price risk that the hedgers decided to transfer. This hypothesis
13
was extended by various authors which finally were developed to be the equilibrium-
based generalized hedging pressure hypothesis by Hirshleifer (1989, 1990) where
non-participation effects lead to hedging pressure influencing the risk premium of
commodity futures. The second hypothesis introduced by Working (1949) and
Brennan (1958) which stated that the variation in futures prices comes from the issues
of storage and inventories rather than the risk transfer, which is getting more
acceptance from the recent papers. Actually, the main contributions of Hirshleifer
(1990) are to link backwardation, which is the main focus of Keynes (1930), to lower
levels of hedgers’ hedging pressure, and also contango, which is the main focus of the
Working (1949), to higher levels of hedgers’ hedging pressure, where hedging
pressure measures the propensity of market participants to be net long. Consequently,
the Hirshleifer (1990) generalized hedging pressure hypothesis than synthesizes the
ideas of Keynes (1930) and Working (1949).
According to the early empirical tests of the hedging pressure hypothesis, the role
of own commodity hedging pressure is focused as a determinant of either futures
prices (Houthakker, 1957; Cootner, 1960; Chang, 1985; Bessembinder, 1992) or of
the CAPM risk premium (Dusak, 1973; Carter et al., 1983). For more recent studies, it
focused on the role of hedging pressure as a systematic risk factor. De Roon et al.
(2000) found the cross-commodity hedging pressure effects for individual commodity
futures risk premiums, as proposed in Anderson and Danthine (1981). Acharya et al.
(2010) found that systematic hedging pressure effects can occur in the context of
limits on risk-taking capacity of the speculators.
2.2 Empirical Evidences on the Relationship between Futures Price and Spot
Price
Futures market performs two important functions, one of which is price risk
management and the other one is price discovery (Garbade & Silber, 1983). The
existence of futures markets could bring benefits to producers, investors and
businesses by discovering the present and future price of any commodity or financial
14
asset. Price discovery in futures markets is the situation when the futures prices are
used to determine the expected (future) spot prices (Yang et al., 2001). Prices of
stocks and commodities would move in the same direction as the market participants’
expectations. Hence, the price in the futures market demonstrates the demand and
supply expectation in the future and would undertake the process of price discovery in
the spot market accordingly.
However, the contradict results on causality of relationship between futures
prices and spot prices could be occurred across the tests in different markets as
follows;
1) Futures Price Leads Spot Price
In several markets, most of the studies on the relationship between spot and
futures price found that the futures market plays their price discovery role by leading
the spot market.
For the studies that were conducted during the year of 1987-1999, Kawaller,
Koch, and Koch (1987) found that futures price movement leads the spot index
movement by around 20-45 minutes. Similarly, Stoll and Wheley (1990), who
investigated the causal relationship between intraday returns on stock index and the
returns on stock index futures, found that returns on S&P500 and Major Market index
futures tend to lead the returns on stock market by around 5 minutes, on average. Tan,
Mark, and Choi (1992) investigated the relationship between the Hang Seng index
futures contracts that are traded in Hong Kong market and its underlying Hang Seng
index in spot market. The result shows that futures prices lead spot index price in pre-
crash period. The results on the studies by Stoll and Whaley (1990), Chan (1992), and
Tse (1999) also found that the futures market leads the spot market.
For the studies that were conducted in 2000s, Alphonse (2000) studied on the
efficient price discovery in French stock index cash and futures markets. The result
shows that deviations from the equilibrium relationship are transmitted from futures
market to the cash market. Brooks, Rew, and Ritson (2001) investigated the causality
15
relationship between the prices in spot and futures market of FTSE 100 index. They
applied Engle-Granger method and found that the spot and futures prices have a
strong relationship. They also found that changes in the spot price of index depend on
the lagged changes in spot price index and also futures price. Mattos and Garcia
(2004) study the relationship between cash and futures price in Brazilian agricultural
futures market by focusing on the trading activity impact on price discovery process
of futures market. They found that futures price play more dominant role in the
pricing process. Zapata, Fortenbery, and Armstrong (2005) investigated the
relationship between the futures prices of sugar in New York and the world spot
prices of exported sugar. They found that futures price of sugar leads the price in spot
market in price discovery. Karnade (2006) studied on the linkage between the castor
seed futures in Indian market and spot market by applying the cointegration analysis.
The result shows that futures markets in Mumbai and Ahmedabad are cointegrated.
Overall there was a unidirectional causality from futures to spot market (futures
market leads spot market). Pok (2007) has investigated the impact of the change of
the combination of market agents on the arrival time of the information in Bursa,
Malaysia. In his study, the price discovery role of futures market to spot market was
investigated using three separated sub-periods, which are pre-crisis, crisis, and after
capital control. The Johansen, VECM and Granger causality tests were used in this
analysis. He found that the significant long-run relationship does not exist, but for a
short-run relationship, the results indicate that futures prices lead spot index. Debasish
(2009) investigated the causality of relationships between the Nifty stock market
index in National Stock Exchange (NSE) in India and its options and futures
contracts, and also the derivatives markets’ interrelation by applying ARMA analysis,
and found that the futures price leads the spot price; however, this lead is found to be
reducing slightly over time.
For more recent studies, Hernandez and Torero (2010) investigated the dynamic
relationship between futures and spot prices of agricultural commodities by applying
Granger causality tests to investigate the direction of the flows of information
between futures and spot prices. The results indicate that, most of the time, the
changes in spot prices are led by the change in futures prices. Iyer and Pillai (2010)
16
conducted a research to study whether futures markets play their role in the price
discovery process in Indian market, and found that the process of price discovery
happening in the futures market in five out of six commodities.
In the context of Thailand, Nittayagasetwat and Nittayagasetwat (2010)
investigated the relationship between the spot price and futures price of Ribbed
Smoked Rubber Sheet No. 3 (RSS3) during May 2004 to August 2009, and found that
spot and futures prices are cointegrated. Error Correction Model (ECM) was applied
and found that futures prices lead spot prices. Thongthip (2010) studied the lead-lag
relationship and mispricing of SET50 index in spot and futures market by using both
5-minute prices and daily prices of SET50 Index and SET50 Index futures in the
trading period from October 1, 2008 to September 29, 2009. The Engle Granger and
Johansen methods were applied and found that the SET50 Index spot and futures
prices move together in the long-run. The VECM was applied and found that SET50
Index futures return seemed to lead the SET50 Index spot return under 5-minute data,
while SET50 Index futures return may be independent to SET50 Index spot return
under daily data. Moreover, Granger causality test was applied and found that the
SET50 Index futures leads the index spot return under 5-minute data, however, there
is no lead-lag relationship under daily data. The study also constructed the upper and
lower no-arbitrage bounds and found some mispricing of SET50 Index futures which
may lead to arbitrage opportunities. Songyoo (2013) studied technical trading strategy
in spot and future markets by using 10-minute prices of SET50 Index and SET50
Index futures in the trading period from September 12, 2011 to November 11, 2011.
The Engle and Granger test was applied to test the cointegration. VECM was applied
to test price discovery. The study found that the two prices are mean-reverting. The
study also applied Granger causality test and found that, most of the time, futures
price movement leads its underlying spot price but, for some certain periods, eventual
relationship can be bi-directional.
17
2) Spot Price Leads Futures Price
The spot prices also found to lead the futures price in some markets. Ehrich
(1969) studied the spot-futures price relationships of the live beef cattle markets
during 1948 to 1966. The results suggested that there were long run price
relationships between the spot and futures prices of the sample market and it was also
found that the spot markets lead the futures markets. Shyy, Vijayraghavan and Scott-
Quin (1996) investigated the lead-lag relationship between the cash market and stock
index futures market by using the bid-ask quotes in the France context, and found that
the spot or cash markets leads the stock index futures market. Under Malaysian
context, the study by Zakaria and Shamsuddin (2012) also suggested that the spot
market leads the future market.
3) Bilateral Causality between Futures Price and Spot Price (feedback effect)
Another possible empirical result is bilateral causality of relationship, which is
supported by the study of Tan, Mark, and Choi (1992). They studied on the
relationship between the Hang Seng index futures contracts and its underlying Hang
Seng index in spot market and found that a bilateral causality exists between these
two variables in post-crash period. Similar results are found on the studies by
Abhyankar (1998) who studied on UK stock index futures market, Liu and Zhang
(2006) on Chinese spot-futures markets, and Mukherjee and Mishra (2006) on Indian
stock index in spot-futures markets. Additionally, Fassas (2010) examined the
dynamic relationship between the spot price of FTSE/ASE-20 index and its futures
price index, and also their respective volatilities. The results revealed that the bilateral
causality is running between these spot and futures indices. Choudhary and Bajaj
(2012) investigated the relationship between spot and futures markets in the Indian
stock market in the role of assimilation of information and price discovery. They
found that there is a bi-directional information flows or feedback effect between the
spot and futures markets.
18
4) No Relationship between Futures Price and Spot Price (independence)
MacDonald and Taylor (1988b) investigated the efficiency and cointegration of
metals prices traded in London Metal Exchange. They found that monthly price series
for lead, tin and zinc are I(1). However, none of the metals is cointegrated with each
other. Kenourgios and Samitas (2004) studied the efficiency of copper futures market
traded in London Metal Exchange where both long-run and short-run relationships
were tested and found that this market is inefficient and futures prices do not provide
unbiased estimates of the future spot prices. Chowdhury (1991) and Beck (1994) also
conducted the studies on London Metal Exchange and found that the futures price and
spot price movements are independent.
19
20
21
2.3 Explanation on Ribbed Smoked Rubber Sheet No.3 and SET50 Index
The two pairs of relationships that were selected to study in this paper are as
follows:-
1) Ribbed Smoked Rubber Sheet No.3 (RSS3) VS. Ribbed Smoked Rubber
Sheet No.3 (RSS3) Futures
Natural rubber (NR) is one among the perennial crops subjected to price
stabilization schemes under various historical contexts (Corea, 1992). World prices of
rubbers are subject to the changes in demand and also the force from speculation
regarding futures markets. Thailand is the number one of the world’s largest rubber
producers, while the major futures markets for rubber are in Japan and Singapore
(Chang, Khamkaew, McAleer, & Tansuchat, 2011).
Thailand produced natural rubber about 3.53 million tons domestically and have
exported more than 2.95 million tons in 2011, while the No.2 and 3 producers are
Indonesia and Malaysia, which produced about 3.09, and 1.00 million tons
respectively (Rubber Research Institute Of Thailand, 2013). For domestic
consumption, natural rubber was generally used in a tire industry, rubber stick, latex
glove, and also condom. For export, the important Thai rubber customers are the
United States and Japan. Ribbed smoked rubber sheet (RSS3) takes a largest portion
of the rubber production in Thailand, since it is easy to transport, storage and it is
globally accepted standard (Agricultural Futures Exchange of Thailand, 2013).
In futures market, the RSS3 was listed on AFET on May 28, 2004, with 5,000
kilograms or 5 metric tons per one trading unit and 20,000 kilograms or 20 metric
tons per one delivery unit. The contract months are seven consecutive months from
the nearest contract month. AFET requires "International Standards of Quality and
Packing for Natural Rubber Grades" (IRQPC) as the RSS3 standard for the contract
specification for natural rubber. This standard of RSS3 is widely accepted
domestically and also internationally in rubber trading community. Additionally, the
22
RSS3 could also be used as a hedging tool to other kinds of rubber (Agricultural
Futures Exchange of Thailand, 2013).
Generally, the movement of spot price and futures price of rubber are parallel
since they are influenced by the same factors and will be converged in the expiration
months because of arbitrage activities between the two markets and also the declining
in carrying charges. Most of the time, futures prices can be used as a reference price
for physical trading and futures contracts can directly be used to facilitate physical
trade. Futures markets allow risk shifting because it can be used as a tool for hedging
for risk aversion (The Rubber Economist, 2013). Price discovery is one of main duties
of the futures market; it would help the producers to plan and manage their activities
and time frame on production, processing, storage, and also marketing of
commodities (Khan, 2006). It is generally argued that price discovery is greater
efficient in futures market than in spot market (Brockman & Tse, 1995; Yang &
Leatham, 1999). The availability and effective dissemination of relevant information
helps to stabilize the spot price by decrease their volatility. Hence, futures trading
infuse efficiency in the functioning of a commodity market (Tomek, 1980; Karnade,
2006).
2) SET50 Index VS. SET50 Index Futures
SET50 Index was launched by the Stock Exchange of Thailand (SET) in 1995 as
Thailand’s first large-cap index in order to provide a benchmark of the investment in
SET. It includes the prices of stocks ranked in the top 50 listed companies on SET in
terms of the large market capitalization, high liquidity and also compliance with the
requirements regarding shares distribution to the minor shareholder (Stock Exchange
of Thailand, 2013).
SET50 Index Futures is the first product listed on TFEX. It was introduced on
April 28, 2006, with contract months of the 3 nearest consecutive months and next 3
quarterly months. The 3 nearest consecutive month’s contracts are available since
November, 2012; previously the contracts are available only in quarterly months.
23
SET50 Index Futures got a No-Action Letter issued from Commodity Futures Trading
Commission (CFTC) on Nov 26, 2008 to allow the residents of the United States to
trade it on TFEX (Thailand Futures Exchange, 2013).
According to the theory of efficient market, arbitrage opportunities does not exist,
the returns from derivative securities such as stock index in futures market should
neither lead nor lag returns from the stock index in spot market, and the correlation of
these two indices returns should be matched with each other perfectly (De Jong &
Donders, 1998). Meanwhile, in imperfect markets, where the information was not
fully informed to everyone and the transaction costs exist, the cheaper market would
be preferred by traders. Since, trading in futures markets requires only a little upfront
cash, this benefit of lower cost could cause futures price to lead spot price. The
studies by Modest and Sundaresan (1983), and Mackinlay and Ramaswamy (1988)
found that futures prices shift considerably from their theoretical prices. They found
that the futures markets index movements lead the movements in stock index in spot
market. In this case, it could be said that the futures market has been considered as a
vehicle for price discovery in the spot market. However, Cornell and French (1983)
opposed that there is an equilibrium condition exists between the spot prices and its
futures prices.
24
CHAPTER III
RESEARCH METHODOLOGY
The data collection, methodology, and hypotheses testing would be discussed in
this chapter.
3.1 Data Collection
The data that are used in this paper are gathered from three sources as follows:-
3.1.1 The daily spot prices of RSS3
The daily spot prices of RSS3 in the period of May 28, 2004 – May 31, 2013 are
gathered from The Rubber Replanting Aid fund’s website, by using the daily spot
prices of RSS3 in Hat Yai central rubber market, the first central rubber market in
Thailand, as a proxy for spot price of RSS3 in all markets in Thailand, since the data
on the other two markets are not fully available through the required study period.
3.1.2 The daily futures prices of RSS3
The daily futures prices of RSS3 in the period of May 28, 2004 – May 31, 2013
are the daily settlement prices gathered from Agricultural Futures Exchange of
Thailand (AFET)’s website. The RSS3 futures data would be constructed by using a
roll-over of the nearest month futures contract.
3.1.3 The daily spot prices of SET50 index
The daily spot prices of SET50 index in the period of April 28, 2006 – May 31,
2013 are the daily close prices gathered from SETSMART Multi-Market database of
Stock Exchange of Thailand (SET).
25
3.1.4 The daily prices of SET50 index futures
The daily prices of SET50 index futures in the period of April 28, 2006 – May
31, 2013 are the daily settlement prices gathered from SETSMART Multi-Market
database. The SET50 index futures data would be constructed by using a roll-over of
the nearest month futures contract.
3.2 Methodology
This paper aims to investigate the long-run and short-run relationships between
spot prices and future prices. In order to test these relationships, all variables used in
the model are required to be stationary in the same order and have the long-run
relationship or cointegrated. Hence, the time series analysis that should be used in this
paper are (1) unit root tests in order to test the stationarity properties of the time
series, (2) cointegration test to test the existence of long-run relationship, and (3)
error-correction tests to test the short-run dynamics in the relationship between spot
prices and futures prices. All time series data are transformed to be in natural
logarithm form. This section provides a brief explanation of these tests as follows:-
3.2.1 Unit Root Tests
The existence of unit roots in time series implies that a series is non-stationary.
The Augmented Dickey-Fuller (ADF) tests (Dickey & Fuller, 1981) would be applied
in this paper to test the unit root by running the OLS regression of the first difference
of the time series on the time series lagged one period, lagged difference terms and
optionally a constant and a time trend. This can be expressed as on the below
equation:
(1)
where yt represents the first difference of the time series at time t, t represents time
trend, yt-1 represents the time series lagged one period, yt-i represents the lagged
difference terms, and Ԑt represents the error term.
According to the ADF tests, the null hypothesis (Ho) of δ = 0 would be tested to
identify whether the series hold a unit root and is then considered as non-stationary.
26
This null hypothesis would be rejected when δ is significantly negative. If the
calculated value of ADF statistics is greater than the McKinnon’s critical values, then
the null hypothesis would not be rejected and it can be concluded that the time series
is non-stationary or not integrated of order zero I(0). The failure to reject the null
hypothesis leads to implementing the test on the difference of the series, so further
differencing is implemented until stationarity is reached and the null hypothesis is
rejected. In order to go to further steps, the unit root tests need to be carried out to
make sure that all time series are integrated of the same order; though the time series
are non-stationary in their levels (I(0)), they can be integrated with I(1), when their
first difference are stationary.
3.2.2 Cointegration Tests
The cointegration test could be used to discover the existence of the long-run
relationship between the spot and futures prices. If the result in unit root test shows
that two or more time series are non-stationary in their levels but integrated of the
same order, the cointegration test would be conducted to test whether their linear
combination is stationary at I(0) implying that they are cointegrated. The two or more
time series are said to be cointegrated when the residual of their cointegrating
regression is stationary. Statistically, the long-term relationship implies that the
variables move together in the long-run, therefore the short-run deviations from the
trend in long-run would be corrected (Manning and Andrianacos, 1993). Generally,
the cointegration test would clarify that if two or more series move closely together in
the long-run, although these series are trended, the difference between them is
stationary, these series could be considered to have long-run equilibrium relationship.
However, a lack of cointegration relationship means that the two or more series do not
have a long-run relationship or they can deviate away from each other (Dickey,
Jansen, & Thornton, 1991).
There are two tests for cointegration that are widely used empirically; the single
equation based on Engle and Granger (1987) test and the systems based on Johansen
(1988) test.
27
3.2.2.1 Engle-Granger Method
The Engle and Granger (1987) proposed the single equation based method by the
two-step procedure in order to model the relationship between cointegrated variables.
This test is very popular in the recent years, since it reduces the number of
coefficients to be estimated; hence, it would also reduce the multicollinearity
problem.
Their steps are as follows:
First, estimating the long-run relationship cointegrating regression by OLS
regression:
(2)
where st represents the time series of spot prices, ft represents the time series of
futures prices, and Zt represents the residuals.
Second, retaining the residuals from cointegrating regression in first step:
(3)
Then applying the ADF tests to these residuals as in the equation below:
(4)
where zt represents the first different of residuals at time t, zt-1 represents the
residuals lagged one period, zt-1 represents the first different of residuals lagged one
period, and Ԑt represents the error term.
According to the equation in ADF tests above, the null hypothesis of H0: θ = 0
would be tested against the alternative hypothesis of Ha: θ < 0 using the appropriate
critical values (Engle & Yoo, 1987). If the null hypothesis is rejected, it means that
spot price (st) and futures price (ft) are cointegrated and the residual Zt is a I(0)
28
process or stationary. On the other hand, if st and ft are not cointegrated, the residual
Zt is a unit root process (non-stationary). Hence, whether st and ft are cointegrated or
not, it would conform to whether the Zt follows a unit root process.
3.2.2.2 Johansen Method
The second method proposed by Johansen (1988). This method is considered as
the system method which helps us find out the number of cointegrated relationship
and estimate them by using Maximum Likelihood Estimation in the unified
framework. Particularly, Johansen suggests a multivariate alternative approach. This
approach is to test for multiple cointegrating vectors and would investigate the long
run relationship between variables, by depending on the relations between the rank of
a matrix and its characteristic roots (Eigen values).
If the result shows that system has independently cointegrated relations, then
the following model is tested:
(5)
This model is used to test for the number of characteristic roots which are not
different significantly from the unity, where represents the number of the
characteristic roots being estimated and represents the number of the applicable
observations. The null hypothesis of Johansen trace tests for cointegration is that there
are no more than cointegrating relations , while the alternative hypothesis is
that there are greater than h cointegrating relations .
In addition, the following maximum Eigen value test statistic model could also be
applied:
(6)
29
This model is to test the null hypothesis that the number of cointegrating vectors is
opposed to the alternative hypothesis that .
However, according to Cheung and Lai (1993), the trace test in model (5) is more
vigorous than the maximum Eigen value test; hence, the trace statistic would be used
in this paper.
In order to decide which method is more appropriate for this study, it is widely
acknowledged that the statistical properties of the Johansen (1988) method are
generally better and also have higher power in the cointegration test than the Engle
and Granger (1987). However, their econometric methodologies are different and
could not be compared directly. Hence, the Johansen method could be used as a
confirmation test of the Engle-Granger method. According to Charemza and
Deadman (1992), the single equation based method of Engle-Granger and the systems
based methods of Johansen should be seen as a complementary rather than substitute.
Hence, this paper will use both Engle-Granger and Johansen methods to test for long-
run relationship (cointegration) between spot prices and futures prices.
3.2.3 Vector Error Correction Model (VECM) Tests
The above cointegration test considers only the long-run relationship between
variables; it does not explicitly capture the short-run dynamics in the relationship
between spot prices and futures prices. If the time series are found to be cointegrated,
their short-run dynamics may be deviated from this equilibrium. The next step is to
test whether such disequilibrium converges to the long-run equilibrium or not. The
dynamic model that is suitable for detecting the short-run dynamics between variables
would be Error-Correction Mechanism (ECM) (Engle & Granger, 1987). The single-
equation ECM can be expressed as shown below:
(7)
where the error-correction term is =
30
ECM provides a means whereby a proportion of the disequilibrium is corrected in
the next period; it is a tool to reconcile the short-run and long-run behavior. The short-
run dynamics in the relationship between spot price and futures price are dominated
by any deviation from long-run equilibrium namely “error-correction terms ( ).” If
the variables are cointegrated, the residuals from the cointegrating regression in
Engle-Granger test can be used to estimate an Error-Correction Model.
The VECM (Johansen, 1995) extends the single-equation ECM to allow y and x
to develop jointly over time. In case of the model with two variables, there will be
only one cointegrating relationship. Hence, if futures price (f) and spot price (s)
sequences are cointegrated, the VECM can be presented as:
(8)
(9)
where the error-correction term is , the in error-correction
term is a cointegrating coefficient,. s represents the first difference of spot prices, f
represents the first difference of futures prices, and Ԑ represents the error term.
From the error-correction model, the and are the coefficients of the lags of
, capturing the short-run effects of in the prior period on dependent variable in
the current period. And and are coefficients of lag of , capturing the short-
run effects of in the prior period on dependent variable in the current period. The
and capture the rate at which the dependent variables adjust to the equilibrium
state after a deviation. In other words, it captures the speeds of error-correction.
As the magnitude of the residual is the deviation from long-run relationship
in the prior period; therefore, it is possible to use the retained residuals that is
obtained from cointegrating regression in model (2) in Engle-Granger testing as an
error-correction term in these ECM models. Notice that implies an equilibrium
31
error occurred in the prior period. If is non-zero, the model is out of equilibrium
and vice versa.
3.3 Research Hypotheses
As the objective of this paper is to investigate the existence of long-run
relationship by testing the cointegration and short-run relationship by testing the error
correction model between spot and futures prices in context of Thailand, the
following hypotheses are then tested:-
Unit root hypothesis:
The first test to be carried out is unit root test to make sure that the time series of
spot prices and futures prices are integrated (or being stationary) in the same order, in
order to proceed to the cointegration test in the next step.
H1o: The RSS3 time series contains a unit root.
H1a: The RSS3 time series does not contain a unit root.
H2o: The RSS3 futures time series contains a unit root.
H2a: The RSS3 futures time series does not contain a unit root.
H3o: The SET50 Index time series contains a unit root.
H3a: The SET50 Index time series does not contain a unit root.
H4o: The SET50 Index futures time series contains a unit root.
H4a: The SET50 Index futures time series does not contain a unit root.
Cointegration hypothesis:
After the spot and futures prices are found to be integrated in the same order, the
cointegration test would be applied to test for the long-run relationship by the
following hypotheses:
32
H5o: There is a significant long-run relation between futures prices and spot prices
of RSS3.
H5a: There is no significant long-run relation between futures prices and spot prices
of RSS3.
H6o: There is a significant long-run relation between futures prices and spot prices
of SET50 index.
H6a: There is no significant long-run relation between futures prices and spot prices
of SET50 index.
Error-correction hypothesis:
After the spot and futures prices are found to have long-run relationship from the
above cointegration hypotheses testing, the second objective which aims to determine
the short-run dynamics in the relationship between spot and futures prices would be
tested by the following hypotheses:
H7o: There is no significant short-run relation between futures prices and spot
prices of RSS3.
H7a: There is a significant short-run relation between futures prices and spot prices
of RSS3.
H8o: There is no significant short-run relation between futures prices and spot
prices of SET50 index.
H8a: There is a significant short-run relation between futures prices and spot prices
of SET50 index.
33
CHAPTER IV
PRESENTATION AND CRITICAL DISCUSSION OF RESULTS
The empirical results obtained from Unit Root tests, Cointegration tests, and
VECM tests are presented separately into three parts. For the first part, the results
from Unit Root tests are presented to check for stationary properties of all data series.
The second part reports the results of Cointegration tests to see the long-run
relationships between spot and futures prices. The short-run relationships between
spot and futures prices are presented in the third part.
4.1 Unit Root Tests
The results from the unit root tests are presented in Table 3. For the test on level
series, all computed values of ADF statistics for all series are found to be not
significant at five percent significant levels. Hence, the test fails to reject the null
hypothesis of unit root at level of the series, which indicates that all series being
studied are not I(0) or being non-stationary at level. Consequently, the unit root test
has been carried out at first difference of the series. The results indicate that all ADF
statistics for first difference series are significant at 5 percent. The results from unit
root tests indicate that the series are stationary at first difference or I(1).
Table 3: Results from Unit Root Tests
Series
ADF
Level 1st Diff.
t-Statistic
Critical Value
(5%) t-Statistic
Critical Value
(5%)
RSS3 Spot -1.75202 -2.862221 -47.5158* -2.862221
RSS3 Futures -1.752853 -2.862221
-
28.01424* -2.862221
SET50 Spot -0.292272 -2.862456
-
53.70051* -2.862456
SET50 Futures -0.418673 -2.862456
-
55.58328* -2.862456
* Denotes for 5% significant level (MacKinnon (1996) one-sided p-values)
34
4.2 Cointegration Tests
After all data series are found to be stationary at first difference, the cointegration
test would be the next step. In order to conduct the Johasen cointegration test, the lag
length selection process should be made by using VAR lag order selection criteria,
this process can be found on Appendix B. There are many criterions available in this
process, however in this paper we would follow the Schwarz information criterion
(SIC) by choosing the lag order that give us the lowest SIC. The lag length for
Johansen cointegration tests and VECM tests are the results from VAR lag order
selection criteria minus one. For RSS3 spot and futures price series, the result is one
lag. For SET50 index spot and futures price series, the result is five lags.
The cointegration tests have been carried out between spot price series and
futures price series for RSS3 and also for SET50 index by using those appropriate
lags. The results from the Johansen cointegration tests are presented in Table 4. Trace
statistics in Table 4 for the cointegration rank tests between RSS3 spot prices and
RSS3 futures prices indicate that at least there is one cointegrating equation exist
between the two variables at 5 percent significant levels. Similarly for SET50 index,
the trace test also found that there is at least one cointegrating equation between
SET50 index spot prices and SET50 index futures prices. These results confirm the
existence of a long-run relationship between RSS3 spot prices and RSS3 futures
prices, and between SET50 index spot prices and SET50 index futures prices.
Table 4: Results from Johansen Cointegration Rank Test (Trace)
Variables
Hypothesized
No. of CE(s) Eigenvalue
Trace
Statistic
Critical
Value
(5%) Conclusion
RSS3
None* 0.042578 145.7186 15.49471 1 cointegrating equation
At most 1 0.000794 2.612113 3.841466
SET50
None* 0.022720 59.62463 15.49471 1 cointegrating equation
At most 1 8.32E-05 0.215132 3.841466
*Denotes rejection of the hypothesis at the 5% significant level
35
For the cointegration tests by Engle-Granger method, the results lead to the same
conclusion as Johansen method, which is there are long-run relationship between
RSS3 spot prices and RSS3 futures prices, and between SET50 index spot prices and
SET50 index futures prices. The detailed results can be found in an Appendix B.
4.3 Vector Error Correction Model (VECM)
After the long-run relationships are found in each pair of variables, the next step
would be the test for investigating their short-run relationship by Vector Error
Correction Model (VECM). The results from VECM tests are presented in Table 5
and Table 6.
From Table 5, the results from running VECM test on RSS3 data (Equation 8 and
9) show that the speed of adjustment coefficients and of both RSS3 spot return
and RSS3 futures return equations are statistically significant at 95% level of
confidence. A negative and positive lead to the prediction that the RSS3 spot
price will decrease with 0.0619 speed and the RSS3 futures prices will increase with a
0.0337 speed of adjustment, when the actual RSS3 futures price is lower than the
cost-of-carry fair value. These magnitudes represent for 1/0.0619 = 16 periods (or 16
days) and 1/0.0337 = 30 periods (or 30 days) of adjustments of RSS3 spot and futures
prices to move back to their long-run equilibrium, respectively. For the lead-lag
relationship; in RSS3 spot return equation, the result shows that the lag of RSS3
futures return (∆lnFt-1,T) has a predictive power on the current return of RSS3 spot
(∆lnSt,T) with a 95% level of confidence. For RSS3 futures return equation, the result
also shows that the lag of RSS3 spot return (∆lnSt-1,T) has a predictive power on the
current return of RSS3 futures (∆lnFt,T).
36
Table 5: Results from VECM Test for RSS3
RSS3 ∆lnSt,T ∆lnFt,T
Zt-1 -0.061922* 0.033722*
(0.00927) (0.00811)
∆lnSt-1,T 0.099248* 0.152994*
(0.02135) (0.01867)
∆lnFt-1,T 0.204620* 0.034511
(0.02448) (0.02140)
constant 0.000103 0.000106
(0.00026) (0.00023)
* Denotes that the values are significant at 5% level (Critical Value: 1.96)
Standard errors are presented in parentheses.
Table 6 shows the results from running VECM test on SET50 index data, the
speed of adjustment coefficient for only of SET50 index futures return equation is
statistically significant at 95% level of confidence. A positive leads to the
prediction that the SET50 index futures price will increase with 0.0949 speed of
adjustment, when the actual SET50 index futures price is lower than the cost-of-carry
fair value. This magnitude represents for 1/0.0949 = 11 periods (or 11 days) of
adjustments of SET50 index futures prices to move back to its long-run equilibrium.
For the lead-lag relationship; in SET50 index spot return equation, the result
shows that there is no lag of SET50 index futures return (∆lnFt-i,T) that has a power to
predict the current return of SET50 index spot (∆lnSt,T) with a 95% level of
confidence. For SET50 index futures return equation, the result shows that the second
lag of SET50 index spot return (∆lnSt-2,T) has a predictive power on the current return
of SET50 index futures (∆lnFt,T).
37
Table 6: Results from VECM Test for SET50 Index
SET50 Index ∆lnSt,T ∆lnFt,T
Zt-1 -0.00041 0.094913*
(0.03723) (0.04165)
∆lnSt-1,T -0.180039* 0.125012
(0.07012) (0.07844)
∆lnSt-2,T 0.057521 0.206766*
(0.07133) (0.07980)
∆lnSt-3,T -0.09673 0.079789
(0.06964) (0.07790)
∆lnSt-4,T -0.01386 0.133609
(0.06902) (0.07721)
∆lnSt-5,T -0.049916 0.047262
(0.06463) (0.07230)
∆lnFt-1,T 0.122340 -0.184277*
(0.06397) (0.07156)
∆lnFt-2,T -0.003101 -0.14495*
(0.06526) (0.07300)
∆lnFt-3,T 0.092277 -0.086078
(0.06364) (0.07119)
∆lnFt-4,T 0.019839 -0.120034
(0.06305) (0.07053)
∆lnFt-5,T 0.088422 -0.019008
(0.05874) (0.06571)
constant 0.000240 0.000240
(0.00027) (0.00030)
* Denotes that the values are significant at 5% level (Critical Value: 1.96)
Standard errors are presented in parentheses.
38
CHAPTER V
CONCLUSION, IMPLICATION AND FURTHER STUDY
This chapter is presented the conclusion of this paper, the implication is also
discussed. Moreover, the suggestions for further study regarding empirical
investigation on the lead-lag relationships between futures prices and spot prices
based on Thai data is also presented.
5.1 Conclusion
There are two main objectives in this paper. The first one is to empirically
investigate the existence of long-run relationship between spot and futures prices in
context of Thailand by using the daily prices of the most active futures products from
AFET and TFEX markets as a proxy. The RSS3 and SET50 index were selected to
study. All data series are found to be stationary at first difference in the process of
Unit Root tests. After that the Cointegration tests were applied, both Johansen and
Engle-Granger methods lead to the same result which prove that there are long-run
relationships between RSS3 spot prices and RSS3 futures prices and between SET50
index spot prices and SET50 index futures prices.
The second objective is to detect the short-run dynamic relationship between spot
and futures prices in context of Thailand. The Vector Error Correction Model
(VECM) was applied to investigate the speed of adjustment to long-run equilibrium
after any short-run deviation and the short-run lead-lag relationship between spot and
futures prices of both RSS3 and SET50 index. The results show that RSS3 futures
return has a predictive power on the RSS3 spot return. Additionally, the RSS3 spot
return also has a predictive power on the RSS3 futures return. However, in case of
SET50 index, the result shows that the SET50 index futures return does not provide
any predictive power on the SET50 index spot return. While, the second lag of SET50
index spot return has a predictive power on SET50 index futures return.
39
The finding implicates that in case of Thailand, there is bidirectional relationship
between the spot and futures prices of RSS3. However, for SET50 index, the results
indicate that the spot prices lead the futures prices. In conclusion, the spot prices
seemed to have more predictive power to lead the futures prices than vice versa. This
is contradicted with the findings from the majority of previous studies in the case of
developed markets which most of them found that futures prices lead spot prices.
However, the finding from this study is consistent with the findings from other studies
such as by Zakaria and Shamsuddin (2012) that found the opposite, spot prices lead
futures prices. Chan et al. (1991) stated that this result can be interpreted as there are
spurious leads induced by infrequent trading in futures market.
These results suggest that in case of Thailand stock market, the information flows
from spot market to futures market. This may implies that spot market in Thailand
reflects to the information faster than the futures market, or futures market in Thailand
did not play a price discovery role for stock index price. Consequently, the futures
stock index prices cannot be used as an indicator for the movements in the stock index
price in spot market in Thailand. The results could also imply that financial investors
in Thailand used information in spot market to trade in futures market, and not vice
versa. This may due to the fact that the financial investors in Thailand are more
actively traded in stock market than in futures market which can be considered as new
market to Thai investors.
5.2 Implication
The results of this paper are beneficial to both Thai and foreign investors and
speculators who participate in the trading of RSS3 and SET50 index. They can hedge
their exposure or speculate their returns by investing in RSS3 futures and SET50
index futures properly. Additionally, the rubber tree planters will also get the benefit
from the results of this paper in constructing their hedging strategies to prevent
themselves from unfavorable price movements in the time of harvesting. Moreover,
the corporations that sell or export rubbers and its related products and corporations
that use rubbers as their main raw material can also use the results of this paper to
construct their hedging program more properly.
40
5.3 Further Study
In order to solve the limitations of this paper, the further study on this issue
would be recommended. To make a general conclusion about the relationship between
spot and futures prices in Thailand context, the prices of many futures products should
be investigated. This paper use the prices of only 2 products to investigate, since
many other futures products in Thailand are newly traded which have the historical
prices available less than 5 years. The further study should be extended to use more
futures products if there are enough historical prices available in later time. The
further study should also cover the limitation on the spot prices of RSS3. This paper
use only the price from Hat Yai central rubber market, the first central rubber market
in Thailand, as a proxy for spot prices of RSS3 in Thailand, due to the limited
availability of data in the other markets. The further study might use the average price
of 3 central rubber markets as a proxy for spot prices of RSS3, if the daily prices on
the other 2 central rubber markets are available.
41
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53
APPENDICES
54
APPENDIX A
Futures Contract Specifications
55
RSS3 Futures Contract Specification
56
SET50 Index Futures Contract Specification
57
APPENDIX B
Tests Results
58
Natural log of RSS3 spot prices
First difference of Natural log of RSS3 spot prices
3.2
3.6
4.0
4.4
4.8
5.2
5.6
04 05 06 07 08 09 10 11 12
LSPOT
-.3
-.2
-.1
.0
.1
.2
04 05 06 07 08 09 10 11 12
DLSPOT
59
Natural log of RSS3 futures prices
First difference of Natural log of RSS3 futures prices
3.6
4.0
4.4
4.8
5.2
5.6
04 05 06 07 08 09 10 11 12
LFUTURES
-.12
-.08
-.04
.00
.04
.08
04 05 06 07 08 09 10 11 12
DLFUTURES
60
Unit Root test for RSS3 spot price series at level
Null Hypothesis: LSPOT has a unit root
Exogenous: Constant
Lag Length: 1 (Automatic based on SIC, MAXLAG=28)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -1.752020 0.4049
Test critical values: 1% level -3.432150
5% level -2.862221
10% level -2.567176
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LSPOT)
Method: Least Squares
Date: 08/03/13 Time: 01:40
Sample (adjusted): 5/30/2004 5/31/2013
Included observations: 3289 after adjustments
Variable
Coefficie
nt Std. Error t-Statistic Prob.
LSPOT(-1)
-
0.001357 0.000774 -1.752020 0.0799
D(LSPOT(-1)) 0.186185 0.017137 10.86475 0.0000
C 0.006055 0.003398 1.781666 0.0749
R-squared 0.035358 Mean dependent var 0.000146
Adjusted R-squared 0.034771 S.D. dependent var 0.015350
S.E. of regression 0.015081 Akaike info criterion
-
5.549885
Sum squared resid 0.747331 Schwarz criterion
-
5.544322
Log likelihood 9129.785 F-statistic 60.22248
Durbin-Watson stat 2.009159 Prob(F-statistic) 0.000000
61
Unit Root test for RSS3 spot price series at first difference
Null Hypothesis: D(LSPOT) has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic based on SIC, MAXLAG=28)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -47.51580 0.0001
Test critical values: 1% level -3.432150
5% level -2.862221
10% level -2.567176
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LSPOT,2)
Method: Least Squares
Date: 08/03/13 Time: 01:58
Sample (adjusted): 5/30/2004 5/31/2013
Included observations: 3289 after adjustments
Variable
Coefficie
nt Std. Error t-Statistic Prob.
D(LSPOT(-1))
-
0.814374 0.017139 -47.51580 0.0000
C 0.000119 0.000263 0.450852 0.6521
R-squared 0.407187 Mean dependent var 2.08E-07
Adjusted R-squared 0.407007 S.D. dependent var 0.019590
S.E. of regression 0.015085 Akaike info criterion
-
5.549559
Sum squared resid 0.748029 Schwarz criterion
-
5.545851
Log likelihood 9128.250 F-statistic 2257.751
Durbin-Watson stat 2.008850 Prob(F-statistic) 0.000000
62
Unit Root test for RSS3 futures price series at level
Null Hypothesis: LFUTURES has a unit root
Exogenous: Constant
Lag Length: 3 (Automatic based on SIC, MAXLAG=28)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -1.752853 0.4044
Test critical values: 1% level -3.432151
5% level -2.862221
10% level -2.567177
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LFUTURES)
Method: Least Squares
Date: 08/03/13 Time: 01:43
Sample (adjusted): 6/01/2004 5/31/2013
Included observations: 3287 after adjustments
Variable
Coefficie
nt Std. Error t-Statistic Prob.
LFUTURES(-1)
-
0.001185 0.000676 -1.752853 0.0797
D(LFUTURES(-1)) 0.123224 0.017408 7.078651 0.0000
D(LFUTURES(-2)) 0.053985 0.017661 3.056653 0.0023
D(LFUTURES(-3)) 0.068113 0.017558 3.879281 0.0001
C 0.005345 0.003001 1.780954 0.0750
R-squared 0.027383 Mean dependent var 0.000136
Adjusted R-squared 0.026198 S.D. dependent var 0.013250
S.E. of regression 0.013075 Akaike info criterion
-
5.834666
Sum squared resid 0.561101 Schwarz criterion
-
5.825390
Log likelihood 9594.273 F-statistic 23.10040
Durbin-Watson stat 2.002064 Prob(F-statistic) 0.000000
63
Unit Root test for RSS3 futures price series at first difference
Null Hypothesis: D(LFUTURES) has a unit root
Exogenous: Constant
Lag Length: 2 (Automatic based on SIC, MAXLAG=28)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -28.01424 0.0000
Test critical values: 1% level -3.432151
5% level -2.862221
10% level -2.567177
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LFUTURES,2)
Method: Least Squares
Date: 08/03/13 Time: 01:59
Sample (adjusted): 6/01/2004 5/31/2013
Included observations: 3287 after adjustments
Variable
Coefficie
nt Std. Error t-Statistic Prob.
D(LFUTURES(-1))
-
0.756025 0.026987 -28.01424 0.0000
D(LFUTURES(-1),2)
-
0.121052 0.023242 -5.208221 0.0000
D(LFUTURES(-2),2)
-
0.067525 0.017560 -3.845316 0.0001
C 9.96E-05 0.000228 0.436306 0.6626
R-squared 0.437013 Mean dependent var 4.67E-07
Adjusted R-squared 0.436499 S.D. dependent var 0.017424
S.E. of regression 0.013079 Akaike info criterion
-
5.834339
Sum squared resid 0.561626 Schwarz criterion
-
5.826918
Log likelihood 9592.736 F-statistic 849.4664
Durbin-Watson stat 2.001943 Prob(F-statistic) 0.000000
64
Residual retained from cointegrating regression on RSS3 data
-.3
-.2
-.1
.0
.1
04 05 06 07 08 09 10 11 12
ERROR
65
Engle-Granger Cointegration test for RSS3 data
Null Hypothesis: ERROR has a unit root
Exogenous: None
Lag Length: 4 (Automatic based on SIC, MAXLAG=28)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -9.636443 0.0000
Test critical values: 1% level -2.565666
5% level -1.940920
10% level -1.616635
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(ERROR)
Method: Least Squares
Date: 08/03/13 Time: 13:46
Sample (adjusted): 6/02/2004 5/31/2013
Included observations: 3286 after adjustments
Variable
Coefficie
nt Std. Error t-Statistic Prob.
ERROR(-1)
-
0.081016 0.008407 -9.636443 0.0000
D(ERROR(-1))
-
0.113505 0.017889 -6.345125 0.0000
D(ERROR(-2))
-
0.049847 0.017947 -2.777442 0.0055
D(ERROR(-3))
-
0.053304 0.017824 -2.990584 0.0028
D(ERROR(-4))
-
0.084305 0.017509 -4.814859 0.0000
R-squared 0.068783 Mean dependent var 8.98E-06
Adjusted R-squared 0.067648 S.D. dependent var 0.013105
S.E. of regression 0.012654 Akaike info criterion
-
5.900186
Sum squared resid 0.525355 Schwarz criterion
-
5.890908
Log likelihood 9699.006 Durbin-Watson stat 2.001243
66
VAR Lag length selection for RSS3 data
(Based on SC, 2 lags are selected)
VAR Lag Order Selection Criteria
Endogenous variables: LSPOT LFUTURES
Exogenous variables: C
Date: 08/03/13 Time: 14:11
Sample: 5/28/2004 5/31/2013
Included observations: 3283
Lag LogL LR FPE AIC SC HQ
0 5926.453 NA 9.28e-05 -3.609170 -3.605456 -3.607841
1 19378.09 26878.69 2.57e-08 -11.80146 -11.79031 -11.79747
2 19506.56 256.5443 2.38e-08 -11.87728 -11.85871* -11.87063
3 19514.50 15.84909 2.38e-08 -11.87968 -11.85369 -11.87038
4 19531.48 33.85556 2.36e-08 -11.88759 -11.85416 -11.87562
5 19549.33 35.58196 2.34e-08 -11.89603 -11.85517 -11.88140*
6 19551.40 4.135291 2.34e-08 -11.89485 -11.84657 -11.87757
7 19556.53 10.21181 2.34e-08 -11.89554 -11.83983 -11.87559
8 19570.61 28.00285* 2.32e-08* -11.90168* -11.83854 -11.87907
* indicates lag order selected by the criterion
LR: sequential modified LR test statistic (each test at 5% level)
FPE: Final prediction error
AIC: Akaike information criterion
SC: Schwarz information criterion
HQ: Hannan-Quinn information criterion
67
Johansen Cointegration test for RSS3 data
(Use 1 lag, since we had 2 for the VAR, so 2-1 = 1 lag for the VEC)
Date: 08/03/13 Time: 16:38
Sample (adjusted): 5/30/2004 5/31/2013
Included observations: 3289 after adjustments
Trend assumption: Linear deterministic trend
Series: LSPOT LFUTURES
Lags interval (in first differences): 1 to 1
Unrestricted Cointegration Rank Test (Trace)
Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.042578 145.7186 15.49471 0.0001
At most 1 0.000794 2.612113 3.841466 0.1060
Trace test indicates 1 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized Max-Eigen 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.042578 143.1065 14.26460 0.0001
At most 1 0.000794 2.612113 3.841466 0.1060
Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Cointegrating Coefficients (normalized by b'*S11*b=I):
LSPOT LFUTURES
-35.97870 36.12630
0.662011 2.297884
Unrestricted Adjustment Coefficients (alpha):
D(LSPOT) 0.001721 -0.000347
D(LFUTURES) -0.000937 -0.000342
1 Cointegrating Equation(s): Log likelihood 19544.98
68
Normalized cointegrating coefficients (standard error in parentheses)
LSPOT LFUTURES
1.000000 -1.004103
(0.00681)
Adjustment coefficients (standard error in parentheses)
D(LSPOT) -0.061922
(0.00927)
D(LFUTURES) 0.033722
(0.00811)
69
VECM test for RSS3 data
(Use 1 lag, since we had 2 for the VAR, so 2-1 = 1 lag for the VEC)
Vector Error Correction Estimates
Date: 08/03/13 Time: 15:53
Sample (adjusted): 5/30/2004 5/31/2013
Included observations: 3289 after adjustments
Standard errors in ( ) & t-statistics in [ ]
Cointegrating Eq: CointEq1
LSPOT(-1) 1.000000
LFUTURES(-1) -1.004103
(0.00681)
[-147.411]
C 0.069821
Error Correction: D(LSPOT)
D(LFUTURES
)
CointEq1 -0.061922 0.033722
(0.00927) (0.00811)
[-6.67729] [ 4.15875]
D(LSPOT(-1)) 0.099248 0.152994
(0.02135) (0.01867)
[ 4.64845] [ 8.19493]
D(LFUTURES(-1)) 0.204620 0.034511
(0.02448) (0.02140)
[ 8.35943] [ 1.61238]
C 0.000103 0.000106
(0.00026) (0.00023)
[ 0.40146] [ 0.47037]
R-squared 0.073501 0.048844
Adj. R-squared 0.072655 0.047976
Sum sq. resids 0.717781 0.548802
S.E. equation 0.014782 0.012925
F-statistic 86.86854 56.23125
Log likelihood 9196.131 9637.558
Akaike AIC -5.589621 -5.858047
Schwarz SC -5.582204 -5.850630
Mean dependent 0.000146 0.000133
S.D. dependent 0.015350 0.013247
70
Determinant resid covariance (dof adj.) 2.37E-08
Determinant resid covariance 2.36E-08
Log likelihood 19544.98
Akaike information criterion -11.87898
Schwarz criterion -11.86044
71
Natural log of SET50 index spot prices
First difference of Natural log of SET50 index spot prices
5.2
5.6
6.0
6.4
6.8
7.2
2006 2007 2008 2009 2010 2011 2012
LSPOT
-.20
-.16
-.12
-.08
-.04
.00
.04
.08
.12
2006 2007 2008 2009 2010 2011 2012
DLSPOT
72
Natural log of SET50 index futures prices
First difference of Natural log of SET50 index futures prices
5.2
5.6
6.0
6.4
6.8
7.2
2006 2007 2008 2009 2010 2011 2012
LFUTURES
-.16
-.12
-.08
-.04
.00
.04
.08
.12
2006 2007 2008 2009 2010 2011 2012
DLFUTURES
73
Unit Root test for SET50 index spot price series at level
Null Hypothesis: LSPOT has a unit root
Exogenous: Constant
Lag Length: 1 (Automatic based on SIC, MAXLAG=27)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -0.292272 0.9237
Test critical values: 1% level -3.432683
5% level -2.862456
10% level -2.567303
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LSPOT)
Method: Least Squares
Date: 08/03/13 Time: 02:08
Sample (adjusted): 4/30/2006 5/31/2013
Included observations: 2589 after adjustments
Variable
Coefficie
nt Std. Error t-Statistic Prob.
LSPOT(-1)
-
0.000255 0.000873 -0.292272 0.7701
D(LSPOT(-1))
-
0.054269 0.019654 -2.761247 0.0058
C 0.001894 0.005571 0.339974 0.7339
R-squared 0.003000 Mean dependent var 0.000253
Adjusted R-squared 0.002229 S.D. dependent var 0.013504
S.E. of regression 0.013489 Akaike info criterion
-
5.772677
Sum squared resid 0.470554 Schwarz criterion
-
5.765888
Log likelihood 7475.730 F-statistic 3.890648
Durbin-Watson stat 1.993639 Prob(F-statistic) 0.020552
74
Unit Root test for SET50 index spot price series at first difference
Null Hypothesis: D(LSPOT) has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic based on SIC, MAXLAG=27)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -53.70051 0.0001
Test critical values: 1% level -3.432683
5% level -2.862456
10% level -2.567303
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LSPOT,2)
Method: Least Squares
Date: 08/03/13 Time: 02:08
Sample (adjusted): 4/30/2006 5/31/2013
Included observations: 2589 after adjustments
Variable
Coefficie
nt Std. Error t-Statistic Prob.
D(LSPOT(-1))
-
1.054484 0.019636 -53.70051 0.0000
C 0.000268 0.000265 1.009337 0.3129
R-squared 0.527121 Mean dependent var -5.73E-06
Adjusted R-squared 0.526938 S.D. dependent var 0.019609
S.E. of regression 0.013487 Akaike info criterion
-
5.773416
Sum squared resid 0.470570 Schwarz criterion
-
5.768890
Log likelihood 7475.687 F-statistic 2883.745
Durbin-Watson stat 1.993630 Prob(F-statistic) 0.000000
75
Unit Root test for SET50 index futures price series at level
Null Hypothesis: LFUTURES has a unit root
Exogenous: Constant
Lag Length: 1 (Automatic based on SIC, MAXLAG=27)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -0.418673 0.9037
Test critical values: 1% level -3.432683
5% level -2.862456
10% level -2.567303
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LFUTURES)
Method: Least Squares
Date: 08/03/13 Time: 02:09
Sample (adjusted): 4/30/2006 5/31/2013
Included observations: 2589 after adjustments
Variable
Coefficie
nt Std. Error t-Statistic Prob.
LFUTURES(-1)
-
0.000405 0.000966 -0.418673 0.6755
D(LFUTURES(-1))
-
0.088336 0.019603 -4.506150 0.0000
C 0.002853 0.006164 0.462881 0.6435
R-squared 0.007924 Mean dependent var 0.000253
Adjusted R-squared 0.007157 S.D. dependent var 0.015156
S.E. of regression 0.015101 Akaike info criterion
-
5.546900
Sum squared resid 0.589743 Schwarz criterion
-
5.540111
Log likelihood 7183.462 F-statistic 10.32775
Durbin-Watson stat 1.993923 Prob(F-statistic) 0.000034
76
Unit Root test for SET50 index futures price series at first difference
Null Hypothesis: D(LFUTURES) has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic based on SIC, MAXLAG=27)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -55.58328 0.0001
Test critical values: 1% level -3.432683
5% level -2.862456
10% level -2.567303
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LFUTURES,2)
Method: Least Squares
Date: 08/03/13 Time: 02:11
Sample (adjusted): 4/30/2006 5/31/2013
Included observations: 2589 after adjustments
Variable
Coefficie
nt Std. Error t-Statistic Prob.
D(LFUTURES(-1))
-
1.088650 0.019586 -55.58328 0.0000
C 0.000275 0.000297 0.928197 0.3534
R-squared 0.544262 Mean dependent var -4.65E-06
Adjusted R-squared 0.544085 S.D. dependent var 0.022362
S.E. of regression 0.015099 Akaike info criterion
-
5.547605
Sum squared resid 0.589783 Schwarz criterion
-
5.543079
Log likelihood 7183.374 F-statistic 3089.501
Durbin-Watson stat 1.993947 Prob(F-statistic) 0.000000
77
Residual retained from cointegrating regression on SET50 index data
-.06
-.04
-.02
.00
.02
.04
2006 2007 2008 2009 2010 2011 2012
ERROR
78
Engle-Granger Cointegration test for SET50 index data
Null Hypothesis: ERROR has a unit root
Exogenous: None
Lag Length: 5 (Automatic based on SIC, MAXLAG=27)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -7.717755 0.0000
Test critical values: 1% level -2.565857
5% level -1.940946
10% level -1.616617
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(ERROR)
Method: Least Squares
Date: 08/03/13 Time: 16:11
Sample (adjusted): 5/04/2006 5/31/2013
Included observations: 2585 after adjustments
Variable
Coefficie
nt Std. Error t-Statistic Prob.
ERROR(-1)
-
0.095165 0.012331 -7.717755 0.0000
D(ERROR(-1))
-
0.310455 0.021284 -14.58653 0.0000
D(ERROR(-2))
-
0.138900 0.021668 -6.410327 0.0000
D(ERROR(-3))
-
0.179591 0.021161 -8.486877 0.0000
D(ERROR(-4))
-
0.137403 0.020958 -6.556068 0.0000
D(ERROR(-5))
-
0.110186 0.019570 -5.630302 0.0000
R-squared 0.169936 Mean dependent var 1.49E-06
Adjusted R-squared 0.168327 S.D. dependent var 0.004904
S.E. of regression 0.004472 Akaike info criterion
-
7.979696
Sum squared resid 0.051574 Schwarz criterion
-
7.966100
Log likelihood 10319.76 Durbin-Watson stat 1.999545
79
VAR Lag length selection for SET50 index data
(Based on SC, 6 lags are selected)
VAR Lag Order Selection Criteria
Endogenous variables: LSPOT LFUTURES
Exogenous variables: C
Date: 08/03/13 Time: 16:12
Sample: 4/28/2006 5/31/2013
Included observations: 2583
Lag LogL LR FPE AIC SC HQ
0 8141.245 NA 6.28e-06 -6.302164 -6.297629 -6.300520
1 17646.54 18988.51 4.01e-09 -13.65895 -13.64535 -13.65402
2 17725.47 157.5650 3.78e-09 -13.71698 -13.69430 -13.70876
3 17732.32 13.66243 3.77e-09 -13.71918 -13.68744 -13.70768
4 17754.21 43.61837 3.72e-09 -13.73303 -13.69222 -13.71824
5 17765.42 22.33165 3.70e-09 -13.73862 -13.68873 -13.72054
6 17789.62 48.14482 3.64e-09 -13.75425 -13.69530* -13.73289*
7 17790.87 2.490750 3.65e-09 -13.75213 -13.68410 -13.72747
8 17797.78 13.73228* 3.64e-09* -13.75438* -13.67729 -13.72644
* indicates lag order selected by the criterion
LR: sequential modified LR test statistic (each test at 5% level)
FPE: Final prediction error
AIC: Akaike information criterion
SC: Schwarz information criterion
HQ: Hannan-Quinn information criterion
80
Johansen Cointegration test for SET50 index data
(Use 5 lags, since we had 6 for the VAR, so 6-1=5 lags for the VEC)
Date: 08/03/13 Time: 16:40
Sample (adjusted): 5/04/2006 5/31/2013
Included observations: 2585 after adjustments
Trend assumption: Linear deterministic trend
Series: LSPOT LFUTURES
Lags interval (in first differences): 1 to 5
Unrestricted Cointegration Rank Test (Trace)
Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.022720 59.62463 15.49471 0.0000
At most 1 8.32E-05 0.215132 3.841466 0.6428
Trace test indicates 1 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized Max-Eigen 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.022720 59.40950 14.26460 0.0000
At most 1 8.32E-05 0.215132 3.841466 0.6428
Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon-Haug-Michelis (1999) p-values
Unrestricted Cointegrating Coefficients (normalized by b'*S11*b=I):
LSPOT LFUTURES
-140.6015 139.2272
8.502475 -5.148617
Unrestricted Adjustment Coefficients (alpha):
D(LSPOT) 2.91E-06 -0.000123
D(LFUTURES) -0.000675 -0.000131
1 Cointegrating Equation(s): Log likelihood 17804.44
81
Normalized cointegrating coefficients (standard error in parentheses)
LSPOT LFUTURES
1.000000 -0.990225
(0.00300)
Adjustment coefficients (standard error in parentheses)
D(LSPOT) -0.000410
(0.03723)
D(LFUTURES) 0.094913
(0.04165)
82
VECM test for SET50 index data
(Use 1 lag, since we had 2 for the VAR, so 6-1=5 lags for the VEC)
Vector Error Correction Estimates
Date: 08/03/13 Time: 16:21
Sample (adjusted): 5/04/2006 5/31/2013
Included observations: 2585 after adjustments
Standard errors in ( ) & t-statistics in [ ]
Cointegrating Eq: CointEq1
LSPOT(-1) 1.000000
LFUTURES(-1) -0.990225
(0.00300)
[-329.828]
C -0.066345
Error Correction: D(LSPOT)
D(LFUTU
RES)
CointEq1 -0.000410 0.094913
(0.03723) (0.04165)
[-0.01100] [ 2.27883]
D(LSPOT(-1)) -0.180039 0.125012
(0.07012) (0.07844)
[-2.56749] [ 1.59367]
D(LSPOT(-2)) 0.057521 0.206766
(0.07133) (0.07980)
[ 0.80639] [ 2.59121]
D(LSPOT(-3)) -0.096730 0.079789
(0.06964) (0.07790)
[-1.38906] [ 1.02425]
D(LSPOT(-4)) -0.013860 0.133609
(0.06902) (0.07721)
[-0.20081] [ 1.73049]
D(LSPOT(-5)) -0.049916 0.047262
(0.06463) (0.07230)
[-0.77231] [ 0.65369]
D(LFUTURES(-1)) 0.122340 -0.184277
(0.06397) (0.07156)
83
[ 1.91248] [-2.57516]
D(LFUTURES(-2)) -0.003101 -0.144950
(0.06526) (0.07300)
[-0.04751] [-1.98554]
D(LFUTURES(-3)) 0.092277 -0.086078
(0.06364) (0.07119)
[ 1.45000] [-1.20913]
D(LFUTURES(-4)) 0.019839 -0.120034
(0.06305) (0.07053)
[ 0.31468] [-1.70195]
D(LFUTURES(-5)) 0.088422 -0.019008
(0.05874) (0.06571)
[ 1.50527] [-0.28926]
C 0.000240 0.000240
(0.00027) (0.00030)
[ 0.90662] [ 0.80802]
R-squared 0.011620 0.018168
Adj. R-squared 0.007394 0.013970
Sum sq. resids 0.466392 0.583637
S.E. equation 0.013463 0.015061
F-statistic 2.749876 4.328224
Log likelihood 7473.664 7183.819
Akaike AIC -5.773047 -5.548796
Schwarz SC -5.745856 -5.521605
Mean dependent 0.000250 0.000251
S.D. dependent 0.013513 0.015167
Determinant resid covariance (dof adj.) 3.60E-09
Determinant resid covariance 3.57E-09
Log likelihood 17804.44
Akaike information criterion -13.75508
Schwarz criterion -13.69616