Relationship of single stock futures with the spot price: Evidence from Karachi Stock Exchange

The study is conducted to investigate the relationship of single stock futures with the spot price in Karachi Stock Exchange. Monthly data of twelve companies which are trading single stock futures have been examined for the period 1 January, 2005 to 31 December, 2010 with total of 72 observations for each company. Descriptive statistics, Unit Root test, Co-integration test, Granger Causality test, Vector Error Correction Model based on ARDL approach, Impulse Response and Variance Decomposition tests are used. The existence of long run relationship was found between the futures and spot prices of all the companies. The Granger Causality test reported that the spot prices of FFBL and LUCK assist in forecasting their respective futures prices. The futures prices of HUBC and POL forecast their respective spot prices and play its important role of price discovery. The impulse response analysis revealed that most of the shocks in the futures markets of all the selected companies are explained by their own innovations and their respective spot markets have less influence on them. Variance decomposition test reported that futures market is an exogenous market as majority of its stocks are explained by its own innovation. The results of VECM shows that in case of disequilibrium the adjustment process is quite fast for all the companies.


Introduction
The impact of derivatives trading on the underlying assets has long been studied but still debatable. Derivatives play an important role in risk management and also facilitating capital flow into the market. As a hedging tool, financial futures provide financial institution the ability to eliminate certain risk of holding the underlying commodity (Stoll and Whaley, 1988). They can also cause excessive leverage on the part of market participant. The derivative markets has grown rapidly in the emerging economies especially in those countries which introduces liberalization in their markets removing capital control and have well developed underlying securities market. The derivatives trading also have some negative aspects and their contribution in financial crises, capital outflow, and volatility spill over in the market, manipulating accounting rules decreases Business Review -Volume 8 Number 1 January -June 2013 54 Garbade and Silber (1983) are considered the first investigators who analyses whether the spot or futures prices first reflects the new information for storable products. The lead lag relationship between spot and futures is based on Granger (1969) and Sims (1972) causality methodology. The Stoll and Whaly (1990) methodology for lead lag relationship is different from Engle and Granger (1987) causality as the former uses price data while the later uses the stock index and stock index futures returns data. Although most of the studies reported that futures lead the spot market, yet some others studies like Stoll and Whaly (1990) and Flemming et al (1996) reported the greater integration between the spot and futures market and has weakened the lead of the futures.
The theoretical investigation into the effects of futures trading on the underlying spot market volatility reports inconclusive results. Subrahmanyam (1991) propose theoretical model to investigate the effect of index futures on the underlying spot market volatility and comes with ambiguous results. Chari and Jagnnahthan (1990) concluded that it is not possible to solve the issue of futures trading effect on underlying spot market volatility with theoretical models. Sameulson (1965) argued that futures prices follow no time trend and the change in future prices will be zero on the expiration date. As the time to expiration date come closer, the volatility of the futures prices should increase called Sameulson hypothesis. He argued that the competitive forces keep the futures prices equal to the expected futures spot prices. As the contract reaches near maturit, the rate of information transmission increases which increases the volatility of the futures prices. Hemler and Longstaff (1991) by using a general equilibrium model reported that the futures returns varies with the underlying market volatility which means the required returns changes with the increase in the level of risk.

Literature review 3.1 Futures and price discovery
Futures role in providing information about expected spot prices in the future have great importance for the investors. The price discovery process has been shown to be dominated by the futures market in that at least ninety-five percent of the price discovery is achieved in the futures market (Alphonse, 2000). Yang et al (2001) examined the price discovery role of the futures market for storable and non storable commodities. Commodities futures prices were collected from Chicago Board of Trade for the period January 1, 1992 to June 30 1998. It is concluded that futures prices provide useful information about storable commodities which are needed by the traders but cannot perform the price discovery function for non storable commodities. Similary results were reported by Covey and Bessler (1995). Coverig , Ding and Low (2004) invesitgated the price discovery of the Nikkei 225 spot market, the foreign futures market and domestic futures market. These studies concluded that the spot market contributed 21% to price dicovery while for domestic and foreign futures market the figure was 46% and 33% respectively. Several other studies such as Khan (2006), Ahmad, Shah and Shah ( 2010 have investigated the role of future in price discovery.
The emprical results in the literature are vaned with most of the studies with the consensus that futures play important role in price discovery.

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January -June 2013 55 3.2 Lead lag relationship Pizzi et al (1998) investigating S&P 500 for one minute returns reported bidirectional causality between the futures and the spot market. The futures lead the spot by 20 minutes and the spot leading the futures by 3 to 4 minutes. Kuo et al (2008) explored Taiwan futures market and observed that futures lead the spot market. Schwarz and Laatsch (1991) used minute to minute data to explore the spot and futures market of MMI. They reported that the relationship between the spot and futures are changing over time. The spot was dominated initially but at the end the futures market lead the spot market.
The literature about the lead lag relationship is also providing mix result with most of the studies converging to the lead of futures market over spot market.

Futures and financial crisis
Almost since futures trading began at the Chicago Board of Trade in 1865, there has been concern about the impact of futures on the underlying spot market (Antoniou and Holmes, 1995).The stock market crash of 1987, the mini crash of 1989, and some more recent highly publicized financial debacles have created the impression that derivatives threaten the stability of the international financial system (Antoniou , Koutmos and Pericli, 2005). Investigating FTSE 100 stock index futures contract on the 19th and 20th October 1987, the evidence seems to suggest that whilst the futures market exacerbated the decline, the cause of the breakdown lies with the stock market (Antoniou and Garrett, 1993).
The literature about futures role in financial crisis are not conclusive and despite its probable role in financial crisis, its benefits seems to outweight the cost and it is still traded on most of world stock exchanges.

Do futures need regulation?
Becketti and Roberts (1990) found no relationship between stock market volatlility and stock index future activity and assume that increasing regulation to decrease futures activity will not solve the problem. Illueca and Lafuente (2003) suggests that regulatory initiatives to limit futures trading premised on the assumption that futures trading tends to destabilize spot market prices are not justified, at least in the Spanish stock index futures market.
We can conclude from the above literature that increasing regulation to decrease futures trading cannot be a viable option. Morris (1990) argued that increasing regulation such is circuit breakers may shift invesitors from Futures trading to stock market trading and will make it more volatile.

Data description and methodology
The study includes monthly end futures and spot prices of twelve companies namely BOP (Bank of Punjab limited), DGKC ( D.G. Khan Cement Co), ENGRO (ENGRO Corporation  Where ' ' is return for the given period t, is natural log, is price at the month end, and is price at the end of last month. The data is analyzed by using the following statistical techniques. I

Descriptive statistics
Descriptive statistics are applied to explain the behavior of data. The techniques used are mean, median, maximum, minimum, standard deviation, skewness, kurtosis, variance and Jarque-Bera values. It summarizes the characteristics of time series data under study.

Unit root test
Co-integration requires that times series should be stationary and should be integrated of same order. Stationary series in the data can be confirmed by using different unit root test. For this purpose ADF test (Augmented Dickey Fuller Test) along with PP test (Phillip-Perron Test) will be used. Augmented Dickey Fuller Test assumes that all the error terms are independently distributed and have a constant variance. Augmented Dickey Fuller Test is assumed a strict parameter due to its strict assumptions. A simple ADF test can be written as An AR (1)  The first Deference of the time series has been taken to make it stationery. Augmented Dickey Fuller test is considered a strict parameter therefore another test can also be applied called Phillip Peron test which is relatively less strict parameter to check for the unit root. Phillip Peron test is explained by using the following equation:

………..……… (1.4)
Johnson and Julius's Approach is applied further to check for the existence of any long term relationship between the time series data.

Vector auto regression (var technique)
Akaike information criterion (AIC) and Schwarz information criterion (SIC) are applied to select proper lag length for Vector Auto regressive process. Selection of lag length is pre-requisite before exploring long term relationship through Co-integration test.

Johansen and Juselius co-integration test
The time series data should be integrated of same order to test for the Co-integration. The assumption of Co-integration is that if two time series are individually non-stationary, their linear combination might be stationery. Co-integration is applied to explore any long term relationship between two or more variables. Although Co-integration does not explain the cause and effect relationship between two variables, it does explore the co-movement between two time series. The test is based on empirical evidence. The relationship between time series might have an economic reasoning behind them and it might not be explained through an economic reason. Two different approaches exist to apply the Co-integration which are: • J.J Approach ( Johnson and Juselius Approach) • ARDL ( Auto Regressive Distribution Lag Approach) The J.J approach of Co-integration is applied on time series which are integrated of the same order, otherwise the ARDL (Auto Regressive Distribution Lag Approach) is used to the test for the Co-integration. In the above equations, and represents the constants, , , and are coefficients whereas m and i represents positive integers and number of values respectively. The error term is represented by .

Granger causality test
Granger Theorem is based on the principal that if two variables are co-integrated, there must be a causal relationship between them at least in one direction. Co-integration investigates the existence of long run relationship but does not explain the lead lag relationship which is important in price discovery. Granger Causality is used to determine the lead lag relationship. If the leading series is determined, the other lag series can be predicted. Causality in one direction is known as unidirectional causality which means the flow of information from one market to another market.
If the existence of lead lag relationship is reported in both directions, it means the flow of information occurs from both sides and both the markets are exerting pressure on each other. This is called bi-directional causality.

Impulse response function
The change in Standard Deviation of one series due to one Standard Deviation change in another series is explained by the impulse response function. The impulse response function is also a good parameter which closely observes the random shocks on the market. It further explains the market response to its own shocks and the shocks due to other market innovations. It also explains the speed of adjustment.

Variance decomposition test
The variance decomposition test explains the proportion of the movements in one variable (dependent variable) that are due to its own shocks versus shocks due to the other variables (independent variable). The variance decomposition is considered a better tool for the cumulative effect of shocks.

Vector error correction model
After analyzing the variables for any long term relationship, Error Correction Model is applied to investigate the short term relationship. The equations (1.5) and (1.6) are rearranged for Error Correction Model in the following way:  (1,7) and (1.8) the new terms and represents coefficients of error correction term and ECT represents error correction term.

Results and Discussion
The study uses Descriptive Statistics, Unit Root Test, Vector Auto Regression (VAR Technique), Johansen and Juselius Co-integration Test, Granger Causality Test, Impulse Response Test, Variance Decomposition Test and Vector Error Correction Model to explore the relationship between the futures and spot market. Table 1 give details of the companies which are trading futures and are selected for the study.  The statistics in the table 2 shows that the returns for all the companies are negatively skewed (except futures returns of LUCK and spot returns of NML which is positively skewed) which mean that the distribution has a long left tail with a higher probability of negative returns. When the Kurtosis is 3, the returns are Mesokurtic, when Kurtosis is >3 called Leptokrurtic and lastly when Kurtosis is <3 called Platykurtic. The Kurtosis of the future and spot returns for all the returns are greater than 3 showing that the distribution is peaked (Leptokurtic). It reflects that compared to normal distribution, the distribution of returns have a fat tails and consequently the Jorque-Bera test rejects the null hypothesis of normal distribution for all the companies.

Line graphs of spot and futures returns
https://ir.iba.edu.pk/businessreview/vol8/iss1/5 DOI: https://doi.org/10. 54784/1990-6587.1216 Published by iRepository, March 2021 The statistics provided by the ADF and PP test reported in the table 3 rejects the null hypothesis of unit root. The statistics of both the tests complement each other revealing that the spot and futures monthly data series remains non-stationery at level, but become stationery at difference of 1. The t values of futures and spot prices of all the companies are smaller than the critical values (-3.527045, -2.903566 and -2.589227 at 1%, 5% and 10% significant level, respectively) show the rejection of null hypothesis of unit root at 1%, 5% and 10% significant level. The spot and futures series are integrated of I(1).

Vector auto regression (VAR technique)
The estimation of Johansen and Juselius Co-integration technique required appropriate lag selection. To find out the number of lags, Akaike Information Criterion and Shwarz Bayesian Criterion are the most commonly used methods in financial econometrics. The Values of AIC and SC were found minimum at lag 1 for the eleven companies namely BOP, DGKC, ENGRO, FFBL, HUBC, LUCK, NML, OGDC, POL, PSO and PTC. For FFC lag 3 have been selected for which the values of AIC and SC were at minimum. The statistics are provided in the table 4.

Results of Johansen's co-integration test
For the next step, the study applied Johansen and Juselius bivariate co-integration technique. Table 5 provides results for bivariate co-integration with maximum Eigen value statistics and table 6 provide results of bivariate co-integration with trace statistics for the spot and futures prices of mentioned twelve companies respectively.

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The maximum eigenvalue statistics in table 5 reports one co-integration equation between the spot and futures prices of BOP, DGKC, FFBL, FFC, NML and PTC while two co-integration equation has been found between the spot and futures prices of ENGRO, HUBC, LUCK, OGDC, POL and PSO at 5% critical value.  Table 6 provides bivariate co-integration results for the spot and futures prices of the companies by using trace statistics. The results of eigenvalue statistics have been confirmed by the trace statistics and one co-integration equation between the spot and futures prices of BOP, DGKC, FFBL, FFC, NML and PTC while, two co-integration equations have been found between the spot and futures prices of ENGRO, HUBC, LUCK, OGDC, POL and PSO at 5% critical value.

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The above results suggest the existence of long run relationship between the spot and futures prices of these companies.

Results of Granger Causality
Granger Causality test shows that the spot returns of FFBL granger causes FFBL's futures returns (P-value of 0.0133), Futures returns of HUBC granger causes HUBC's spot returns (Pvalue of 0.0281), spot returns of LUCK granger causes futures returns of LUCK (P-value 0.0010) and futures returns of POL granger causes POL's spot returns (P-value of 0.0052). The Granger Causality test for the remaining eight companies (BOP, DGKC, ENGRO, FFC, NML, OGDC, PSO, and PTC) does not predict any causal relationship between their spot and futures returns. The futures can help to forecast the spot in case of HUBC and POL and play its important role of price discovery. The spot can forecast the futures in case of FFBL and LUCK and the result is line with Khan (2006)

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The above Figure provides results of impulse response test for the twelve companies. The impulse response analysis represents that the shocks in the futures markets of all the selected companies are explained by their own innovations and their respective spot markets have less influence on them. Table 8 provides results for Variance Decomposition test. The results shows that any variation in futures returns is explained more by its own lag returns (100%) than by the lag retunes of spot. From the results of variance decomposition test, we can conclude that futures market of all the companies is an exogenous market as majority of its stocks are explained by its own innovations. Lein (1996) argued that when two series are found to be co-integrated, a VAR technique along with error correction term should be estimated. The error correction model based on ARDL  1994 99.1959 99.1953 99.1951 99.1951 99.1951  approach has been applied to test for the short term relationship between the spot and futures returns of the mentioned companies. The coefficient ECM (-1) shows how much of the short run disequilibrium will be eliminated in the long run. The error correction variable ECM for all the companies has been reported negative and also statistically significant. Futures returns have been considered as dependent variable while spot return as independent variable.

Results of Vector Error Correction Model
From the result of Vector Error Correction Model in table 9, it is clear that 100% of the previous month's disequilibrium in the futures returns will be corrected in the current month for the BOP, while this figure for DGKC, ENGRO, FFBL, FFC, HUBC, LUCK, NML, OGDC, POL, PSO and PTC is quite high with value of 150%, 143%, 151%, 252%, 143%, 149%, 133%, 148%, 146%, 151% and 142%. We can conclude that the adjustment process in case of disequilibrium is quite fast for all the companies.

Conclusion
The study was conducted to analyze the relationship of single stock futures with the underlying stock on which future is traded. Twelve companies from different sectors which are https://ir.iba.edu.pk/businessreview/vol8/iss1/5 DOI: https://doi.org/10. 54784/1990-6587.1216 trading single stock futures on their stocks were considered for a period of six years from 1 January, 2005 to 31 December, 2010 for this study. The result of unit root indicates that the series of futures and spot are non-stationery at level, but become stationery at first difference. To check for any long run relationship, Johansen's co-integration technique was used. The maximum eigenvalue statistics and trace statistics reports one co-integration equation between the spot and futures prices of BOP, DGKC, FFBL, FFC, NML and PTC while two co-integration equations has been found between the spot and futures prices of ENGRO, HUBC, LUCK, OGDC, POL and PSO at 5% critical value. The results confirm the existence of long run relationship between the futures and spot prices of all the companies. To explore the causal effect, Granger Causality test has been applied. The result of Granger Causality test predicts that the spot prices of FFBL and LUCK assist in forecasting their respective futures prices which is in line with the results reported by Khan (2006). The futures prices of HUBC and POL forecast their respective spot prices. Thus the lead lags relationship between spot and futures are mix. The Futures for HUBC and POL can predict the expected spot prices in the future and play its important role of price discovery. No causal relationship has been found between the spot and futures returns of the remaining eight companies.
Vector error correction model based on ARDL approach captures the short-run dynamics of relationship between the spot and futures returns. The results of VECM establish that the error correction variable ECM (-1) for all the companies has been found negative and also statically significant. The results of VECM reported that 100% of the previous month's disequilibrium in the futures returns will be corrected in the current month for the BOP, while this figure for DGKC, ENGRO, FFBL, FFC, HUBC, LUCK, NML, OGDC, POL, PSO and PTC is quite high with value of 150%, 143%, 151%, 252%, 143%, 149%, 133%, 148%, 146%, 151% and 142%. The results of VECM shows that in case of disequilibrium the adjustment process is quite fast for all the companies.
To investigate the dynamic response between spot market and futures market, impulse response and variance decomposition tests are applied. The impulse response analysis represents most of the shocks in the futures markets of all the selected companies are explained by their own innovations and their respective spot markets have less influence on them. From the results of variance decomposition test we can conclude that futures market is an exogenous market as majority of its stocks are explained by its own innovations.
The empirical results of the study suggest the existence of long run relationship between the spot and futures market. The existence of long run relationship can provide benefits to investors by using futures and spot market in their hedging strategy. Ederington (1979) presumes that strong co movement between two markets is necessary for efficient hedging. The result of impulse response shows that the futures of all companies have a small response to the shock in the underlying spot market and the impulse response gradually dies out predicting co-integration between the spot and futures market which confirm Johansen's co-integration results.
The probability of negative returns is high than positive returns in both the spot and futures returns of the companies which mean downside risk is more compare to upside risk. The returns are more volatile between 2008 and 2009 which can be attributed to both financial crisis and political instability in the country.