Price efficiency in Commodities Future Market A case study for Gold Futures in India

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1 Price efficiency in Commodities Future Market A case study for Gold Futures in India Commodities play a very important role in the macroeconomic environment of an economy. Shortage of commodities can lead to higher levels of volatility leading to higher risk premia for investors. Excess availability of the same would lead to depressed prices forcing producers to go out of business.. Commodities are typically traded in various market layers starting with large wholesale trading between producers and investors and ending with retail small quantity trading between retailers and end users. A commodity market generally attracts large numbers of middlemen and financing agents who take possession of the physical assets and store them at warehouses to sell them at an appropriate time to take profits and stay in the business. Depending on the layers of middlemen in the market structure, the end users price deviates from the producers price. The spot commodities market deals in the physical form of commodity movement. Prices of commodities which are perishable in nature (like agricultural products) behave no differently than the prices of non-perishable commodities like metals and energy.. However, commodities futures markets have been able to bring stability to the spot markets. The theory of storage and the normal backwardation theory explain the relationship between the spot and futures prices in commodity markets. Spot and Futures markets are linked in terms of their price movements. Higher liquidity in these markets make price discovery more efficient. Discovery of efficient prices is a predominant function of the futures market as the market is likely to be used by traders, producers, marketing agents and processors. Numerous studies show that the futures market reacts faster to new information than the spot market as it is cheaper to execute a trade in the futures market than in the physical spot market. As earlier studies show futures markets play a very critical role in efficient price discovery. The futures market is linked to the spot market through a cost of carry component which not only accounts for the cost of inventory holding but also any convenience yield arising out of such physical holdings. The prices in the futures and

2 spot markets are systematically related both in the short and long run and any deviation should be rationally explained. The presence of an equilibrium relation binding together the two prices of the futures and spot markets is the main theme behind efficient price formation. As a large number arbitragers exist in the system and they can fund their position through borrowing mechanism by paying appropriate cost, any disparity in price between spot and futures market is likely to be exploited by these arbitragers. An Efficient price discovery mechanism through the above equilibrium process leads to better decision making that ultimately results in an optimal allocation of physical resources. Futures on commodities are widely traded in global markets and in India, Government allowed trading in commodity futures in Among the commodities futures contracts traded in India, Gold accounts for the largest share of contracts. The trading on gold is also concentrated in one Exchange 3. The spot gold market typically exists across all geographical locations in India but the price fixation at either Mumbai or Ahmedabad is accepted among the traders for delivery. Gold, being a commodity, attracts State level taxes, if any. Hence, traders prefer to take delivery of physical gold in a center where the tax is relatively lower. Ahmedabad as a delivery center for gold has been growing in importance in recent years and it is well accepted among the traders. The Indian Commodity Exchanges typically use spot price for delivery at Ahmedabad as the settlement price for their futures contract in Gold. The price and production behaviour of gold differs from most other commodities. During the recent financial crisis, the gold price increased by 6% while many key mineral prices fell and equities dropped by around 40%. The unique and diverse drivers of gold demand and supply do not correlate highly with changes in other financial assets (WGC, 2009). Efficient price discovery mechanism is an important issue in a competitive market. Price behavior in the physical and financial markets determine how the agents of the market like producers, speculators, financiers and users would behave. If price discovery is 3 Multi Commodity Exchange (MCX) accounts for lion s share in Commodity Futures contracts traded in India.

3 inefficient, liquidity becomes the biggest challenge for all. This paper looks at the mechanism of efficient price discovery in Gold spot and Futures market and their interlinkages. The rest of the paper is organized into the seven sections. Section 2 deals with Indian gold market microstructure. Section 3 presents analysis on price dissemination in spot and futures market and data used for the study, Section 4 outlines the existing literature reviews, Section 5 details methodology Section 6 gives the empirical findings and Section 7 gives the concluding remarks. The last section summarizes the empirical results and findings. 2. Indian Gold Market More than 95% of gold imported for the domestic market is in the form of small cast bars weighing 10 tolas (3.75 oz), widely known as TT bars or biscuits. Most imported TT bars are produced by 8 major gold refiners in Switzerland, South Africa, United Kingdom and Australia. Imported gold is distributed nationwide through secondary and lower tier bullion dealers that fall below the primary tier of bank and PSU importers. The most important dealers are located in cities where the State sales tax is low:ahmedabad, Jaipur, Mumbai and Gurgaon. Historically India is one of the largest importers of gold in the world. Gold is held as a family jewel for most families in the country and very rarely families sell gold for pecuniary purposes. Before early nineties, gold market is India attracted lot of parallel transaction as the imports were restricted combined with high import duties. The hawala market operated leading to increased black market transactions in gold. However, financial sector reforms process in nineties brought much needed reforms to the gold market and market was freed up from high import duties and restriction on imports. The international price and domestic market price of gold almost synchronized till Government introduced high import duties on gold imports in The Government hiked import duty in August 13 on refined gold bars for a third time in eight months to 10 per cent from the earlier 8 per cent in order to curb the demand and restricts its impact on Current Account Deficit (CAD) and exchange rate.

4 The gold import has been rising unabatedly for last few years and such large import of gold has become one of the major source of our high trade deficit. The CAD has deteriorated significantly in recent times due to large gold imports. This resulted in depreciation of the Indian currency and resulted in reduction of the foreign exchange reserves. This high current account deficit and falling Indian Rupee in 2013 forced RBI and the Government to introduce restrictions on gold imports as well as introducing duties on import of Gold. However, the differential pricing between international and domestic prices has resulted in increasing unauthorized market taking shape through hawala route. The aggregate demand for gold in India is influenced by many social, economic and cultural factors. Gold is a chosen investment for many as it is considered a hedge against inflation. Indian has been passing through high inflationary situation for last few years and this might have contributed to such high demand for gold. Further, return on alternate assets have not been lucrative enough for investors to diversify into those assets. The performance of gold against other comparable financial assets in recent years is another possible reason for the shift towards investment in gold in India. Rising global gold prices in recent years did not affect the domestic demand of the gold in India implying that investment in gold is becoming price inelastic. International gold prices have increased exponentially in recent years and domestic gold prices have moved in tandem with international gold prices in recent years. In recent years, the gold loan market in India has grown rapidly. Large number of Non-Banking Financial Companies are involved in gold loan business in India who source funds from banking sector. Till recently, banks were very active in providing gold loans to customers.

5 Year Table 1: Global Gold Supply and India s Demand for Gold 4 Gold Demand Growth of from Global Gold (Tonnes) Supply (%) Global Gold Supply $ (Tonnes) Growth of Gold Demand from India (%) $ - calendar - Financial Year From the above Table, few interesting points may be derived. If we consider the entire period to map the changing demand for gold in India against the change in global gold supply, we find very little relationship 5. The relationship is interesting if we divide the period into two parts (a) and (b) During the first phase, we find a negative relationship between change in world supply of gold and change in Indian demand for gold 6 while during the second phase the relationship is positive and significant at 5% level 7. Table -2: Simple Descriptive Statistics of Growth of Demand and Supply ( ) 4 Source: World Gold Council and Estimations from DGCI&S Data 5 Correlation coefficient is 0.15 but insignificant. 6 Correlation coefficient is but not statistically significant and R-sq is Correlation coefficient is 0.74 and statistically significant at 5% level with R-sq of 0.54.

6 (%) Variable N Mean Std Dev Minimum Maximum World Supply Indian Demand Indian s demand for gold has been rising steadily over the years and as of 2012, it has surpassed one-fourth of world supply of gold. However, in spite of this large consumption India is more of a price taker than a price setter as domestic prices typically synchronize with global gold prices set at London after adjusting for duties. Chart -1: India's Gold Demand as % of World Supply and Imports Growth 27.0% 25.0% 23.0% 21.0% 19.0% 17.0% 15.0% 13.0% 11.0% 9.0% India's Gold Demand Imports Linear (India's Gold Demand) Linear (Imports ) 70.0% 60.0% 50.0% 40.0% 30.0% 20.0% 10.0% 0.0% -10.0% Investment in gold has been traditionally used in India as a hedge against inflation. Hence it is expected to have a very high correlation with average WPI growth. As Indian consumers are witnessing high level of inflationary pressure since , the demand for gold started rising. The change in domestic gold prices fairly provided a coverage for high inflation measured in terms of WPI. Table 3: Annualized Indian Monthly Average Growth in Gold Price and WPI 8 8 Source: Government of India Data release, DGCI&S Data

7 Growth Avg. WPI Growth Avg. Gold Price Growth (%) (%) Further, demand for gold has been price inelastic. Though there is a negative relationship between the change in gold price and the change in gold demand, the same is statistically insignificant. The yearly change in gold demand has also a positive relationship with the WPI but the same is not statistically significant. However, WPI and gold price changes have positive correlation but statistically significant only at 10% level. As we find demand for gold is price inelastic, imports have been increasing at a rapid pace (till imposition of duties on import of gold in 2013 and further restriction imposed by RBI of gold import funding). The large gold imports have led substantial increase in CAD and also impacted the exchange rate. Table 4: Simple Descriptive Statistics of Annual Growth ( to ) Variables N Mean Std Dev Minimum Maximum WPI Annual Gold Price Change Annual Gold Demand Change Annual Imports Change Gold imports stood at `269563crores as of As domestic production of gold has been at insignificant level for a long time, the consumption demand is met entirely 9 Quantity 10 Value

8 through imports. Gold investment returns has been above 18% on an average in domestic market while since 2000, the international gold prices have grown at compound annual growth rate of 16.3%. Imports in terms of value have grown at a rate of about 30% during 10 years. As expected, gold imports have a very strong correlation with the demand for gold and also has a reasonably good correlation with WPI 11. Gold demand and gold price has an expected negative relationship but it was not statistically significant indicating inelastic nature of the demand. India has been exporting a certain portion of its gold imports in the form of re-exports of gold jewelry as global demand for such items has been picking up. However, such reexports have steadily fallen fall 41% in to 29.2% in A higher percentage of gold imports are being used for meeting domestic demand. Hence, increasing domestic consumption of gold import is clearly a concern for external sector sustainability. Table 5: Pearson Correlation Coefficients of Annual Growth Data, N = 11 ( to ) Prob > r under H0: Rho=0 WPI Gold Price Change Gold Demand Change Gold Imports WPI Gold Price Change Gold Demand Change Gold Imports Typically frequency of monthly average gold price remained above the previous six months average price for most part of the period. This implies building up of positive expectations by gold investors as the present spot price is above the last 6-month s average price. 11 Significant at 10%

9 Apr-04 Oct-04 Apr-05 Oct-05 Apr-06 Oct-06 Apr-07 Oct-07 Apr-08 Oct-08 Apr-09 Oct-09 Apr-10 Oct-10 Apr-11 Oct-11 Apr-12 Oct-12 Apr-13 Oct-13 Gold Price (INR) Chart - 2: Gold Price - Spot and 6-Month Average Price AVG6M SPOT Difference Investment is gold has been significantly rising over years as investors use the same increasing as a hedge against inflation in India. The investment has paid off handsomely vis-à-vis other financial assets. The gold imports appear to be price inelastic in India. India has a tradition and social customs warranting purchase of gold for specific occasions irrespective of the price. 3. Price Dissemination in Spot and Futures Market Spot gold price for India is obtained typically for ex-ahmedabad delivery or ex-mumbai delivery. The ex-ahmedabad delivery has been more popular among traders and the largest commodity futures exchange in terms of volume of contracts traded uses the said price for settlement purpose. The spot price used by the leading commodities futures exchange for settlement is arrived at by way of polling the rates from group of jewelers and processors 12. Spot gold price for India is also disseminated by World Gold council. 12 The Exchange has not provided any clarity on the process of polling, the names of entities polled and the process and methodology of arriving at the final price for settlement of contracts. Higher level of transparency in fixing spot price is likely to improve the quality of the spot price used for settlement. Exchange has also not provided historical delivery statistics in their website to understand how much contracts are settled for physical delivery.

10 May-05 Oct-05 Mar-06 Aug-06 Jan-07 Jun-07 Nov-07 Apr-08 Sep-08 Feb-09 Jul-09 Dec-09 May-10 Oct-10 Mar-11 Aug-11 Jan-12 Jun-12 Nov-12 Apr-13 Sep-13 Feb-14 However, the said price does not take into account the import duties introduced in 2013 by the Government to ward off the pressure on Current Account Deficit. Hence the global gold price and Indian domestic gold price have diverged in recent times and due to import restrictions and duties, the domestic gold price trades at a premium over the global gold price. Domestic gold prices have been trading at least 6-7% higher than global prices in Feb 14. The premia is likely to come down as the currency has been appreciating and demand for gold has decelerated because of many regulatory directives. To start with the relaxation process, RBI eased gold import norms by trading houses as well as allowing banks to give Gold Metal Loans (GML) to domestic jewellery manufacturers out of the eligible domestic import quota of 80% to the extent of GML outstanding in their books as on March 31, Chart - 3: Global and Domestic Gold Prices Movement (`) % 15.00% 10.00% 5.00% 0.00% -5.00% % MCXSPOT WGCSPOT Difference Physical Gold was also traded in National Spot Exchange (NSEL) 13 using e-contracts but as it was found later, the contracts were paired ones for borrowing and lending money and most of the warehouses did not have physical gold in their vaults to support the transactions. It was later found out that only a few lenders and borrowers were misusing the NSEL trading platform for executing borrowing and lending activities without any significant participation from retail investors. Large amount of artificial trading activities 13 Criminal investigation by Indian Regulatory bodies have been initiated against NSEL in 2013 and estimated loss for lenders against gold contracts is about `5600crores (1crore = 10million).

11 were entered by Indian Bullion Market Association (IBMA), a subsidiary of the exchange. Due to absence of a functional, well regulated and transparent spot trading environment, most trades in physical gold happens amongst second tier dealers and jewelry processors play a very important role in most of these deals. Gold futures 14 trading started in multiple exchanges in India in 2003 and trades on these future exchanges are concentrated in near month contracts. However, most of the trading does not result in delivery and speculative trading drives the market for gold futures. Many studies have found the bi-directional causality between gold futures and gold spot prices. Table 6: Descriptive Statistics Gold and Gold Futures (India and Global) May 05 to Mar 14 MCX SPOT (`) MCX FUTURES (`) CME FUTURES ($) LONDON SPOT ($) Mean Standard Dev Minimum Maximum Median Months The descriptive statistics clearly points out that gold spot and futures move in tandem like any other spot and future relationship. The monthly returns show a very close similarity for both Futures and Spot markets in both India and global market under our study. Monthly price changes (logarithmic returns) also show that Indian market (both Futures and Spot) has given better returns with lower risk vis-à-vis global market represented by CME futures and London spot prices. Indian market has provided an annual return of about 18% with an annual volatility of 14.5% while global market (measured in term CME Futures and London spot) has provided a return of 13% with a volatility of 15%. 14 A standard contract has a trading unit of 1 kilogram or 1,000 grams, while a mini contract has a trading unit of 100 grams.

12 Indian market provided an arbitrage opportunity to investors. Descriptive statistics are reported in Table X. The sample means of spot and futures market returns are positive. The values of skewness and excess kurtosis indicate that the distributions of spot and futures market returns are negatively skewed and leptokurtic relative to the normal distribution. Table 7: Descriptive Statistics of Monthly Price Changes of Spot and Future Gold Prices LONDON MCX SPOT MCX FUT CME FUT SPOT Mean Standard Error Median Standard Deviation Sample Variance Kurtosis Skewness Minimum Maximum Observations The prices have very high correlation CME and London Spot have a near 100% corelation in their movements while MCX Futures and Spot have very marginally lower correlation than the correlation between CME and London Spot. However, London Spot and Indian Spot prices have about 85% correlation the same as the correlation between CME futures and MCX Futures. This high correlation is intuitively expected as gold is an international commodity and Indian market is more of a price taker though it has a substantial part in total gold consumption and demand and produces almost negligible amount.

13 Table - 8: Pearson Correlation Coefficients Monthly Price chnages, N = 107 Prob > r under H0: Rho=0 MCX SPOT MCX FUTURES CME FUTURES LONDON SPOT MCX SPOT <.0001 <.0001 <.0001 MCX FUTURES <.0001 <.0001 <.0001 CME FUTURES <.0001 <.0001 <.0001 LONDON SPOT <.0001 <.0001 <.0001 The volatility of the markets have high correlation indicating volatility spillover possibility. It is expected that the volatility of global market is likely to transmit to Indian market as Indian market is predominantly a price taker. In 2013, volatility in Indian market increased while the same has declined in the global markets. This may be due to the imposition of restrictions on gold imports during Table - 9 : Monthly Returns Volatility (measured by Standard Deviation) Year MCX SPOT MCX FUTURES CME FUTURES LONDON SPOT % 2.71% 2.75% 2.63% % 6.18% 6.53% 6.58% % 3.47% 3.33% 3.36% % 5.58% 6.34% 6.40% % 3.98% 3.78% 3.89% % 2.78% 2.67% 2.69% % 4.33% 4.58% 4.61% % 2.29% 3.31% 3.32% % 4.82% 3.05% 2.97% % 0.11% 1.42% 1.27% % 4.18% 4.41% 4.43% 15 For 2014, we have used only 3 months data.

14 The volatility show some interesting correlation among markets. Volatility in London Spot market and CME Futures have a very strong correlation at 99.94% and indicate that but Indian Spot market and Futures markets have a relatively low correlation at 94.21%. Indian Spot and London Spot markets have about 92% correlation with the MCX Gold Futures market has lower correlation with London Spot and CME Futures at 88%. Table 10: Pearson Correlation Coefficients Annual Volatility Comovements, N = 10 Prob > r under H0: Rho=0 MCXSPOT MCXFUTURES CMEFUTURES LONDONSPOT MCXSPOT < MCXFUTURES < CMEFUTURES <.0001 LONDONSPOT <.0001 By performing a linear regressions of the monthly returns of gold spot versus the futures, we find that the linear relationship is strong. We summarize the regression results, including the slope, intercept, R-Sq, and root mean squared error (RMSE). The R-Sq values are all greater than 95%, indicating a strong linear fit for both markets. For Indian market, the slope is 0.98 and the intercept is essentially zero. The slope for Indian market suggests that the price sensitivity of futures with respect to the spot is slightly less than 1. While this suggests that the futures prices should be marginally less volatile than the spot return for Indian market, for global market, the slope is slightly greater than 1 indicating the futures prices should be marginally more volatile than the spot return for global market. However, we find for both markets, volatility of Futures market is marginally lower than the volatility of spot markets. Table 11: Regression Results Spot versus Futures Gold Monthly Returns Type Response Slope Intercept R-Sq RMSE DW Indian Market MCX FUTURES Global Market CME FUTURES E

15 London Spot Market and CME Futures have very strong relationship and the information in one market is well captured in the other market as can be seen from very high R- square. The data suggests that traders arbitrage in an extremely efficient manner. Compared to the same, Indian spot and MCX Futures show a much weaker relationship with a relatively low R-Square. This may be due to various Tax and duty structures which does not allow efficient arbitrage opportunities 16. Further, movement of Gold from one delivery center to another involves cost and Traders may prefer to buy Gold from local suppliers rather than taking delivery in Ahmedabad or Mumbai and shifting the same to their place of business. Trading in Gold Future Contracts in CME typically concentrate on 3-month contracts while in trades in MCX Gold Futures has high concentration on 1-month contracts. We have computed monthly implied cost of carry from both markets for most liquid contracts using expiry period, spot and future prices. MCX market show wider variation vis-à-vis CME market. Table 12: Implied Cost of Carry Monthly Average Implied Return - CME Implied Return - MCX Mean Standard Error Median Standard Deviation Sample Variance Kurtosis Skewness Minimum Maximum Observations Further, the implied cost of carry for CME Gold Futures and MCX Gold Futures also widely vary. The CME Gold Futures implied cost of carry shows a stable pattern while MCX Gold Futures implied cost of carry show volatile patter. 16 Delivery volumes have been very low and negligible for standard MCX Futures contracts.

16 Chart - 4: Implied Cost of Carry - CME vesrus MCX Gold Futures (May'05 - Mar'14) 30.00% 20.00% 10.00% 0.00% May % Sep-06 Jan-08 Jun-09 Oct-10 Mar-12 Jul % % % % IRMCX IRCME 4. Review of Literature Literature on commodities futures-spot price relationships has been voluminous and the interest on the subject has been growing as commodity markets around the world are going through cyclical changes. Gardbade and Silber (1983) used daily spot and futures prices for four storable agricultural commodities to understand the price discovery process in storable agricultural commodities. They found that the futures markets dominate the spot markets for wheat, corn and orange juice but not for but for oats. Oellermann et al. (1989) and Schroeder and Goodwin (1991) found that the futures markets capture the information first and then transfer it to the spot markets. Brockman and Tse (1995) found that the futures market leads the spot market for all four commodities they studied. Koutmos and Tucker (1996) studided the temporal relationships and dynamic interactions between S&P 500 Index and Index futures and reported that volatility in both markets is an asymmetric function of past innovations. Yang et al. (2001) examined the price discovery performance of the futures markets for storable and non-storable commodities and found that futures markets lead the spot markets in the case of both storable and non-storable commodities. Moosa (2002) examined the daily data of spot and one-month future prices of WTI crude oil covering and found that sixty percent of the price discovery function is performed in futures

17 market. Mattos and Garcia (2004) studied Brazilian agricultural markets and found that the futures and the spot prices were cointegrated in the case of live cattle and the coffee markets but not in other commodities traded in Brazil. While studying NYNEX E-mini futures contracts, Tse and Xiang (2005) found that NYNEX E-mini futures contracts on gas and crude contribute more than thirty per cent of price discovery even though they account for less than one per cent of the volume of standard contracts. Chin and Coibion (2013) found that there is quite general declines in the ability of futures prices to predict subsequent price changes since the early 2000s while studying futures prices for energy, agricultural, precious and base metal commodities. Thomas and Karande (2001) studied the price discovery process in the castor seed futures market and found that Ahmedabad and Mumbai markets react differently to information in the price discovery of castor seed. Kumar and Sunil (2004) investigated the price discovery of five agricultural commodities futures contracts and found inefficiency of Indian agricultural commodities futures markets in absorbing information. Iyer and Pillai (2010) found that commodity futures market prices play the vital role in the price discovery process. Pavabutr and Chaihetphon (2010) examined the price discovery process of the nascent gold futures contracts and found that standard and mini futures contracts exhibit a stronger influence over spot prices both in the short-run and long-run. 5. Methodology The prices of near month contract can objectively be used as an efficient predictor of the cash prices, provided that the value of basis on the maturity date of one month contract becomes zero (Garbade and Sibler (1983)). The daily data on near month contract are used to represent the commodity future price for the whole period. The well-known rationale behind the use of nearby contract is that it is the most actively traded contract. The more actively traded an instrument is, more is the information contained in its price. A nearby contract always exhibits more trading volume than those contracts of other maturities. A contract becomes nearby at the beginning of the previous contract s expiration month, thereby avoiding the often-noted expiration effect.

18 Before conduct the empirical analysis, may recapitulate the theoretical underpinnings of the tests conducted. Recent empirical research in the futures markets in commodities suggests that for a hedge to result in an overall price risk reduction, there must be a stable long-run relationship between the cash and futures price movements. Testing for the existence of this long-term relationship provides evidence on the extent to which one price can be used to predict the other. Again if the relationship between spot and futures price is found to be stable, then the participants trading in cash markets can effectively use futures positions to minimize cash price risk. According to Granger, 1986, if spot and futures prices are co-integrated, then causality must exist in at least one direction. The existence of a price discovery function in futures markets hinges (A circumstance upon which subsequent events depend) on whether price changes in futures markets lead price changes in cash markets more often than the reverse. The market efficiency can be analyzed by studying the possible existence of a long-term stable relation between spot and futures prices. To establish whether there is a long-run equilibrium relationship among the variables, futures prices and spot prices, need to employ the concept of co-integration developed by Johansen and Juselius (1990). The basic idea of co-integration is that two or more non-stationary time-series may be regarded as defining a long-run equilibrium relationship if a linear combination of the variables in the model is stationary. Thus, if the link between the futures price and spot price describes a stationary long-run relationship, this can be interpreted to mean that the stochastic trend in the variables is related. In other words, even though deviations from the equilibrium should occur, they are meant averting. A prerequisite in applying the cointegration procedure is to test the unit root properties of the series. The most common way to test for the existence of unit roots, and to determine the degree of differencing necessary to induce stationary, is to apply the ADF test. Market efficiency can be analyzed by using a unit root test on a time series analysis technique called co-integration test. The unit root test identifies variables that are nonstationary. Cointegration is an equilibrium relationship that provides a formal framework

19 for testing and estimating long-run relationship among economic variable that would otherwise be immune to accurate analysis. To study the market efficiency of the MCX Gold Futures market, a co-integration test by Johansen and Juselius (1990) is studied. However, the application of co-integration test requires the time-series to be nonstationary in level i.e., it should contain a unit root. Therefore, before conducting cointegration test, first check the properties of the time-series by conducting a unit root test using ADF test. If the time-series is non-stationary after conducting unit root test at level, then move further to 1st difference in order to check the stationary of time-series and so on. To test for Granger causality and cointegration, we use the standard methodology proposed by Granger (1969, 1986) and Engle and Granger as described in Enders (1995). All tests are performed on natural logarithm of the indices time series using OLS estimation procedure. In order to test for Granger causality among two market data series (in our case spot and futures in both markets) I f yt and y t, we estimate the equation y I t n m I 0 1 i yt i i 1 i 1 y 2i f t 1...(1) 1t y f t n m f I 0 1 i yt i 2i yt 1 2t...(2) i 1 i 1 and perform an F test for joint insignificance of the coefficients. The null hypothesis claims that f yt does not Granger cause I y t or vice versa. Therefore, a rejection of the null hypothesis indicates a presence of Granger causality. For each pair of stock market indices, we perform two Granger causality tests so that we can decide whether f y t Granger causes I y or y I t t Granger causes f y t or both, or none.

20 In order to examine the co-movement between the spot market and the future market, we strictly follow the standard methodology available in the literature. We first study the relationship between the spot and future market by the simple regression: y I t y f t e t [3] where the endogenous variable I y t represents the spot market; the exogenous variable f y t is the futures market; e t is the error term. The validity and reliability of the regression relationship require the examination of the trend characteristics of the variables and cointegration test as the presence of unit root processes in the data results in the spurious regression problem. Before testing for cointegration, we need to go for stationary test. In order to do so, we apply the Dickey- Fuller (1979, 1981) (DF) and augmented Dickey-Fuller (ADF) unit root tests based on the following regression p t 1 i 1 y b a t a y b y...(4) t i t 1 t where y t y t y t 1 and y t can be I y t, f y t or fi y t includes a drift term (b 0 ) and a deterministic trend (a 0 t)., t is the error term. Regression [2] In addition, we apply the PP test developed by Phillips and Perron (1988) to detect the presence of a unit root. The PP test is nonparametric with respect to nuisance parameters and thereby is suitable for a very wide class of weakly dependent and possibly heterogeneously distributed data. If both y I t, f fi y t ( y t ) are of the same order, say I(d), d>0, we then estimate the cointegrating parameter in (1) or (2) by OLS regression. If the residuals are stationary, the series, I y t and f fi y t ( y t ) said to be cointegrated. Otherwise, I y t and f fi y t ( y t ) are not cointegrated.

21 Cointegration exits for variables means despite variables are individually non-stationary, a linear combination of two or more time series can be stationary and there is a long-run equilibrium relationship between these variables. If the error term in (1) or (2) is stationary while the regressors are individually trending, there may be some transitory correlation between the individual regressors and error term. However, in the long run, the correlation must be zero because of the fact that trending variables must eventually diverge from stationary ones. Thus the regression on the level of the variables is meaningful and not spurious. The most common tests for stationarity of estimated residuals are Dickey-Fuller (CRDF) and Augmented Dickey-Fuller (CRADF) tests based on the regression: eˆ t eˆ p t 1 i 1 eˆ t 1...(5) t where ê t are residuals from the cointegrating regression (1) and p is chosen to achieve empirical white noise residuals for CRADF and set to zero for CRDF test. We further apply the multivariate cointegrated system developed by Johansen (1988a,b). Assume each component yi,t i= 1,.,k, of a vector time series process yt is a unit root / process, but there exists a k r matrix β with rank r<k such that yt is stationary. Clive Granger has shown that under regularity conditions we can write cointegrated process yt as a Vector Error Correction Model (VECM): y t y y y 1 t 1 2 t 2 p 1 t p 1 y t t p [6] where t ~ iid(0, Ω). The basic idea of the Johansen procedure is simply to decompose Π into two matrices α and β, both of which are k r such that ' and so the rows of β may be defined as the distinct cointegrating vectors. Then a valid cointegrating vector will produce a significantly non-zero eigenvalue and the estimate of the cointegrating eigenvecor. Johansen proposes a trace test for determining the cointegrating rank r, such that:

22 trace k r T ln 1 ˆ i r 1 i, r=0,1,2,.n-1 [7] and proposes another likelihood ratio test whether there is a maximum of r cointegrating vectors against r+1 such that: max r, r 1 T ln 1 r 1 with critical values given in Johansen (1995). ˆ [8] Stock and Watson (1988) proposed statistics for common trends testing. The null hypothesis is that the -dimensional time series has common stochastic trends, where and the alternative is that it has common trends, where. The test procedure of versus common stochastic trends is performed based on the first-order serial correlation matrix of. Let be a matrix orthogonal to the cointegrating matrix such that and. Let and. Then Combining the expression of and, The Stock-Watson common trends test is performed based on the component whether has rank against rank. by testing 6. Empirical Findings The most popular test for determining whether or not a series is stationary is the (augmented) Dickey-Fuller test. Consider the AR (1) model Y t =ρy t-1 + v t. The process is stationary when ρ < 1, but, but when ρ =1, it becomes the nonstationary random walk process Y t =Y t-1 + v t. Thus, one way to test for stationarity is to test H0: ρ=1 against the alternative H1: ρ < 1. Since we are testing the null hypothesis ρ=1 the test is known

23 as a unit root test for stationarity. The test is generally carried out by subtracting y t-1 from both sides of the equation to obtain Y t - Y t-1 =ρy t-1 - Y t-1 + v t Rewriting the same as Δy t = (ρ-1) Y t-1 +v t = γy t-1 + v t Where γ = ρ-1 and Δyt = Y t - Y t-1. Now we test null hypothesis H0: γ =0 (nonstatinarity) against H1: γ < 0 (stationary). The differenced series of all four variables in our study have a non-zero mean but appear to wander around a constant amount. Thus we may choose an Augmented Dickey Fuller (ADF) test with a constant but no time trend for our data series. If Y t is nonstationary, the usual p-values and t-statistics do not apply. We need to find the test statistics tau (τ) statistics and its value must be compared to the specially generated critical values 17. These critical values are different than the standard critical values used in most hypothesis tests. The ADF test adds lagged differences of y t to the model. The lag structure has to be decided on the basis of the data in use. This is important as adding more lagged values may help in ensuring the residuals are uncorrelated. In our data, we have used one lagged difference term to eliminate autocorrelation in the residuals of our data series. Table 13: Critical Values (Davidson and MacKinnon) Series Characteristics Equation 1% 5% 10% No Constant and No Trend Δy t = γy t-1 + v t Constant but No Trend Δy t = α+γy t-1 + v t Constant and Trend Δy t = α+γy t-1 +λt+ v t The regression results for all four variables (level) with ADF test show that the tau (τ) statistics is higher than the critical values in all cases. Hence we fail to reject the null hypothesis that the series is nonstationary. 17 Critical values are taken from R Davidson and J G MacKinnon (1993), Estimation and Inference in Econometrics, Oxford University Press.

24 Table 14: Augmented Dickey-Fuller Unit Root Tests Results for Level Series Parameter Estimates for MCX GOLD FUTURES Variable DF Estimate Standard t Value Approx Critical Vlue Error Pr > Intercept MCXF (lag) DIFF (LAGMCXF) Parameter Estimates for MCX GOLD SPOT Intercept MCXSPOT(lag) DIFF (LAGMCXSPOT) Parameter Estimates for CME Futures Intercept CME(Lag) DIFF(LAG CME) Parameter Estimates for London Gold Spot Intercept LAG(LONDON SPOT) DIFF(LAGLONDONSPOT) We also estimated another alternate test for unit root for all four variables (level) with Phillips-Perron test and the regression results show that the tau (τ) statistics is higher than the critical values in all cases. Hence we fail to reject the null hypothesis that the series is nonstationary. The Phillips Perron test statistics have the same asymptotic distribution as the corresponding ADF tests. The results also show that all four series are nonstationary. For all four series, the test statistics are greater than the corresponding critical values at 5% level of significance. For our results, Zero Mean is of primary importance as we have not included a trend in our regression.

25 Table 15: Phillips-Perron Unit Root Test Results for Level Series Parameter Estimates for MCX GOLD FUTURES Type Lags Rho Pr < Rho Tau Pr < Tau Zero Mean Single Mean Trend Parameter Estimates for MCX GOLD SPOT Type Lags Rho Pr < Rho Tau Pr < Tau Zero Mean Single Mean Trend Parameter Estimates for CME Futures Type Lags Rho Pr < Rho Tau Pr < Tau Zero Mean Single Mean Trend Parameter Estimates for London Gold Spot Type Lags Rho Pr < Rho Tau Pr < Tau Zero Mean Single Mean Trend So far, we have considered only whether our four data series are stationary or nonstationary. It may be possible that the first difference of a nonstationary process is stationary. This concept is known as order of intergration. A series, y t, that can be made stationary by taking the first difference is said to be integrated or order 1, denoted as I(1). In order to test whether the first difference, Δy t, is stationary, we need to run a regression to regress Δ(Δy t ) on Δy t-1. As the differenced series of our variables appear to wander around zero mean, we will use the Dickey-Fuller test with no constant and no trend to test for stationarity of the differenced series.

26 Table 16: Augmented Dickey-Fuller Unit Root Tests Results for Differenced Series Variable DF Estimate Standard t Value Approx Critical Value Error Pr > Parameter Estimates for MCX GOLD FUTURES Differenced DIFF (LAGMCXF) < Parameter Estimates for MCX GOLD SPOT Differenced DIFF (LAGMCXSPOT) < Parameter Estimates for CME Futures Differenced DIFF(LAGCME) < Parameter Estimates for London Gold Spot Differenced DIFF(LAGLONDONSPOT) < We also tested the stationarity using Phillip-Perron Test for the differenced series. The results are placed below. Since we did not include an intercept or trend in our estimation, we will use the results from Zero Mean. All four differenced series show that they are stationary as Phillips-Perron test strongly rejects the null hypothesis of nonstationarity (as all critical values are higher than the estimated Tau values), which leads us to conclude that four data series are stationary in their first difference. Table 17: Phillips-Perron Unit Root Test for Differenced Series Parameter Estimates for MCX GOLD FUTURES Differenced Type Lags Rho Pr < Rho Tau Pr < Tau Zero Mean < <.0001 Single Mean <.0001 Trend <.0001 Parameter Estimates for MCX GOLD SPOT Differenced Type Lags Rho Pr < Rho Tau Pr < Tau Zero Mean < <.0001 Single Mean <.0001 Trend <.0001 Parameter Estimates for CME Futures Differenced Type Lags Rho Pr < Rho Tau Pr < Tau

27 Zero Mean < <.0001 Single Mean <.0001 Trend <.0001 Parameter Estimates for London Gold Spot Differenced Type Lags Rho Pr < Rho Tau Pr < Tau Zero Mean < <.0001 Single Mean <.0001 Trend <.0001 As a general rule, nonstationary time-series variables should not be used in regression models to avoid the problem of spurious regression. Cointegration is an exception to the rule. There is an important case when e t = y t - β 1 - β 2 x t is a stationary I(0) process. In this case y t and x t are said to be cointegrated. Cointegration implies that y t and x t share similar stochastic trends, and, since the difference e t is stationary, they never diverge too far from each other Two nonstationary time series are cointegrated if they tend to move together through time. For example, the Dickey-Fuller tests have led us to conclude that MCX SPOT Gold prices and the MCX Gold Futures prices rate series are both nonstationary. However, the plots of these series indicate that they tend to follow a similar path over time. If y t and x t are nonstationary I (1) variables, but if there is a linear combination of these variables that is a stationary I (0) process, then the two series are cointegrated. A natural linear combination to examine is the error e t = y t β 1 -β 2 x t. Since we cannot observe the error, we test the stationarity of the least squares residuals e t = y t b 1 b 2 x t. Testing for cointegration involves regressing one I (1) variable on another using least squares. Test the residuals for stationarity using the augmented Dickey-Fuller (ADF) test. The null hypothesis is that the residuals are nonstationary. Rejection of this leads to the conclusion that the residuals follow a stationary I(0) process and the series are cointegrated. The test for stationarity is based on the equation e t = γe t 1 + v t. The regression has no constant term because the mean of the regression residuals is zero. We are basing this test upon estimated values of the residuals

28 Again, there are three sets of critical values depending on whether the residuals are derived from a regression equation with no constant term, a constant and no trend, or a constant and a trend. The critical values for the cointegration test are slightly different because the test is based upon estimated values. These critical values 18 are given in Table. This cointegration test is often referred to as the Engle-Granger test. Table 18: Critical Values (Hamilton) Series Characteristics Equation 1% 5% 10% No Constant and No Trend y t = βx t + e t Constant but No Trend y t = β 1 + β 2 x t + e t Constant and Trend y t = β 1 + β 2 x t +δ t + e t In order to test cointegrating relationship between Spot Gold prices and MCX Futures Gold Prices, we regress one variable on other. Both the series are I(1) since they are found to be nonstationary, but their first differences are stationary using the regression equation B t = β 1 + β 2 F t + e t. We estimate the regression and save the residuals for use in the ADF regression later. We test for stationarity in the residuals. Estimate the model e t = γe t 1 +α 1 e t 1 +v t, which is the augmented Dickey-Fuller regression with one lagged term to correct for autocorrelation. Since the residuals have a mean of zero, we did not want to include an intercept in the equation while testing for stationarity of residuals. It may be noted that this is the augmented Dickey-Fuller version of the test with one lagged term, e t 1, to correct for autocorrelation. The null hypothesis is that the residuals are nonstationary and thus series are not cointegrated. The alternative hypothesis is the residuals are stationary and hence the series are cointegrated. Table 19: Engle Granger Cointegration Test Results Parameter Estimates for MCX Futures on SPOT Variable DF Estimate Standard t Value Approx Critical Error Pr > t Value ehat Diff(ehat1) < The critical values are taken from J Hamilton (1994), Time Series Analysis, Princeton University Press