Arbitrage Opportunities in Major Gold Futures Markets: Evidence from High Frequency Data

Transcription

1 Arbitrage Opportunities in Major Gold Futures Markets: Evidence from High Frequency Data Pornchai Chunhachinda* and Rapeesorn Fuangkasem** This study investigates cross-market arbitrage opportunities under synchronous trading time, and uses 5-minute intraday data that mitigates the stale price problem. Three major gold futures markets: COMEX, MCX, and TOCOM, and spot gold are examined using a modified interval pricing model. The evidence reveals both futures-spot and futures-futures arbitrage opportunities, especially in the more recently established markets. Moreover, the average profits of futures-futures arbitrage exceed those of futures-spot arbitrage. Finally, the evidence highlights differences among markets in both speed of price adjustment and lead-lag relationship. JEL Classification: G14, G15 Keywords: arbitrage opportunities, gold futures, gold spot markets 1. Introduction Gold differs from agricultural commodities, and its uniqueness lies in its uniformity, durability, and storability. No matter where gold is traded, it has the same fundamental characteristics, and gold prices tend to exhibit a common pattern despite differences in purity, contract terms or trading currency. According to Harris et al. (1995), markets in which the traded assets are fundamentally related are termed informationally linked markets. This concept can be applied to gold or its derivatives that are traded on different exchanges. The concept is also linked to cointegration mechanisms which state that assets that share common fundamentals should have long-term relationships. Thus it is expected that regardless of the market gold is traded on, gold prices are linked and should be consistent. Otherwise, arbitrage opportunities will emerge whereby traders can simultaneously buy at a low price and sell at a higher price. A perfect market should offer no arbitrage opportunities. Returns on derivative securities like gold futures contracts should be perfectly correlated with the return of spot gold. However, in an imperfect market with asymmetric information and transaction costs, traders favor low cost and high leverage and will make tradeoffs for the sake of these two parameters. Since a trade in a futures market requires relatively little upfront cash (initial margin deposits are only a fraction of the total value of the underlying asset) and can be effectuated immediately, while purchasing a basket of physical gold requires a greater initial investment and may take longer to implement, the preference for cost efficiency causes the futures market to lead the spot market. *Corresponding Author: Department of Finance, Faculty of Commerce and Accountancy, Thammasat University, Bangkok 10200, Thailand, address: pchinda@tu.ac.th **School of Economics, Bangkok University, Bangkok 10110, Thailand. 1

2 Therefore, it is interesting to explore cross-market arbitrage opportunities among gold futures markets and spot gold since previous studies [e.g. Brennan et al. (1990), Habeeb et al.(1991), Neal (1996), Fung and Dropper (1991), and Lee (2005)] focused only on arbitrage opportunities among stock markets. This study investigates the three main gold futures markets, namely the Commodity Exchange (COMEX) division of the New York Mercantile Exchange (NYMEX) in the U.S., the Multi Commodity Exchange (MCX) in India, and the Tokyo Commodity Exchange (TOCOM) in Japan. To the best of our knowledge, this paper is the first to utilize high frequency synchronous trading time data that gives 5-minute intraday spot gold and gold futures prices. This mitigates the stale price problem and may better capture arbitrage opportunities among studied markets. Another major contribution of this paper is that it modifies the interval pricing model of Modest and Sundaresan (1983), and Klemkosky and Lee (1991) by incorporating all associated costs, including foreign exchange hedging, to derive no-arbitrage bands that should be more appropriate for the case of gold futures. The remainder of this paper is organized as follows: Section 2 reviews the literature, Section 3 presents the data in detail, Section 4 discusses the study methodology, Section 5 discusses the empirical results, and Section 6 gives conclusions. 2. Literature Review Schwartz and Laatsch (1991) conducted empirical analysis of the Major Market Index (MMI) using intraday, daily, and weekly data from 1985 to They considered the closeness between futures and spot markets based on the supply of arbitrage, and concluded that persistent mispricing occurs on a daily basis, and sometimes persists overnight. Meanwhile, the relationship between spot and futures markets is not stable over time, highlighting the time variance element. Brennan and Schwartz (1990) examined the profitability of unwinding arbitrage positions early using 15-minute price data for the S&P 500 Index covering four years since Early unwinding might occur when the initial mispricing considerably exceeds the transaction cost, but the arbitrageurs still elect the risky arbitrage based on the expectation that the combined profit from both early unwinding and arbitrage in the initial time will fully offset the transaction costs. The authors found that on average this arbitrage strategy yielded a profit after eliminating the transaction costs incurred. Habeeb, Hill, and Rzad (1991) highlighted the suggestion that arbitrageurs must set profit levels for the entry and exit of arbitrage trades. They described that arbitrage trades can be launched when mispricing exceeds the sum of the associated transaction costs and required entry profit. Meanwhile, early unwinding can occur when mispricing reversal equals or exceeds the sum of the transaction costs and required exit profit. Through empirical research on S&P 500 Index 5- minute interval price data from 1987 to 1990, they found the entry profit level ranges from 0.8 to 0.9 index points, while the exit profit level ranges from 0.2 to 0.4 points. This strategy brings the highest returns for futures-spot arbitrage. Neal (1996) used minute-by-minute data to analyze 837 arbitrage trades on the NYSE for the contract in 1989 using a LOGIT regression model. The results showed a significant positive coefficient between mispricing reversal and absolute mispricing; meanwhile, a negative coefficient existed between absolute mispricing 2

3 and number of days for delivery. Restated, arbitrageurs wish to construct an arbitrage position between the stock index futures and spot market under conditions of high mispricing volatility, which make the early unwinding of that position more valuable. Gay and Jung (1999) used the cost-of-carry model to investigate the differences between actual futures prices and theoretical values. The sample period in this study covers approximately two-years, beginning with the establishment of the Korean futures market on May 3, 1996 and continuing through May 12, Gay and Jung (1999) found that futures are persistently mispriced (usually underpriced) especially during periods of downward market trends. This study also found that transaction costs explain a substantial portion of the underpricing. However, high mispricing remained even after accounting for the transaction costs faced by the lowest cost trader group (exchange members). This is attributed partly to the restrictions on short sales. These instances of mispricing imply that either the cost-of-carry model is inaccurate or the Korean futures market contains pricing inefficiencies. Consequently, the cost-of-carry model may fail to capture the dynamic interactions between the stock and futures markets. Fung and Draper (1999) analyzed the mispricing of the Hong Kong Hang Seng Index futures contracts by deliberately focusing on the short-selling constraint. Since short sale restrictions impede long-hedge arbitrage (long futures contract position and short stock position), arbitrage profits would not be realized when stock is overpriced. The tests in this study were conducted over three distinct regulatory regimes relating to the short selling of stocks in Hong Kong during April 1993 to September Two major changes in short-selling restrictions occurred during the sample period. The first regime covered the period April 1993 to January 1994, during which short-selling was prohibited. The second regime covered the period during which The Stock Exchange of Hong Kong (SEHK) allowed 17 of the 33 stocks comprising the Hang Seng Index (HSI) to be sold short. The HSI stocks are the largest, most liquid, and most actively traded stocks on the market. Finally, the last regime covered the period during which short sale restrictions were completely lifted, allowing more complete and effective arbitrage. Fung and Draper (1999) concluded that the improved ability to take long hedge positions due to the lifting of short selling constraints increased the reaction speed of the market. In short, traders were able to react faster to mispricing opportunities, leading to their being extinguished. Lee (2005) explored index arbitrage opportunities in the Korea Stock Price Index 200 (KOSPI 200) futures and KOSPI 200 cash indexes during May 3, 1996 to August 31, 2001 using one-minute interval price data for nearby futures contracts. To find the mispricing between the futures and cash markets, Lee constructed noarbitrage bounds on the KOSPI 200 futures price in terms of the KOSPI 200 cash prices and transaction costs, including bid-ask spread and taxes. If the actual futures price is above the upper bound or below the lower bound, then it is considered mispriced and profitable arbitrage strategies can be executed. In the case that the actual futures price exceeds the upper bound, a short hedge (short futures and long stock) needs to be taken. On the other hand, a long hedge (long futures and short stock) is profitable for a futures contract whose price is below the lower bound. Lee (2005) investigated the arbitrage opportunities on both an ex-post and ex-ante basis. An ex-post basis refers to an arbitrage opportunity where the 3

4 assumption is that an arbitrage position can be established the moment a futures contract is identified as mispriced. An ex-ante basis refers to an opportunity where an arbitrage position can be formed only after the price violation. Lee applied three lags for ex-ante investigation, namely the first, second, and third time-matched sets of prices following the initial mispricing. The empirical results show that arbitrage profits from both the ex-post and ex-ante basis are positive and significant even for the third lag time-matched set of prices after the actual violation. This implies that profitable arbitrage opportunities persist in the Korean market, and mispricing between KOSPI 200 futures and cash markets is corrected too slowly. Consequently, Lee (2005) concluded that the KOSPI 200 futures and cash markets are extremely inefficient. To date, few studies have examined the gold and gold futures markets, and none have investigated associated arbitrage opportunities. For example, Bertus and Stanhouse (2001) studied bubbles in quarterly gold futures prices using dynamic factor analysis. They built an explicit model of the supply and demand for gold to obtain a fundamental price and used this to estimate the difference between the market price and true value. They then used this to create a time series for the bubble component in the market price. However, since the bubble component was found to be insignificant they concluded that no bubble existed. Bhar and Hamori (2004) investigated the pattern of information flow between the percentage price change and trading volume in gold futures contracts. They utilized daily NYMEX settlement price data from January 3, 1990 to December 27, Meanwhile, the AR-GARCH model and Schwarz Baynesian information criteria (SBIC) were used to select the final model from various possible AR- GARCH specifications. The GARCH (2,1) model was chosen for the percentage price change, while the GARCH (1,1) model was chosen for the trading volume. The results show that the information flows between price change and trading volume affect both mean movements and volatility movements in these markets, which indicates the sequential information linkage. Dhillon, Lasser, and Watanabe (1997) examined volatility in the United States (US) and Japanese gold futures markets using trading prices and volumes for nearby gold futures contracts traded on COMEX and TOCOM. Four daily return series, namely open-to-close, close-to-open, close-to-close, and open-to-open, were estimated and intraday high and low prices were used to estimate the variance. However, at the time there was no overlapping of trading hours between the two markets. The whole sample period from July 1987 to May 1992 was divided into three subperiods to separate the influences of trading volume and trading mechanism on futures price volatility. The first subperiod ran from July 1987 to October 1989, and was characterized by Walrasian-type trading with a relatively low volume. The second subperiod was from November 1989 to March 1991, and was characterized by Walrasian-type trading with high volume. Finally, the last subperiod was from April 1991 to May 1992, and was characterized by continuous trading with high volume. The evidence indicates that prices in double auction markets exhibit greater intraday volatility than those in Walrasian auction markets. Moreover, more information appears to be released in gold markets during US trading hours relative to Japan, and exchange volume conveys private information both within and across COMEX and TOCOM markets. More specifically, returns for the COMEX gold futures contracts exhibit consistently higher intraday variance than those of 4

5 TOCOM, which may result from differences in trading mechanisms and volumes across markets. Xu and Fung (2005) examined the patterns of cross-market information flows for precious metal futures contracts traded on both the US and Japanese markets. They extended the study of Dhillon et al. (1997) in several ways. First, they investigated three precious metals futures contracts, gold, platinum, and silver, using daily data during November 1994 and March Xu and Fung applied a bivariate ARMA-GARCH model that allows simultaneous analysis of the pricing transmission and volatility spillover to investigate the market linkages. Second, they analyzed intraday information flows to see the effect of the US market close on the opening price of the Japanese market. Conversely, they also examined the effect of trading information in Japan after the market close there on the opening price of the US market. Finally, as US and Japan are generally regarded as the two centers of the global precious metal futures market, Xu and Fung shed light on which market has the more important information, and on the direction of information transmission between the two markets. The results indicated strong and significant pricing transmission between the US and Japan, implying bidirectional transmission between the two markets. The cross-market coefficient of gold futures is much larger in the US equation, which suggests that the relative impact of the US market is stronger in terms of pricing transmission, and that US information plays a leading role in the futures market. Volatility analysis indicates that both the US and Japanese markets receive important information from each other, and strong feedback effects exist between the two. The significance of both sets of feedback effects appears similar, implying that each market exerts a similar influence on the other. Chaihetphon and Pavabutr (2010) examined the price discovery process of nascent gold futures contracts in the Multi Commodity Exchange (MCX) of India during 2003 to The vector error correction model is employed to show that futures prices of standard and mini gold futures contracts lead the spot price, indicating that price discovery occurs in the futures market. This study also compared the contributions to price discovery of standard and mini gold futures contracts traded on electronic platforms. Although mini contracts capture only 2% of the trading value on the MCX, they contribute approximately 37% to price discovery. It was thus concluded that contract separation need not compromise market quality. Standard gold futures contracts remain the main source of price discovery and liquidity, and mini contracts aid price discovery and serve smaller participants. 3. Data A set of intraday observations has been obtained from Bloomberg Pro to investigate cross-market arbitrage in COMEX U.S.A., MCX India, and TOCOM Japan. Table 1 lists the details of each gold futures contract. Given that the timematching interest rate strictly tailored for the maturity of the gold futures contract is unavailable in the market, the 3-month Treasury bill in a particular country is used as a rough proxy of risk-free interest rate. The interest rate data are obtained from the Datastream. To enable comparison of the gold price among particular countries, it is converted into the domestic currency price for a given amount of gold. For example, the futures contract of TOCOM and MCX are quoted as JPY per gram and INR per 5

6 10 grams respectively, but the spot price is quoted in USD per troy ounce. Since the contract sizes for the MCX and TOCOM are 1 kilogram per contract, while that for COMEX is 100 troy ounces, the gold price conversion formula for each market is calculated as follows: 1 gram price of gold in TOCOM = Spot price / x (JPY/USD) (1) 10 grams price of gold in MCX = Spot price / x (INR/USD) x 10 (2) To mitigate the stale price problem and more precisely measure arbitrage opportunities across markets, 5-minute intraday analysis is applied. Since the COMEX gold futures market operates almost 24 hours a day, while TOCOM and MCX do not, we select only those overlapped trading times of the three exchanges to investigate cross-market arbitrage opportunities. After converting the operating times of the Japanese and Indian markets to match that of the New York market, the analysis period was 10 hours per trading day, from 4 A.M. to 1 P.M., New York time as shown in Figure 1. Because this study investigates inter-market arbitrage opportunities, the data should be collected during a period of high volatility. Thus, an observation period running from April to August 2011 is selected, and prices of the nearest gold futures contracts for the three studied markets are used. Converting prices of MCX and TOCOM yields the gold futures price quoted in USD per troy ounce for a purity of (reported in Table 2). On average, the highest gold futures prices are in the Indian market, at USD 1,555, while the prices in the US and Japanese markets are almost the same, at USD 1,532 to 1,534. The returns of gold futures contracts as calculated using high frequency data are extremely low, and the average returns of COMEX, MCX, and TOCOM are , , and , respectively. Using daily intervals, the average returns are , , and for COMEX, MCX, and TOCOM, respectively. Prices of gold futures differ among all the exchanges. This basically reflects the differences in domestic risk-free rates each country uses to calculate the futures prices. Unsurprisingly, the US and Japan, both of which face economic recessions, have lower domestic interest rates, and hence lower gold futures prices. In contrast, due to higher interest rates compared with the other two markets, the MCX gold futures prices are highest. 4. Methodology 4.1 Type of Arbitrage The cost-of-carry approach states that futures prices should depend on both the cash price of a commodity and the cost of storing the underlying goods until the delivery date of the futures contract. Mathematically, F S 1 C ) (3) where and C t, T t, T t ( t, T F t, T is the futures price at t=0 for delivery at time t, St is the cash price at t, is the carrying charges, expressed as a fraction of the cash price, needed to store the good until the delivery date of the futures contract. In the case of gold, the most significant carrying charge in the futures market is the financing cost. Most participants in futures markets face short-term financing 6

7 charges that equal the risk-free interest rate. Carrying charges are crucial in determining the relationship between spot and futures prices, as well as that among prices of futures contracts with different maturities. Arbitrage opportunities occur when the prices of futures contracts do not conform to cost-of-carry prices. Our research focuses on two forms of arbitrage related to the gold futures market; futures-spot arbitrage and futures-futures arbitrage Futures-spot Arbitrage Investors can engage in futures-spot arbitrage when the prices of gold futures deviate from their theoretical value. However, if transaction costs and market restrictions are considered, the theoretical value of futures is not a specific numerical value but rather a price band called the no-arbitrage band. If futures prices exceed the upper limit of this band, investors can profit through cash-andcarry arbitrage in which they take a short (sell) position in gold futures and a long (buy) position in spot gold then clear both positions at the settlement date. Meanwhile, if futures prices fall below the lower limit of the band, investors can profit through reverse cash-and-carry arbitrage, which involves the same procedure but taking opposite positions. Figure 2 presents the process of futures-spot arbitrage in simplified form Futures-futures Arbitrage Prices of the same type of futures contract on different exchanges may deviate differently from theoretical prices and result in different values. Simultaneously, the price of a futures contract might be higher than the no-arbitrage bound on one exchange and lower on another. Investors can then achieve arbitrage profits by simply taking a long position in futures contracts that are underpriced and a short position in futures contracts that are overpriced. To simplify this, Figure 3 shows the process of futures-futures arbitrage. Notably, arbitrage opportunities can exist even when both markets are mispriced in the same direction. This can occur when one market has an extremely high (overpricing) or extremely low (underpricing) mispriced value while the other has a smaller mispricing in the same direction. However, these kind of arbitrage opportunities are less pronounced because the discrepancies between two markets are much smaller than for opposite direction mispricing. 4.2 Modified Interval Pricing Model The ordinary interval pricing model concentrates only on trading commissions and impact costs. However, in real world situations, other factors can affect arbitrage behavior. Thus, this study discusses some of these effects for the case of the gold market. a. Tax rate Generally, investors who profit from investing in physical gold have no obligation to pay capital gains tax. Similarly, investors are exempted from capital gains tax for gold futures traded on the COMEX, MCX, and TOCOM. Foreign investors are not subject to any trading restrictions, and nor is there any need for special or qualified foreign institutional investor s accounts. b. Interest rate uncertainty 7

8 In the cash-and-carry strategy, the arbitrageur assumes that he will be able to borrow at a certain rate until a futures contract expires. Similarly, in the reversecash-and-carry strategy, the arbitrageur assumes he will be able to invest the proceeds from the sale of gold at a particular rate of interest. However, the uncertainty about this interest rate directly influences the profits generated from arbitrage positions. c. Commission fees The only costs arising from trading spot gold are bid-ask spread, which can vary on a minute-by-minute basis. Most international bullion houses charge no brokerage. The average spread during the study period was typically basis points for spot gold. Thus, we impose bid-ask spread costs at 65 basis points in this study. However, in the context of the futures market, traders face commission fees that vary across markets. For COMEX, many providers set competitive commission rates for trading gold futures. Table 3 shows brokerage commissions in the US, Japan, and India as examples. d. Foreign exchange rate uncertainty This study employs futures contracts as the hedging instrument. Three foreign exchange (FX) futures are used in this study: (1) USD futures contract of the Chicago Mercantile Exchange (CME), (2) INR/USD futures contract of the Multi Commodity Exchange (MCX), and (3) JPY/USD futures contract of the Tokyo Commodity Exchange Market (TOCOM). e. Short selling transaction The main transaction costs associated with futures-spot arbitrage are the bid-ask spread costs of the gold spot market and the round-trip commission fees charged on long and short futures contracts. To make a short sale on spot gold, investors must pay a specified interest rate to the physical gold provider, which is normally their own broker. We also consider these costs to create upper and lower no arbitrage bounds. Next, this study modifies the interval pricing models developed by Modest and Sundaresan (1983), and Klemkosky and Lee (1991) by incorporating all associated costs to create alternative no-arbitrage bounds. 1 Our modified interval pricing model that reflects all associated costs is more appropriate for application to gold futures. Table 4 defines the parameters in our modified model Modified Upper Limit of the No-Arbitrage Bound The cost of creating a futures position is the sum of the transaction costs for taking both long and short positions in gold futures contracts. Similarly, the cost of taking a spot gold futures position includes the cost of buying and selling spot gold. Therefore, we can derive the upper limit of the no-arbitrage bound through the process illustrated in Table 5. Therefore, the modified upper limit is as follows. 1 We employ futures contract as a hedging tool in this study because the price of futures contract can be obtained, and the expired date of futures contract can be matched with our arbitrage strategies. Since the results from Chunhachinda et al. (2012) indicated that COMEX plays the leading role in price discovery, we use USD as our domestic currency. 8

9 F T F TT S ( C t st 1 C sl fs )(1 r) (1 r') ft fl (1 r') st ss ft FX (4) Modified lower limit of no-arbitrage bound The lower limit is derived using the same principles as the upper limit. Table 6 lists the process of lower limit derivation. Thus, the modified lower limit is as follows. FTT St ( Cst ss )(1 r') ft (1 r) ft FX FT (5) 1 C (1 r) 6. Empirical Results a. Futures-Spot Arbitrage Opportunities fl To identify potential arbitrage opportunities, we analyze the futures-spot setting over three gold futures markets. The sample period runs from April, 2010 to August, 2011, during which time the global gold market experienced large fluctuations that provide a good chance to examine the functionality of our approach. As our data has a high frequency format and contains numerous observations it is difficult to plot the graph of the whole sample because the lines of upper limit, lower limit, and price of gold futures are difficult to distinguish from one another. Thus, we show the example data for one trading day (July 29, 2011) for the case of MCX in Figure 4. Even in developed markets, many arbitrage opportunities exist. We can thus conclude that gold markets offer arbitrage opportunities. To precisely identify the existence of potential arbitrage opportunities, we analyze the potential asymmetry between overpricing and underpricing. We expect both larger and more frequent overpricing in gold futures contracts because of the costs of short selling physical gold and the high expectation of increasing gold prices. U AF F e U S ; AF F (6) F L AF e L S ; AF F (7) where F U and F L are the upper and lower no-arbitrage bounds, while e+ and e- represent overpricing and underpricing of the futures contract relative to F U and F L. From Panel C of Table 7, the characteristic of mispricing in TOCOM appears symmetric. The percentages of overpricing and underpricing are similar (40.89% versus 49.63%). On the other hand, in Panel B, MCX has the largest percentage of overpricing (94.30%). This reflects a high expectation that the gold price will increase in India. Moreover, the results listed in Table 7 are consistent with the concept of different speeds of price adjustment among markets. From Panel A, COMEX, which plays a leading role in price discovery, has the lowest percentage of mispricing of gold futures (86.03%), while TOCOM, which has the fastest price adjustment in correcting mispricing errors, captures second place (90.53%). Although arbitrage profits exist in all three markets, their average sizes are trivial, at %, %, and % for COMEX, MCX, and TOCOM, respectively. 9 fs st sl

10 b. Futures-futures arbitrage opportunities This section provides evidence of arbitrage opportunities between any two gold futures exchanges. Profits generated from cross-futures markets are likely to exceed those from futures-spot arbitrage because investors can choose to purchase underpriced futures contracts and simultaneously sell overpriced futures contracts. The mispricing is calculated from the deviation of the theoretical price obtained from the cost-of-carry approach. Overpricing occurs when the observed price is higher than the theoretical price, while underpricing occurs in the opposite situation. Once again, three exchanges with synchronous trading times are investigated to find profits in cross-futures markets. The results from Table 7 also show that MCX has the highest frequencies of overpricing, at a fraction of 94.30%, while TOCOM has the highest frequencies of underpricing, at a fraction of 49.63%. Therefore, the longest distance between any two gold futures exchanges representing the highest profit of arbitrage transaction is likely to occur by being long TOCOM gold futures and short MCX gold futures. Moreover, the TOCOM and MCX size of gold futures contracts are the same at 1 kilogram bullion gold. Arbitrage between MCX and TOCOM can be performed straightforwardly simply by purchasing the underpriced gold futures contract and selling the overpriced gold futures contract. However, since the size of the COMEX gold futures contract is 100 troy ounces, the performance of cross market arbitrage transaction such as COMEX and MCX or COMEX and TOCOM requires adjusting all the transaction costs to match the contract size of TOCOM and MCX gold futures. Only a specific fraction of transaction costs are used to calculate upper and lower bounds. Since three futures exchanges participated in this analysis, three potential cross market arbitrage opportunities are investigated. The evidence from Table 8 is consistent with the result of our previous study [Chunhachinda et al. (2012)] which found that COMEX is where price discovery takes place and that TOCOM has the fastest price adjustment toward a new equilibrium. Starting from Panel B, the pair of COMEX (which plays a leading role) and TOCOM (which has the fastest price adjustment to correct mispricing error) has the fewest mispricing errors. For Panel A, with the effect of fast price adjustment to correct mispricing error of TOCOM, the pair MCX-TOCOM captures second place at 86.23% while that of COMEX-MCX has the highest percentage of mispricing errors at 97.79%. Moreover, the average profits of futures-futures arbitrage between the two major gold futures markets exceed those of futures-spot arbitrage (1.0249% for MCX-COMEX, % for COMEX-TOCOM, and % for MCX-COMEX). 7. Conclusion In this study, we investigated two types of arbitrage opportunities; (1) between gold futures and spot markets and (2) between the gold futures and gold futures exchange markets. To detect mispricing errors, we modified the financial theory by incorporating market restrictions to derive a new modified formula. Two modified interval pricing models proposed by Modest and Sundaresan (1983), and Klemkosky and Lee (1991) were reviewed because they apply to the case of gold futures. Besides the consideration of market restrictions mentioned in these two models, the risk exposures associated with exchange rate fluctuation are also incorporated into the modified interval pricing model to deal with cross-market 10

11 boundaries. Therefore, the cost-of-carry model is modified to account for differential transaction costs and obtain the upper and lower bounds of gold futures prices. For futures-spot arbitrage, the evidence from our 5-minute time series data shows that developed gold futures exchanges exhibit low arbitrage profits, with average arbitrage profits of COMEX, MCX, and TOCOM being just 0.03%, 0.84%, and 0.49% respectively. Arbitrage opportunities also exist for futures-futures arbitrage, and the average arbitrage profits for COMEX-MCX, COMEX-TOCOM, and MCX-TOCOM are 1.02%, 0.74%, and 1.51%, respectively. This evidence sheds light on the topic of arbitrage and global gold markets. The findings with regard to the existence of arbitrage opportunities are consistent with previous research investigating arbitrage opportunities for other securities, such as Lee (2005). Notably, this evidence of arbitrage across markets could occur because of the limitations of the futures pricing model. This study considers all costs of market restrictions and incorporates them into the classic cost-of-carry model, which is most widely used to price futures securities. This model was initially formulated under the assumptions of perfect markets and a non-arbitrage argument, and thus might not completely fit the imperfect market case. Thus a further investigation of alternative futures pricing models is suggested. Moreover, the empirical results presented in this study confirm previous findings of a long run equilibrium relationship in gold markets. However, the speed of adjustment to new arrival information differs among gold exchanges in different regions. Even using data for 5-minute intervals, arbitrage opportunities can still be detected. Hopefully, this empirical result will be useful for gold market participants, including hedgers, arbitrageurs, and speculators. References Bhar, R. and Hamori, S. (2004). Information flow between price change and trading volume in gold futures contracts. International Journal of Business and Economics, 3, Bertus, M. and Stanhouse, B. (2001). Rational speculative bubbles in the gold futures market: An application of dynamic factor analysis. Journal of Futures Markets, 21 (1), Brennan, M. J., and Schwartz, E. S. (1990).Arbitrage in stock index futures. Journal of Business, 63(1), S7-S32. Chaihetphon P., and Pavabutr P. (2010). Price discovery in the Indian gold futures market. Journal of Economics and Finance, 34(4), Chunhachinda P., Fuangkasem R., and Nantapan S. (2012). Information transmission among major gold futures markets: Evidence from a high frequency data. Working paper. Dhillon, U. S., Lasser, D. J., and Watanabe, T. (1997). Volatility, information, and double versus walrasian auction pricing in US and Japanese futures markets. Journal of Banking and Finance, 21, Fung, J. K. W., and Draper, P. (1999).Mispricing of index futures contracts and short sales constraints. Journal of Futures Market, 19, Fung, H. G., Leung, W. K., Xu, X. E. (2001). Information role of U.S. futures trading in a global financial market. The Journal of Futures Markets, 21(11),

12 Gay, G. D., and Jung, D. Y. (1999). A further look at transaction costs, short sales restrictions, and futures market efficiency: the case of Korean stock index futures. Journal of Futures Market, 19, Habeeb.G., Hill, J. M., and Rzad, A. J. (1991). Potential rewards from path dependent index arbitrage with S&P 500 fututres. Review of Futures Markets, 10(1), Harris, M. H., McInish, T. H., Shoesmith, G. L., and Wood, R. A. (1995). Cointegration, error correction, and price discovery on informationally linked security markets. Journal of Financial and Quantitative Analysis, 39 (4), Klemkosky, R. C., and Lee, J. H. (1991). The intraday ex post and ex ante profitability of index arbitrage. Journal of Futures Markets, 11(3), Lee, J. H. (2005). Index arbitrage with the KOSPI200 futures. The 2002 Annual Pacific-Basin Capital Markets (PACAP) Finance Conference. Modest, D. M., and Sunderesan, M. (1983). The relationship between spot and futures prices in stock index futures markets some preliminary evidence. Journal of Futures Market, 3(1), Neal, R. (1996). Direct tests of index arbitrage models. Journal of Financial and Quantitative Analysis, 31, Schwartz, T., and Laatsch, F. (1991). Price discovery and risk transfer in stock index cash and futures markets. Journal of Futures Markets, 11, Xu, X., and Fung, H. (2005). Cross-market linkages between U.S and Japanese precious metals futures trading. International Financial Markets, 15(2), Figure 1: Gold Futures Trading Hours of the Three Exchanges, New York Time Remark: Trading hours of TOCOM and MCX are converted into New York time before making a comparison. 12

13 Figure 2: Process of Cross-Market Arbitrage between Spot and Futures Markets Calculate no-arbitrage band Estimate arbitrage opportunity Exceed upper limit Below lower limit Buy spot gold and sell gold futures Sell spot gold and buy gold futures Sell spot gold and close futures position Buy spot gold and close futures position Figure 3: Process of Cross-Market Arbitrage between Futures Markets Calculate no-arbitrage band Estimate arbitrage opportunity Exceed upper limit Below lower limit Buy gold futures from underpriced market and sell another gold futures from overpriced market Make a reverse transaction to close futures position 13

14 INR Proceedings of Eurasia Business Research Conference Figure 4: MCX Mispricing with Upper and Lower Limits 23,400 MCX 23,300 23,200 23,100 23,000 22,900 22, Upper MCX Lower Obs Table 1: Details of Gold Futures Contract Specifications COMEX TOCOM MCX Year of start trading Underlying asset Fine gold bar Fine gold bar Fine gold bar Contract size 100 t oz 1 kilogram 1 kilogram Quality specification purity purity purity Price quote USD per t oz JPY per gram INR per 10 grams Tick size USD 0.10 per t oz JPY 1 per gram INR 1 per 10 grams Settlement type Physical delivery Physical delivery Physical delivery Sources: COMEX, MCX, TOCOM 14

15 Stat Table 2: Summary Statistics of 5-Minute Intraday Price Data of the Three Futures Markets COMEX MCX TOCOM Price (USD ) 5-min Return Daily Return Price (USD ) 5-min Return Daily Return Price (USD ) 5-min Return Daily Return Mean 1, E , E , E Med 1, , , Max 1, , , Min 1, , , Std Obs 8,066 8, ,066 8, ,066 8, Table 3: Commission Fees in Major Gold Futures Markets Panel A: Example of commission fee charged in USA Type of investor Non-NYMEX member NYMEX member Contracts per month Per side (USD) Per round trip (USD) Per side (USD) Per round trip (USD) Level 1: $2.07 $4.14 $1.55 $3.10 Level 2: $2.00 $3.99 $1.48 $2.95 Level 3: $1.92 $3.84 $1.40 $2.80 Level 4: $1.85 $3.69 $1.33 $2.65 Level 5: $1.77 $3.54 $1.25 $2.50 Level 6: $1.57 $3.14 $1.05 $2.10 Level 7: $1.55 $3.09 $1.03 $2.05 Level 8: $1.53 $3.06 $1.01 $2.02 Level 9: $1.52 $3.04 $1.00 $2.00 Source: Velocity Futures, LLC. Panel B: Example of commission fee charged in Japan Number of contracts (Lots)* 1 lot 5 lots 10 lots 25 lots 50 lots 100 lots TOCOM commission fee per round trip (JPY) 944 4,720 9,440 23,600 47,200 94,400 Remark: * The commission fee is imposed according to a number of gold futures contract. Source: TOCOM official website Panel C: Example of commission fee charged in India For MCX, the commission fee is charged at 0.03% per side or 0.06% per round trip. In this case, MCX commission fee is not a fixed value but it is depended on the price of gold futures contract. The MCX standard gold futures commission fee is calculated from following equation. Commission fee = (brought price x Lot Size x ) + (sold price x Lot Size x ) 15

16 Source: MCX official website Table 4: Definition of Parameters Used to Construct No-Arbitrage Bounds Parameters Definition S t Price of spot gold at time t S T Price of spot gold at time T (T > t) C st C sl C ss C ft C fl C fs C FX F t F T F TT r' r T-t Trading commission of spot gold trading Bid-ask spread cost of buying spot gold Bid-ask spread cost of selling spot gold Transaction cost gold futures trading Bid-ask spread cost of buying gold futures contract Bid-ask spread cost of selling gold futures contract Hedging cost of foreign exchange exposures Price of gold futures contract at time t Price of gold futures contract at time T Theoretical price of gold futures contract at time T Borrowing rate Lending rate The holding period from t to T 16

17 Table 5: Derivation of the Modified Upper Limit of the No-Arbitrage Bound Transaction costs: Long gold futures contract: Short gold futures contract: C ft +F T C fl C ft (1+r ) (T-t) +F T C fs (1+r ) (T-t) Buy spot gold: S t (C st +C sl )(1+r) (T-t) Sell spot gold: S T (C st +C ss ) FX hedging: C FX Total costs of arbitrage: C ft +F T C fl + C ft (1+r ) (T-t) +F T C fs (1+r ) (T-t) + S t (C st +C sl )(1+r) (T-t) + S T (C st +C ss )+ C FX Check whether F T -F TT > total costs of arbitrage: F T -F TT >C ft +F T C fl + C ft (1+r ) (T-t) +F T C fs (1+r ) (T-t) + S t (C st +C sl )(1+r) (T-t) + S T (C st +C ss )+ C FX At maturity date, price of futures contract is the same as price of underlying asset. Then, substituting F T with S T, we obtain: F T F TT S ( C t st 1 C sl fs )(1 r) (1 r') ft fl (1 r') st ss ft FX 17

18 Table 6: Derivation of the Modified Lower Limit of the No-Arbitrage Bound Transaction costs: Long gold futures contract: Short gold futures contract: C ft (1+r) (T-t) +F T C fl (1+r) (T-t) C ft +F T C fs Buy spot gold: S T (C st +C sl ) Sell spot gold: FX hedging: S t (C st +C ss )(1+r ) (T-t) C FX Total costs of arbitrage: C ft (1+r) (T-t) +F T C fl (1+r) (T-t) + C ft +F T C fs + S T (C st +C sl )+ S t (C st +C ss )(1+r ) (T-t) + C FX Check whether F T -F TT > total costs of arbitrage: F T -F TT >C ft (1+r) (T-t) +F T C fl (1+r) (T-t) + C ft +F T C fs + S T (C st +C sl )+ S t (C st +C ss )(1+r ) (T-t) +C FX At maturity date, price of futures contract is the same as price of underlying asset. Then, substituting F T with S T, we obtain: F T F TT S ( C t st ss 1 C fl )(1 r') (1 r) fs ft (1 r) st sl ft FX 18

19 Table 7: The Mispricing and Arbitrage Opportunities between Gold Spot and Gold Futures Markets Panel A: COMEX Mispricing Error Mean Std dev Min Med Max Obs/ Total obs occur e ,379/8, % e ,561/8, % [e] ,940/8, % Panel B: MCX Mispricing Error Mean Std dev Min Med Max Obs/ Total obs occur e ,606/8, % e /8, % [e] ,692/8, % Panel C: TOCOM Mispricing Error Mean Std dev Min Med Max Obs/ Total obs occur e ,299/8, % e ,004/8, % [e] ,302/8, % Table 8: The Mispricing and Arbitrage Opportunities among Gold Futures Markets Panel A: MCX-TOCOM Error Mean Std dev Min Med Max Obs/ Total obs Mispricing occur e ,955/8, % Panel B: COMEX-TOCOM Mispricing Error Mean Std dev Min Med Max Obs/ Total obs occur e ,372/8, % Panel C: MCX-COMEX Error Mean Std dev Min Med Max Obs/ Total obs Mispricing occur e ,888/8, % 19