Proceedings of Eurasia Business Research Conference
16 - 18 June 2014, Nippon Hotel, Istanbul, Turkey, ISBN: 978-1-922069-54-2
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, E-mail address: pchinda@tu.ac.th
**School of Economics, Bangkok University, Bangkok 10110, Thailand.
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Proceedings of Eurasia Business Research Conference
16 - 18 June 2014, Nippon Hotel, Istanbul, Turkey, ISBN: 978-1-922069-54-2
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 1988. 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 1983. 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 5minute 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
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Proceedings of Eurasia Business Research Conference
16 - 18 June 2014, Nippon Hotel, Istanbul, Turkey, ISBN: 978-1-922069-54-2
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, 1998.
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 1996. 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
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Proceedings of Eurasia Business Research Conference
16 - 18 June 2014, Nippon Hotel, Istanbul, Turkey, ISBN: 978-1-922069-54-2
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,
2000. Meanwhile, the AR-GARCH model and Schwarz Baynesian information
criteria (SBIC) were used to select the final model from various possible ARGARCH 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
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Proceedings of Eurasia Business Research Conference
16 - 18 June 2014, Nippon Hotel, Istanbul, Turkey, ISBN: 978-1-922069-54-2
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 2001. 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 2007. 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
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Proceedings of Eurasia Business Research Conference
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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 / 31.1034768 x (JPY/USD)
(1)
10 grams price of gold in MCX = Spot price / 31.1034768 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 0.995 (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
0.0000018, 0.0000019, and 0.0000019, respectively. Using daily intervals, the
average returns are 0.0012, 0.0010, and 0.0007 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,
Ft ,T  S t (1  Ct ,T )
(3)
where Ft ,T is the futures price at t=0 for delivery at time t, S t is the cash price at t,
and C t ,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
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Proceedings of Eurasia Business Research Conference
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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.
4.1.1 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.
4.1.2 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
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Proceedings of Eurasia Business Research Conference
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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 60-70 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.
4.2.1 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.
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FT 
FTT  S t (Cst  Csl )(1  r ) (T t )  C ft (1  r ' ) (T t )  C ft  C FX
1  C fs (1  r ' ) (T t )  C fl  Cst  Css
(4)
4.2.2 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  S t (Cst  Css )(1  r ' ) (T t )  C ft (1  r ) (T t )  C ft  C FX
(5)
FT 
1  C fl (1  r ) (T t )  C fs  Cst  Csl
6. Empirical Results
a. Futures-Spot Arbitrage Opportunities
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.
AF  F U
e 
U
S
; AF  F
(6)
L
F  AF
e 
L
S
; AF  F
(7)
where FU and FL are the upper and lower no-arbitrage bounds, while e+ and erepresent overpricing and underpricing of the futures contract relative to F U and FL.
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
0.0280%, 0.8433%, and 0.4925% for COMEX, MCX, and TOCOM, respectively.
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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, 0.7363% for COMEX-TOCOM, and 1.5057% 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
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Proceedings of Eurasia Business Research Conference
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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, 45-56.
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), 79-108.
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), 455-467.
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, 1045-1061.
Fung, J. K. W., and Draper, P. (1999).Mispricing of index futures contracts and
short sales constraints. Journal of Futures Market, 19, 695-715.
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), 1071-1090.
11
Proceedings of Eurasia Business Research Conference
16 - 18 June 2014, Nippon Hotel, Istanbul, Turkey, ISBN: 978-1-922069-54-2
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, 153-174.
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),
180-203.
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), 563–579.
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), 291-311.
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), 15-41.
Neal, R. (1996). Direct tests of index arbitrage models. Journal of Financial and
Quantitative Analysis, 31, 541-562.
Schwartz, T., and Laatsch, F. (1991). Price discovery and risk transfer in stock
index cash and futures markets. Journal of Futures Markets, 11, 669-683.
Xu, X., and Fung, H. (2005). Cross-market linkages between U.S and Japanese
precious metals futures trading. International Financial Markets, 15(2), 107-124.
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.
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16 - 18 June 2014, Nippon Hotel, Istanbul, Turkey, ISBN: 978-1-922069-54-2
Figure 2: Process of Cross-Market Arbitrage between Spot and Futures Markets
Calculate no-arbitrage band
Estimate arbitrage opportunity
Below
lower limit
Exceed
upper 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
Below
lower limit
Exceed
upper limit
Buy gold futures from underpriced market
and sell another gold futures from overpriced market
Make a reverse transaction to close futures position
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Figure 4: MCX Mispricing with Upper and Lower Limits
MCX
23,400
23,300
INR
23,200
23,100
23,000
22,900
22,800
1
11
21
31
41
51
Upper
61
71
MCX
81
91
101
Obs
Lower
Table 1: Details of Gold Futures Contract Specifications
COMEX
TOCOM
MCX
1974
1982
2003
Fine gold bar
Fine gold bar
Fine gold bar
100 t oz
1 kilogram
1 kilogram
Quality specification
0.995 purity
0.995 purity
0.995 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
Settlement type
Physical delivery
Physical delivery
INR 1 per 10
grams
Physical delivery
Year of start trading
Underlying asset
Contract size
Sources: COMEX, MCX, TOCOM
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Table 2: Summary Statistics of 5-Minute Intraday Price Data of the Three Futures Markets
COMEX
Stat
Price
(USD
)
MCX
5-min
Return
(%)
Daily
Return
(%)
Price
(USD
)
TOCOM
5-min
Return
(%)
Daily
Return
(%)
Price
(USD
)
5-min
Return
(%)
Daily
Return
(%)
Mean
1,532 1.8E-05
0.0012
1,555 1.9E-05
0.0010
1,534 1.9E-05
0.0007
Med
1,523
0.0000
0.0016
1,543
0.0000
0.0007
1,525
0.0000
0.0008
Max
1,682
0.0156
0.0334
1,705
0.0191
0.0248
1,688
0.0268
0.0432
Min
1,416
-0.0321
-0.0315
1,431
-0.0348
-0.0276
1,419
-0.0595
-0.0562
Std
56.01
0.0009
0.0085
52.50
0.0009
0.0070
57.17
0.0013
0.0092
Obs
8,066
8,065
261
8,066
8,065
261
8,066
8,065
261
Table 3: Commission Fees in Major Gold Futures Markets
Panel A: Example of commission fee charged in USA
Type of investor
Contracts per month
Level 1: 0-2499
Level 2: 2500-4999
Level 3: 5000-9999
Level 4: 10000-14999
Level 5: 15000-19999
Level 6: 20000-49999
Level 7: 50000-499999
Level 8: 500000-999999
Level 9: 1000000+
Non-NYMEX member
Per side
Per round trip
(USD)
(USD)
$2.07
$4.14
$2.00
$3.99
$1.92
$3.84
$1.85
$3.69
$1.77
$3.54
$1.57
$3.14
$1.55
$3.09
$1.53
$3.06
$1.52
$3.04
NYMEX member
Per side
Per round trip
(USD)
(USD)
$1.55
$3.10
$1.48
$2.95
$1.40
$2.80
$1.33
$2.65
$1.25
$2.50
$1.05
$2.10
$1.03
$2.05
$1.01
$2.02
$1.00
$2.00
Source: Velocity Futures, LLC.
Panel B: Example of commission fee charged in Japan
Number of contracts (Lots)*
TOCOM commission fee
per round trip (JPY)
1 lot
944
5 lots
4,720
10 lots
9,440
25 lots
23,600
50 lots
47,200
100 lots
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 0.0003) + (sold price x Lot Size x 0.0003)
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Source: MCX official website
Table 4: Definition of Parameters Used to Construct No-Arbitrage Bounds
Parameters
Definition
St
Price of spot gold at time t
ST
Price of spot gold at time T (T > t)
Cst
Trading commission of spot gold trading
Csl
Bid-ask spread cost of buying spot gold
Css
Bid-ask spread cost of selling spot gold
Cft
Transaction cost gold futures trading
Cfl
Bid-ask spread cost of buying gold futures contract
Cfs
Bid-ask spread cost of selling gold futures contract
CFX
Hedging cost of foreign exchange exposures
Ft
Price of gold futures contract at time t
FT
Price of gold futures contract at time T
FTT
Theoretical price of gold futures contract at time T
r'
Borrowing rate
r
Lending rate
T-t
The holding period from t to T
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Table 5: Derivation of the Modified Upper Limit of the No-Arbitrage Bound
Transaction costs:
Long gold futures contract:
Cft+FTCfl
Short gold futures contract:
Cft(1+r’)(T-t)+FTCfs(1+r’)(T-t)
Buy spot gold:
St(Cst+Csl)(1+r)(T-t)
Sell spot gold:
ST(Cst+Css)
FX hedging:
CFX
Total costs of arbitrage:
Cft+FTCfl+ Cft(1+r’)(T-t)+FTCfs(1+r’)(T-t)+ St(Cst+Csl)(1+r)(T-t)+ ST(Cst+Css)+ CFX
Check whether FT-FTT> total costs of arbitrage:
FT-FTT>Cft+FTCfl+ Cft(1+r’)(T-t)+FTCfs(1+r’)(T-t)+ St(Cst+Csl)(1+r)(T-t)+ ST(Cst+Css)+ CFX
At maturity date, price of futures contract is the same as price of underlying asset. Then, substituting
FT with ST, we obtain:
FT 
FTT  S t (Cst  Csl )(1  r ) (T t )  C ft (1  r ' ) (T t )  C ft  C FX
1  C fs (1  r ' ) (T t )  C fl  Cst  Css
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Table 6: Derivation of the Modified Lower Limit of the No-Arbitrage Bound
Transaction costs:
Long gold futures contract:
Cft(1+r)(T-t)+FTCfl(1+r)(T-t)
Short gold futures contract:
Cft+FTCfs
Buy spot gold:
ST(Cst+Csl)
Sell spot gold:
St(Cst+Css)(1+r’)(T-t)
FX hedging:
CFX
Total costs of arbitrage:
Cft(1+r)(T-t)+FTCfl(1+r)(T-t)+ Cft+FTCfs+ ST(Cst+Csl)+ St(Cst+Css)(1+r’)(T-t)+ CFX
Check whether FT-FTT> total costs of arbitrage:
FT-FTT>Cft(1+r)(T-t)+FTCfl(1+r)(T-t)+ Cft+FTCfs+ ST(Cst+Csl)+ St(Cst+Css)(1+r’)(T-t) +CFX
At maturity date, price of futures contract is the same as price of underlying asset. Then, substituting
FT with ST, we obtain:
FT 
FTT  S t (Cst  Css )(1  r ' ) (T t )  C ft (1  r ) (T t )  C ft  C FX
1  C fl (1  r ) (T t )  C fs  Cst  Csl
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Table 7: The Mispricing and Arbitrage Opportunities between Gold Spot and Gold
Futures Markets
Panel A: COMEX
Error
e+
e[e]
Mean
0.000286
0.000271
0.000280
Std dev
0.000279
0.000419
0.000338
Min
0.000000
0.000000
0.000000
Med
0.000168
0.000171
0.000169
Max
0.002683
0.003929
0.003929
Obs/
Total obs
4,379/8,066
2,561/8,066
6,940/8,066
Mispricing
occur
(%)
54.29%
31.75%
86.03%
Max
0.022001
0.002160
0.022001
Obs/
Total obs
7,606/8,066
86/8,066
7,692/8,066
Mispricing
occur
(%)
94.30%
1.07%
95.36%
Obs/
Total obs
3,299/8,066
4,004/8,066
7,302/8,066
Mispricing
occur
(%)
40.89%
49.63%
90.53%
Panel B: MCX
Error
e+
e[e]
Mean
0.008520
0.000738
0.008433
Std dev
0.004487
0.000614
0.004537
Min
0.000003
0.000025
0.000003
Med
0.008758
0.000467
0.008672
Panel C: TOCOM
Error
e+
e[e]
Mean
0.006492
0.003634
0.004925
Std dev
0.010998
0.003699
0.008009
Min
0.000005
0.000003
0.000003
Med
0.003003
0.002495
0.002713
Max
0.063969
0.029152
0.063969
Table 8: The Mispricing and Arbitrage Opportunities among Gold Futures Markets
Panel A: MCX-TOCOM
Mispricing
occur
(%)
Error
Mean
Std dev
Min
Med
Max
Obs/
Total obs
e
0.010249
0.005489
0.000016
0.010018
0.035706
6,955/8,066
86.23%
Max
0.070226
Obs/
Total obs
6,372/8,066
Mispricing
occur
(%)
79.00%
Mispricing
occur
(%)
97.79%
Panel B: COMEX-TOCOM
Error
e
Mean
0.007363
Std dev
0.008940
Min
0.000004
Med
0.005153
Panel C: MCX-COMEX
Error
Mean
Std dev
Min
Med
Max
Obs/
Total obs
e
0.015057
0.005092
0.002029
0.014933
0.030622
7,888/8,066
19