AN ARBITRAGE OPPORTUNITY IN THAI GOLD FUTURES...

AN ARBITRAGE OPPORTUNITY IN THAI GOLD

FUTURES MARKETS

THANAPHOT ARTMAPRASANGSA

ID 5302042451

MASTER OF SCIENCE PROGRAM IN FINANCE

(INTERNATIONAL PROGRAM)

FACULTY OF COMMERCE AND ACCOUNTANCY

THAMMASAT UNIVERSITY, BANGKOK, THAILAND

JUNE 2012

AN ARBITRAGE OPPORTUNITY IN THAI GOLD

FUTURES MARKETS

THANAPHOT ARTMAPRASANGSA

MASTER OF SCIENCE PROGRAM IN FINANCE

(INTERNATIONAL PROGRAM)

FACULTY OF COMMERCE AND ACCOUNTANCY

THAMMASAT UNIVERSITY, BANGKOK, THAILAND

JUNE 2012

An Arbitrage Opportunity in Thai Gold Futures Markets

Thanaphot Artamaprasangsa

An Independent Study

Submitted in Partial Fulfillment of the Requirements

for the Degree of Master of Science (Finance)

Master of Science Program in Finance

(International Program)

Faculty of Commerce and Accountancy

Thammasat University, Bangkok, Thailand

June 2012

Thammasat University

Faculty of Commerce and Accountancy

An Independent Study

By

Thanaphot Artamaprasangsa

“An Arbitrage Opportunity in Thai Gold Futures Markets”

has been approved as a partial fulfillment of the requirements

for the Degree of Master of Science (Finance)

In June 2012

Advisor: ……………………………………

(Prof. Dr. Pornchai Chunhachinda)

Co-Advisor: ……………………………………

(Asst. Prof. Dr. Sarayut Nathaphan)

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ABSTRACT

This study investigates outright and inter-month spread arbitrage opportunities using cost-

and-carry model. Dataset consists of 10-minute gold futures prices series traded in Thailand

Futures Exchange (TFEX) during August 28, 2011 to February 29, 2012. Cointegration test is

applied to prove long-run relationship between gold futures and gold spot as well as distant-

maturity and nearby-maturity gold futures contracts; however, the futures prices sometimes

deviate from the cost-and-carry fair value. This is also occurring in both outright and inter-

month arbitrage positions as mispricing, and arbitragers will enter into the market when the

mispricing is sufficiently large to compensate for transaction costs and associated interest rate

risks. Then an estimate of non-arbitrage bounds in the incomplete market by direct and

indirect method is applied as guidance to find arbitrage opportunities. In conclusion, the

existences of arbitrage opportunities and limitations in Thai gold futures markets have been

proved in both outright and inter-month spread arbitrage positions. However, the results in

both direct and indirect method are different due to their particular perceptions in estimate

non-arbitrage bounds.

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I. INTRODUCTION

Gold futures contracts offer investors low-cost trading to invest in gold market. Not only

reducing cost of custody physical gold and eliminating the hassles for investors, it also

provides investors greater liquidity and reliable real-time price. Because they are traded in

real time on exchange trade derivatives, Thailand Futures Exchange (TFEX) and controlled

cash settlement and guaranteed the contractual compliance by clearing house. Typical costs

for trading gold futures are such as bid-ask spread, brokerage and commission fees, and

financing costs of the margin. The most common advantage of gold future is that in trading

gold futures, investors can make profits from speculating bullish and bearing outlook of gold

price. Exploiting profit on the price difference between two or more markets called arbitrage

and diversifying market risk on the investment portfolio are also applied in wide range.

Therefore, the objectives of this paper are to prove existence of arbitrage opportunities in

retail investors to Thai gold futures market. To prove this, we first estimate non-arbitrage

bounds, which are boundary of non-arbitrage area. Two different methods developing from

cost-and-carry model to estimate non-arbitrage bounds are applied in this paper. The first

method is “Direct” method, which estimates the non-arbitrage bounds from replicating

arbitrage positions. The second one is “Indirect” method, which estimates the non-arbitrage

bounds from mispricing errors from Threshold Autoregressive (TAR) model. For both

methods, we applied them into outright and inter-month spread strategies. Finally, the

arbitrage opportunities in Thai gold futures market from August 28, 2011 to February 28,

2011 are explained and demonstrated in statistic form.

The contributions of this paper are that (1) to introduce possible arbitrage strategies in Thai

gold futures market, (2) to estimate the upper and lower no-arbitrage bound of Thai gold

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futures, (3) to demonstrate arbitrage opportunities in two perspectives in comparison, and (4)

to demonstrate existence of arbitrage opportunities in Thai gold futures markets.

This paper is organized as follows. Section II presents the literature review. The methodology

and the data are described in Section III and Section IV, respectively. Section V and Section

VI elaborates upon empirical results and conclusions. Reference books and papers that we

based on are noted on the Section VII.

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II. LITERATURE REVIEW

Arbitrage is a common financial strategy that has been studied in wide range of aspects. To

examine about arbitrage opportunities, we have to understand how to price gold futures.

Following Kolb and Overdahl (2007), cost-of-carry model the classical model of future and

forward pricing are referred in many papers to explain relationship between future price and

cash price of the underlying assets follow such model. Conceptually, futures price will be

based on its underlying price and its cost of carrying from the present to its maturity date. In

addition, Martens, Kofman and Vorst (1998) also apply the cost-of-carry model with the

financing cost and propose a log transformation to simplify the equation and regress for the

mispricing error in long-run equilibrium.

Spread costs are added into account of the cost-of-carry model. Because Kee-Hong Bae,

Kalok Chan and Yan-Leung Cheung (1998) mention that without spread cost, the model will

process two significant biases in evaluating arbitrage profitability. First, the frequency of

arbitrage opportunities is overstated. Suppose that a futures transaction takes place at the bid

price and, based on the bid price, we conclude that the futures are underpriced. Therefore the

arbitrage strategy is to buy the underpriced futures. However, the price that we could buy at is

the ask, not the bid. If we use the correct price (the ask), there might be no arbitrage

opportunities. Second, the size of arbitrage profits is overstated. Suppose the futures (at the

ask). If only transaction prices are observed, one might mistakenly use a sale price (at the bid)

for a futures purchase, so that the purchase price is understated and the arbitrage profit is

overstated. To correct for the biases, the bid-ask quotation price should be applied to the

evaluation of arbitrage profitability.

In mispricing regression, non-stationary, which is inherent risk of time series, have to be

considered. Greene (2002) has explained how to transform data to mitigate non-stationary

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problem. If the two series are both I (1), then this partial difference between them might be

stable around a fixed mean. The implication would be that the series are drifting together at

roughly the same rate. Two series that satisfy this requirement are said to be conintegrated.

Apart from this, in many literatures (e.g. Poitras (1990), Brenner and Kroner (1995), Hansen

(2011)), they are mentioned that, under certain conditions, the futures and spot price are

cointegrated. It means that its residual of the linear combination is stationary, white noise

series.

Finally, the arbitrage opportunity will occur together with mispricing of gold futures prices

occurs. However, mispricing may not be exploited by arbitrageurs because the basis or spread

is lower than transaction costs or there is no transaction to trade at certain period. Therefore,

the gold futures and the gold spot, or the gold future and inter-month gold futures will move

together within a no-arbitrage bound, otherwise the future prices that sometime deviated from

the cost-of-carry fair value will lead to mispricing situation and arbitrage opportunities. The

estimation of practical upper and lower no-arbitrage bounds in the incomplete market are

developed by both direct and indirect methods as guideline whether the mispricing of Thai

gold futures markets is relevant enough to exploit an arbitrage transaction as mentioned on

many literatures such as e.g. Yadav, Pope and Paudyal (1994), Marten, Kofman and Vorst

(1998), Hensen (2011).

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III. METHODOLOGY

Mispricing and arbitrage opportunity between prices of gold spot and gold futures (called

Basis), and between prices of gold futures series (called Spread) are our main objectives.

First, investors will understand futures pricing model of cost-of-carry model. Second,

estimating non-arbitrage bounds are proposed in two different methods; direct and indirect

method. In both methods, we applied quoted price of bid and ask price into the model to

ignore the bias of overstated frequency of arbitrage opportunities and overstated size of

arbitrage profits as mentioned on Section III. Under indirect method, cointegration test will be

applied to prove stationary of mispricing error. Finally, an idea of mispricing and arbitrage

opportunity will be introduced.

3.1 Model for Futures Pricing

Martens, Kofman and Vorst (1998) proposed the cost-of-carry model to describe the

relationship between index cash and futures prices.

The cost-of-carry models for basis arbitrage are referred as follows:

(2.1)

The cost-of-carry models for inter-month spread arbitrage are referred as follows:

(2.2)

where is the futures price at time t and maturity at time T, is the cash price at time t,

is the futures price at time t for the distant maturity contract maturing at time d, while

is the futures price at time t for the nearby maturity contract maturing at time n, denotes

financial cost to hold underlying assets from initial time t to maturity time T, denotes

financial cost to hold underlying assets from nearby maturity time to distant maturity time

of futures contracts.

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Martens, Kofman and Vorst (1998) simplify and format the future pricing model on Equation

(2.1) and (2.2) into regression form, a log transformation and regression parameters as

follows:

(2.3)

(2.4)

where and

are the mispricing error from outright arbitrage and inter-month spread

arbitrage, respectively.

3.2 Gold Futures Mispricing and No-arbitrage Bound

Although long-run relationship is confirmed, the futures prices sometimes deviate from the

cost-of-carry fair value. The accumulated deviation would lead to mispricing of futures price,

and the arbitrage opportunities may occurs if the mispricing is relevant enough compensate

for transaction costs and associated interest rate risks. Then the deviation will disappear when

arbitrageurs find and immediately exploit. The estimation of practical upper and lower no-

arbitrage bounds take an important role in explanation of arbitrage opportunities. In order to

capture the no-arbitrage bound construction, we assume the strategy of arbitrageurs to hold

the futures contracts to maturity and perfect market.

3.2.1 Direct method

This method applies the cost-and-carry model to construct the no-arbitrage bound. In

cash-and-carry arbitrage, arbitrageurs can borrow funds to buy the underlying assets, and

upper no-arbitrage bound can be constructed. On the other hand, in reverse cash-and-

carry arbitrage, arbitrageurs can lend funds from sell the underlying assets, and lower no-

arbitrage bound can be constructed.

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Arbitrage between gold index cash and futures prices

Derivation of the lower no-arbitrage bound of futures index

Suppose gold futures price tend to go down, arbitrageurs would apply strategy of reversed

cash-and-carry by going short gold spot and long gold futures, and subsequently reverse

the positions at the futures maturity. Net cash flow is provided on Table I.

At time t the net cash flow is equal to zero. Therefore, to preclude arbitrage profit, the

payoff at time T cannot be greater than zero, and rearranging terms gives the following

lower bound:

(2.5)

where denotes lower no-arbitrage bound of gold future at time t and maturity at time

T in basis arbitrage. In case of gold futures, cost of trading futures, is given as a

constant factor and same value to all arbitrage transactions. denotes a bid at time t

and denotes a final settlement price at time T. is average saving rate of four Thai

main commercial banks such as Bangkok Bank, Siam Commercial Bank, Kasikornthai

Bank and Krungthai Bank and represented as the cost of lending. denotes an ask

gold futures price at time t and maturity at time T. or IM denotes an initial margin

required by broker as guarantee.

Derivation of the upper no-arbitrage bound of futures index

Suppose gold futures price tend to go up, arbitrageurs would apply strategy of cash-and-

carry by going long gold spot and short gold futures, and subsequently reverse the

positions at the futures maturity. Net cash flow is provided on Table II.

(2.6)

where denotes upper no-arbitrage bound of gold future at time t and maturity at time

T in basis arbitrage. denotes an ask gold spot price at time t and denotes a final

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settlement price at time T. is minimum retail rate in Thailand and represented as the

cost of borrowing. denotes a bid gold futures price at time t and maturity at time T.

Arbitrage among futures prices in difference series

Derivation of the lower no-arbitrage bound of futures index

Suppose gold futures price of nearby maturity tend to go down, arbitrageurs would apply

strategy of reversed forward cash-and-carry by going short gold futures of nearby

maturity and long gold futures of distant maturity, and subsequently reverse the positions

at each futures maturity. Net cash flow is provided in Table III.

(2.7)

where denotes lower no-arbitrage bound of gold future at time t and maturity at time

T in inter-month spread arbitrage. denotes a bid gold futures price at time t and

maturity at time n or nearby contract. denotes an ask gold futures price at time t and

maturity at time d or distant contract. and

denotes a final settlement price at time T

for distant maturity and nearby maturity.

Derivation of the upper no-arbitrage bound of futures index

Suppose gold futures price of nearby maturity tend to go up, arbitrageurs would apply

strategy of forward cash-and-carry by going long gold futures of nearby maturity and

short gold futures of distant maturity, and subsequently reverse the positions at each

futures maturity. Net cash flow is provided on Table IV.

(2.8)

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where denotes upper no-arbitrage bound of gold future at time t and maturity at time

T in inter-month spread arbitrage. denotes an ask gold futures price at time t and

maturity at time n or nearby contract. denotes a bid gold futures price at time t and

maturity at time d or distant contract.

3.2.2 Indirect method

Following Marten, Kofman and Vorst (1998), the mispricing error of futures prices is

considered as the key factor to estimate non-arbitrage bound. The mispricing error may be

caused by a transaction costs, bid-ask spread costs, interest rate risk, etc. Area between

upper non-arbitrage bound and lower non-arbitrage bound are considered as the expected

(risk-adjusted) returns that do not exceed the expected costs from an arbitrage transaction.

Due to all gold futures and gold spot series seem to be non-stationary, therefore the study

uses the cointegration test to avoid the spurious problem. To test unit root, Dickey and

Fuller (DF) would be applicable and also uses Schwarz information criterion (SIC)

determining the appropriate number of lags for mispricing error of each arbitrage

position. The mispricing error ( ) are derived from the Equation (2.3) and (2.4) are tested

with Augmented Dickey-Fuller (ADF) method.

Martens, Kofman, and Vorst (1998) adopt threshold autoregressive (TAR) model to

collect the error-correction term under the long-run equilibrium assumption. TAR for the

mispricing error can be stated as follows:

, (2.9)

Refer to Equation (2.3) and (2.4) and

are the deviation derived from long-

run equilibrium in the cost-of-carry model. for are autoregressive

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coefficients, assumed to be constant over time. and threshold lag is a

positive integer. The thresholds are ; is

i.i.d. , which stands for white-noise term with constant variance.

For simplify the case, we assume the threshold lag and with two regimes to demonstrate

the reaction of arbitrageurs to mispricing error in the prior period as follows:

, (2.10a)

, (2.10b)

, (2.10c)

When arbitrageurs take place into the market, the next observation of mispricing error

will move rapidly towards zero. Otherwise, the deviation from zero must be very small.

Refer to Equation (2.10a), (2.10b) and (2.10c), a linear Autoregressive (AR) model will

be applied in each regime. In such setting, a change of regime caused different set of

coefficients. Thus, AR ( ) coefficient to be close to one means deviation is small.

To construct an indirect no-arbitrage bound of outright arbitrage, we take exponential

function into Equation (2.3) and (2.4) with different threshold candidates.

represents as threshold candidates for lower bound of outright arbitrage market and

represents as threshold candidates for upper bound of outright arbitrage

market. For an indirect no-arbitrage bound of inter-month spread arbitrage,

represents as threshold candidates for lower bound of inter-month spread arbitrage market

and represents as threshold candidates for upper bound of inter-month spread

arbitrage market. To select the threshold candidates, we select the lowest residuals

regressed from the Equation (2.9). Based on the exponential function, the positive value

of will return the value higher 1, and the negative value of will return the value

from zero to one. Then, to construct the upper bound, the lowest residuals regressed from

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the Equation (2.9), which related to positive will be selected. The lowest residuals

related to negative will in contrast be selected to construct the lower bound.

Therefore, the upper no-arbitrage bounds and lower no-arbitrage bounds are constructed

as follows:

No-arbitrage bounds of outright arbitrage

(2.11)

(2.12)

No-arbitrage bounds of inter-month spread arbitrage

(2.13)

(2.14)

where and

denotes futures fair value at time t with maturity at time T in basis

arbitrage market and at time t with maturity at time d in inter-month arbitrage market.

3.3 An Arbitrage Opportunity

An arbitrage opportunity occurs when the mispricing error is out of the non-arbitrage

bound. Percentage of existence of the arbitrage opportunity in each arbitrage position and

both direct method and indirect method and its distribution are the relative magnitude of

arbitrage profit are measured.

Relative magnitude of arbitrage profit of outright arbitrage market is demonstrated as

follows:

- Arbitrage position is to long gold futures contract and to short gold spot.

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(2.15)

- Arbitrage position is to long gold spot and to short gold futures contract.

(2.16)

, and relative magnitude of arbitrage profit of inter-month spread arbitrage market is

demonstrated as follows:

- Arbitrage position is to long distant-maturity gold futures contract and to short nearby-

maturity gold futures contract.

(2.17)

- Arbitrage position is to long nearby-maturity gold futures contract and to short

distant-maturity gold futures contract.

(2.18)

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IV. DATA

The dataset consists of 10-minute gold futures prices series traded in Thailand Futures

Exchange (TFEX) during August 28, 2011 to February 29, 2012 such as December 2011 and

February 2012 series for both 10-Bath and 50-Baht gold futures contracts. We employ

intraday bid-ask quotation of gold futures, gold spot quoted in US dollar and exchange rate

from Bloomberg. Bid and ask quotation price of gold spot are translated with selling rate and

buying rate, respectively. The returns of each price series are calculated as the changes in the

natural logarithms of prices multiplied by 100. Main costs of arbitrage transactions for gold

futures markets consist of interest rate and brokerage fees. Interest rates, both saving deposit

and minimum retail rate, which are published on website of the Bank of Thailand

(www.bot.or.th), are represented cost of lending and cost of borrowing, respectively. Average

of interest rate on four Thai main commercial banks such as Bangkok Bank, Siam

Commercial Bank, Kasikornthai Bank and Krungthai Bank are used as cost of financing in

this paper. Brokerage fee and initial margin are dominated individually by each brokerage

under TFEX’s regulations and based on daily trading volume of each investor. To simplify

parameter in estimating non-arbitrage bound, I apply the middle level of brokerage fees of

Baht 8.56 per 1-Baht gold (including VAT) and initial margin at 10% of future contract price

as constant factors.

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V. EMPIRICAL RESULTS

This chapter presents the estimated results including their interpretations with regard to

the methodology mentioned in the chapter 2. We use 10-minute gold futures and gold

spot during August 28, 2011 to February 29, 2012 to prove the arbitrage opportunities.

During the study, we found the limitation to take outright arbitrage opportunities in

backwardation since there is no gold supplier who lends gold to investors. The results are

divided into 3 parts following the main objectives as the following:

First, cointegration between gold futures and gold spot, and between inter-month spread

gold futures are proved. We test unit root of gold futures and gold spot series by Dickey

Fuller (DF) test. On Table V, all tau statistics of gold futures and gold spot series are very

small. While all tau statistics of the difference of each gold futures and gold spot series

sufficiently large exceeding critical values as p-values are very small indicating that the

null hypothesis of unit root is rejected. Thus we conclude that each gold futures and gold

spot series are integrated order 1 or I (1). The linear combinations between them are also

determining the appropriate number of lags by Schwarz information criterion (SIC). On

Table VI and Table VII, we test unit root test of mispricing error (z) from outright

arbitrage positions and inter-month spread arbitrage positions by Augmented Dickey-

Fuller (ADF) test, and find that the null hypothesis of unit root is rejected. It means that

these series are drifting together at roughly the same rate with cointegration order (1,1).

Second, on Table VIII, short-hedged outright arbitrage positions (Ft > E(St)) in contango

provide profit over initial margin paid to arbitrageurs of 0.38%-0.64%. On Table IX,

long-hedged inter-month spread arbitrage positions (Fd-Fn < E(Sd)-E(Sn)) in

backwardation provide profit over initial margin paid to arbitrageurs of 74.67%-74.88%

when no returns on short-hedged inter-month spread arbitrage positions (Fd-Fn > E(Sd)-

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E(Sn)). It represents temporary backwardation expectation in gold futures markets, which

arbitrageurs exploited long-hedged position. Note that there is no long-hedged outright

arbitrage position because of the limitation as mentioned above. In practice, direct method

on Equation (2.5) to (2.8) can be adjusted its transaction costs based on trading volume.

Third, the arbitrage opportunities in the view of indirect method are confronted with

Equation (2.11) to (2.14). The arbitrage profits based on this method are much lower than

view in direct method. On Table VIII, we find that short-hedged outright arbitrage

positions (Ft > E(St)) provide profit over initial margin paid to arbitrageurs of 0.24%-

1.92%. On Table IX, we find short-hedged inter-month spread arbitrage positions (Fd-Fn

> E(Sd)-E(Sn)) in contango and long-hedged inter-month spread opportunities (Fd-Fn <

E(Sd)-E(Sn)) in backwardation provide profit over initial margin paid to arbitrageurs of

0.29%-0.93% and 0.03%-0.58%, respectively.

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VI. CONCULSION

Based on our sampling data between August 28, 2011 and February 28, 2012, gold

futures and gold spot tend to move together in long-run following the cost-and-carry

model. Gold futures and gold spot are non-stationary data and they move together in

long-run and in the same order as same relationship between distant-maturity and nearby-

maturity futures, which mean that they are cointegated.

The existences of arbitrage opportunities are proved by comparing between actual price

of gold future series and the non-arbitrage bounds being estimated by both direct and

indirect method. For direct method, we take transaction costs such as brokerage fees into

account and concern about initial margin paid as guarantee to hold gold future contracts.

The interest will also be significant costs to hold futures position to maturity. For indirect

method, the mispricing error or deviation between futures price and theoretical price will

be captured the most appropriate under Threshold Autoregressive (TAR) model. The

mispricing errors are such as the transaction costs, illiquidity risks, which make the

futures price deviate from the theoretical price.

Based on the studied period, direct method demonstrates that the inter-month spread

strategy provides arbitrage profit in long-hedged position much more than those of the

outright strategy. Since there is temporary backwardation in taking inter-month spread

arbitrage before moving back to contango. In inter-month spread arbitrage, the gap

between distant-maturity and nearby-maturity futures price is much lower than the gap

between theoretical prices of gold spot in distant-maturity and nearby-maturity period. In

outright arbitrage, futures prices is not significant different from the theoretical price of

gold spot. Arbitrageurs therefore tend to exploit such mispricing by taking long-hedged

positions in inter-month spread strategy. There is then no short-hedge position in inter-

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month spread arbitrage. For indirect method, the results in both outright and inter-month

spread arbitrage are not significantly different and their arbitrage profits are a little bit

higher than their financing and transaction costs. Furthermore, there is no long-hedge

position since there is no gold supplier who lends gold to investors.

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VII. REFERENCES

Books

Ender, Walter, 2004, Applied Econometric Time Series, (John Wiley & Sons).

Damodar N. Gujarati, 2004, Basic Econometrics, (The McGraw-Hill Companies).

Hull, John C., 2009, Fundamentals of Futures and Options Markets, (Pearson Education, Inc.,

Prentice Hall).

Kolb R. and Overdahl, J.A., 2007, Futures, Options and Swaps, (Perason Education, Inc.,

New Jersey).

William H. Greene, 2002, Econometric Analysis, (Pearson Education, Inc., Prentice Hall).

Articles

Alex Frino and Michael D. Mckenzie, 2002, The Pricing of Stock Index Futures Spreads at

Contract Expiration, The Journal of Futures Markets 22, 451-469.

Bruce E. Hansen, 2011, Threshold Autoregression in Economics, Statistics and Its Interface

4, 123-127.

Geoffrey Poitras, 1990, The Distribution of Gold Futures Spreads, The Journal of Futures

Markets 10, 643-659.

Gerald D. Gay and Dae Y. Jung, 1999, A Further Look at Transaction Costs, Short Sale

Restrictions, and Futures Market Efficiency: The Case of Korean Stock Index Futures,

The Journal of Futuers Markets 19, 153-174.

Ira G. Kawaller, Paul D. Koch and Ludan Liu, Winter 2002, Calendar Spreads, Outright

Futures Positions, and Risk, The Journal of Alternative Investment, 59-74.

Kee-Hong Bae, Kalok Chan and Yan-Leung Cheung, 1998, The Profitability of Index Futures

Arbitrage: Evidence from Bid-Ask Quotes, The Journal of Futures Markets 18, 743-763.

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Martin Martens, Paul Kofman and Ton C.F. Vorst, 1998, A Threshold Error-Correction

Model for Intraday Futures and Index Returns, Journal of Applied Econometrics 13, 245-

263.

Robin J. Brenner and Kenneth F. Kroner, 1995, Arbitrage, Cointegration, and Testing the

Unbiasedness Hypothesis in Financial Markets, The Journal of Financial and

Quantitative Analysis 30, 23-42.

Sunthorn Thongthip, 2010, Lead-lag Relationship and Mispricing in SET50 Index Cash and

Futures Markets, Faculty of Economics, Thammasat University, Bangkok Thailand.

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TABLE INDEXES

Table I Strategy of reversed cash-and-carry by going short gold spot and long gold futures:

Time t Time T

Short gold spot

Long futures -

Cost of buying futures -

IM (install) settle

Cost of selling futures -

Lending with s rate

Net cash flow -

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Table II Strategy of cash-and-carry by going long gold spot and short gold futures:

Time t Time T

Long gold spot

Short futures -

Cost of selling futures -

IM (install) settle

Cost of buying futures -

Borrowing with MRR rate

Net cash flow -

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Table III Strategy of reverse forward cash-and-carry by going short nearby-maturity gold futures and long distant-maturity gold futures:

Time t Time n Time d

Short futures of nearby maturity -

-

Cost of selling futures - -

IM (install) settle

-

Cost of buying futures - -

Long futures of distant maturity - -


IM (install) settle -


Lending with s rate -


-

Net cash flow - -

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Table IV Strategy of reverse forward cash-and-carry by going long nearby-maturity gold futures and short distant-maturity gold futures:

Time t Time n Time d

Long futures of nearby maturity -

-


IM (install) settle

-


Short futures of distant maturity - -


IM (install) settle -


Lending with s rate -


- -

Net cash flow - -

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Table V Unit root test for time series data of gold futures and gold spot:

Dickey-Fuller Test

Series Price Type Rho Pr <

Rho

Tau Pr <

Tau

Ft-Dec11 Bid 10-Baht Gold

Futures

-0.0135 0.6801 -0.97 0.2982

ΔFt-Dec11 Bid -

4366.07 0.0001 -69.24 < 0.0001

Ft-Dec11 Ask -0.0121 0.6804 -0.92 0.3177

ΔFt-Dec11 Ask -4608.1 0.0001 -70.1 < 0.0001

Ft-Dec11 Bid 50-Baht Gold

Futures

-0.0134 0.6801 -0.96 0.2993

ΔFt-Dec11 Bid -

4323.76 0.0001 -68.72 < 0.0001

Ft-Dec11 Ask -0.0121 0.6804 -0.92 0.3171

ΔFt-Dec11 Ask -

4536.34 0.0001 -69.1 < 0.0001

Ft-Feb12 Bid 10-Baht Gold

Futures

-0.0034 0.6824 -0.22 0.6094

ΔFt-Feb12 Bid -

7275.99 0.0001 -97.32 < 0.0001

Ft-Feb12 Ask -0.0136 0.68 -1.03 0.2747

ΔFt-Feb12 Ask -

4773.16 0.0001 -77.48 < 0.0001

Ft-Feb12 Bid 50-Baht Gold

Futures

-0.0037 0.6824 -0.21 0.6108

ΔFt-Feb12 Bid -

6363.13 0.0001 -83.26 < 0.0001

Ft-Feb12 Ask -0.0176 0.6791 -1.22 0.2054

ΔFt-Feb12 Ask -

4485.55 0.0001 -68.28 < 0.0001

St Bid Gold spot -0.0101 0.6809 -0.68 0.4233

ΔSt Bid -

4174.21 0.0001 -65.87 < 0.0001

St Ask -0.0101 0.6809 -0.68 0.423

ΔSt Ask -

4104.63 0.0001 -64.75 < 0.0001

Table VI Unit root test for mispricing error (z) of outright arbitrage positions:

Arbitrage Positions Augmented Dickey-Fuller Test

Short Type Long Type Lags Rho Pr <

Rho

Tau Pr <

Tau

Ft-Dec11 10-Baht

Gold

Futures

St Gold

spot

5 -103.222 0.0001 -7.12 < 0.0001

Ft-Dec11 50-Baht

Gold

Futures

St Gold

spot

5 -99.9592 < 0.0001 -7.01 < 0.0001

Ft-Feb12 10-Baht

Gold

Futures

St Gold

spot

5 -84.8778 < 0.0001 -7.45 < 0.0001

Ft-Feb12 50-Baht

Gold

Futures

St Gold

spot

9 -56.2187 < 0.0001 -5.33 < 0.0001

- 26 -

Table VII Unit root test for mispricing error (z) of inter-month spread arbitrage:

Arbitrage Positions Augmented Dickey-Fuller Test

Short Type Long Type Lags Rho Pr <

Rho

Tau Pr <

Tau

Fd-Feb12 10-Baht

Gold

Futures

Fn-

Dec11

10-Baht

Gold

Futures

10 -25.8676 0.0002 -3.94 < 0.0001

Fn-Dec11 10-Baht

Gold

Futures

Fd-

Feb12

10-Baht

Gold

Futures

4 -88.625 < 0.0001 -8.67 < 0.0001

Fd-Feb12 10-Baht

Gold

Futures

Fn-

Dec11

50-Baht

Gold

Futures

5 -47.6816 < 0.0001 -6.7 < 0.0001

Fn-Dec11 50-Baht

Gold

Futures

Fd-

Feb12

10-Baht

Gold

Futures

4 -93.206 < 0.0001 -8.94 < 0.0001

Fd-Feb12 50-Baht

Gold

Futures

Fn-

Dec11

10-Baht

Gold

Futures

9 -26.1565 0.0002 -3.82 0.0001

Fn-Dec11 10-Baht

Gold

Futures

Fd-

Feb12

50-Baht

Gold

Futures

8 -40.1974 < 0.0001 -4.47 < 0.0001

Fd-Feb12 50-Baht

Gold

Futures

Fn-

Dec11

50-Baht

Gold

Futures

9 -27.6451 0.0001 -3.95 < 0.0001

Fn-Dec11 50-Baht

Gold

Futures

Fd-

Feb12

50-Baht

Gold

Futures

8 -43.4331 < 0.0001 -4.66 < 0.0001

- 27 -

Table VIII Arbitrage opportunities for outright arbitrage

Figure

No.

Short Type Long Type Observation % of

Arbitrage

Profit

Mean Stdev Min Max Observation % of

Arbitrage

Profit

Mean Stdev Min Max

1 Ft > E(St),

upper

bound

Ft-Dec11 10-Baht

Gold

Futures

St Gold spot 4,020 0.40% 10.13 27.65 - 287.58 4,020 0.31% 7.86 26.80 - 292.84

2 Ft > E(St),

upper

bound

Ft-Dec11 50-Baht

Gold

Futures

St Gold spot 3,993 0.38% 9.65 26.85 - 317.58 3,993 0.24% 6.11 23.85 - 310.91

3 Ft > E(St),

upper

bound

Ft-Feb12 10-Baht

Gold

Futures

St Gold spot 5,906 0.64% 16.25 47.40 - 444.60 5,906 1.21% 30.46 66.91 - 497.13

4 Ft > E(St),

upper

bound

Ft-Feb12 50-Baht

Gold

Futures

St Gold spot 5,879 0.59% 15.05 45.10 - 429.86 5,879 1.92% 48.27 85.22 - 553.83

Arbitrage Positions Direct Method Indirect Method

Table IX Arbitrage opportunities for inter-month spread arbitrage

Figure

No.


Arbitrage

Profit


Arbitrage

Profit

Mean Stdev Min Max

5 Fd-Fn >

E(Sd)-

E(Sn),

upper

bound

Fd-

Feb12

10-Baht

Gold

Futures

Fn-

Dec11

10-Baht

Gold

Futures

4,338 0.00% - - - - 4,338 0.41% 10.56 23.62 - 177.73

Fd-Fn <

E(Sd)-

E(Sn),

lower

bound

Fn-

Dec11

10-Baht

Gold

Futures

Fd-

Feb12

10-Baht

Gold

Futures

4,338 74.88% 1,899.67 126.76 833.08 2,172.56 4,338 0.03% 0.70 4.96 - 147.93


- 28 -

Figure

no.


Arbitrage

Profit


Arbitrage

Profit

Mean Stdev Min Max

6 Fd-Fn >

E(Sd)-

E(Sn),

upper

bound

Fd-

Feb12

10-Baht

Gold

Futures

Fn-

Dec11

50-Baht

Gold

Futures

4,322 0.00% - - - - 4,322 0.69% 17.87 34.53 - 306.93

Fd-Fn <

E(Sd)-

E(Sn),

lower

bound

Fn-

Dec11

50-Baht

Gold

Futures

Fd-

Feb12

10-Baht

Gold

Futures

4,322 74.72% 1,895.38 131.71 39.76 2,132.10 4,322 0.58% 14.94 25.66 - 187.33

7 Fd-Fn >

E(Sd)-

E(Sn),

upper

bound

Fd-

Feb12

50-Baht

Gold

Futures

Fn-

Dec11

10-Baht

Gold

Futures

4,320 0.00% - - - - 4,320 0.93% 24.08 43.37 - 236.45

Fd-Fn <

E(Sd)-

E(Sn),

lower

bound

Fn-

Dec11

10-Baht

Gold

Futures

Fd-

Feb12

50-Baht

Gold

Futures

4,320 74.84% 1,898.42 127.04 852.95 2,132.77 4,320 0.20% 5.01 14.24 - 147.40

8 Fd-Fn >

E(Sd)-

E(Sn),

upper

bound

Fd-

Feb12

50-Baht

Gold

Futures

Fn-

Dec11

50-Baht

Gold

Futures

4,318 0.00% - - - - 4,318 0.29% 7.59 19.34 - 241.59

Fd-Fn <

E(Sd)-

E(Sn),

lower

bound

Fn-

Dec11

50-Baht

Gold

Futures

Fd-

Feb12

50-Baht

Gold

Futures

4,318 74.67% 1,894.16 131.77 49.69 2,142.05 4,318 0.14% 3.59 11.52 - 156.87


- 29 -

FIGURE INDEXES

Figure 1 Short-hedged outright position of 10-Baht gold future (December 2011 series)

Direct method

Indirect method

23000

24000

25000

26000

27000

28000

29000

1

20

1

40

1

60

1

80

1

10

01

12

01

14

01

16

01

18

01

20

01

22

01

24

01

26

01

28

01

30

01

32

01

34

01

36

01

38

01

40

01

GF10Z11 (bid) Upper bound

23000

24000

25000

26000

27000

28000

29000

1

20

1

40

1

60

1

80

1

10

01

12

01

14

01

16

01

18

01

20

01

22

01

24

01

26

01

28

01

30

01

32

01

34

01

36

01

38

01

40

01

GF10Z11 (bid) Upper bound

- 30 -

Figure 2 Short-hedged outright position of 50-Baht gold future (December 2011 series)

Direct method

Indirect method

23000

24000

25000

26000

27000

28000

29000 1

20

1

40

1

60

1

80

1

10

01

12

01

14

01

16

01

18

01

20

01

22

01

24

01

26

01

28

01

30

01

32

01

34

01

36

01

38

01

GFZ11 (bid) Upper bound

23000

24000

25000

26000

27000

28000

29000

1

20

1

40

1

60

1

80

1

10

01

12

01

14

01

16

01

18

01

20

01

22

01

24

01

26

01

28

01

30

01

32

01

34

01

36

01

38

01

GFZ11 (bid) Upper bound

- 31 -

Figure 3 Short-hedged outright position of 10-Baht gold future (February 2012 series)

Direct method

Indirect method

23000

24000

25000

26000

27000

28000

29000 1

2

01

4

01

6

01

8

01

1

00

1

12

01

1

40

1

16

01

1

80

1

20

01

2

20

1

24

01

2

60

1

28

01

3

00

1

32

01

3

40

1

36

01

3

80

1

40

01

4

20

1

44

01

4

60

1

48

01

5

00

1

52

01

5

40

1

56

01

5

80

1

GF10G12 (bid) Upper bound

23000

24000

25000

26000

27000

28000

29000

1

20

1

40

1

60

1

80

1

10

01

1

20

1

14

01

1

60

1

18

01

2

00

1

22

01

2

40

1

26

01

2

80

1

30

01

3

20

1

34

01

3

60

1

38

01

4

00

1

42

01

4

40

1

46

01

4

80

1

50

01

5

20

1

54

01

5

60

1

58

01

GF10G12 (bid) Upper bound

- 32 -

Figure 4 Short-hedged outright position of 50-Baht gold future (February 2012 series)

Direct method

Indirect method

23000

24000

25000

26000

27000

28000

29000 1

2

01

4

01

6

01

8

01

1

00

1

12

01

1

40

1

16

01

1

80

1

20

01

2

20

1

24

01

2

60

1

28

01

3

00

1

32

01

3

40

1

36

01

3

80

1

40

01

4

20

1

44

01

4

60

1

48

01

5

00

1

52

01

5

40

1

56

01

5

80

1

GFG12 (bid) Upper bound

23000

24000

25000

26000

27000

28000

29000

1

20

1

40

1

60

1

80

1

10

01

1

20

1

14

01

1

60

1

18

01

2

00

1

22

01

2

40

1

26

01

2

80

1

30

01

3

20

1

34

01

3

60

1

38

01

4

00

1

42

01

4

40

1

46

01

4

80

1

50

01

5

20

1

54

01

5

60

1

58

01

GFG12 (bid) Upper bound

- 33 -

Figure 5 Hedged inter-month spread of 10-Baht gold future (December 2011 series) and 10-

Baht gold future (February 2012 series)

Direct method

Indirect method

23000

24000

25000

26000

27000

28000

29000

30000

31000

1

20

1

40

1

60

1

80

1

10

01

12

01

14

01

16

01

18

01

20

01

22

01

24

01

26

01

28

01

30

01

32

01

34

01

36

01

38

01

40

01

42

01

GF10G12 (bid) GF10G12 (ask) Lower bound Upper bound

23000

24000

25000

26000

27000

28000

29000

1

20

1

40

1

60

1

80

1

10

01

12

01

14

01

16

01

18

01

20

01

22

01

24

01

26

01

28

01

30

01

32

01

34

01

36

01

38

01

40

01

42

01


- 34 -



Direct method

Indirect method

23000

24000

25000

26000

27000

28000

29000

30000

31000

1

20

1

40

1

60

1

80

1

10

01

12

01

14

01

16

01

18

01

20

01

22

01

24

01

26

01

28

01

30

01

32

01

34

01

36

01

38

01

40

01

42

01

GFG12 (bid) GFG12 (ask) Lower bound Upper bound

23000

24000

25000

26000

27000

28000

29000

1

20

1

40

1

60

1

80

1

10

01

12

01

14

01

16

01

18

01

20

01

22

01

24

01

26

01

28

01

30

01

32

01

34

01

36

01

38

01

40

01

42

01


- 35 -



Direct method

Indirect method

23000

24000

25000

26000

27000

28000

29000

30000

31000

1

20

1

40

1

60

1

80

1

10

01

12

01

14

01

16

01

18

01

20

01

22

01

24

01

26

01

28

01

30

01

32

01

34

01

36

01

38

01

40

01

42

01


23000

24000

25000

26000

27000

28000

29000

1

20

1

40

1

60

1

80

1

10

01

12

01

14

01

16

01

18

01

20

01

22

01

24

01

26

01

28

01

30

01

32

01

34

01

36

01

38

01

40

01

42

01


- 36 -



Direct method

Indirect method

23000

24000

25000

26000

27000

28000

29000

30000

31000

1

20

1

40

1

60

1

80

1

10

01

12

01

14

01

16

01

18

01

20

01

22

01

24

01

26

01

28

01

30

01

32

01

34

01

36

01

38

01

40

01

42

01


23000

24000

25000

26000

27000

28000

29000

1

20

1

40

1

60

1

80

1

10

01

12

01

14

01

16

01

18

01

20

01

22

01

24

01

26

01

28

01

30

01

32

01

34

01

36

01

38

01

40

01

42

01


- 37 -

APPENDICES

Appendix 1 Arbitrage strategies

Arbitrage is the practice of taking advantage of a price difference between two or more

markets. It is lower risk by purchase the cheaper from one market and sell more expensive in

another market. Main strategies on futures market are as follows:

Outright Outright means taking long or short position on a

futures contract on its own in order to speculate to

upside or downside. This is achieved simply by going

long when the price of the underlying asset is expected

to go upwards (a bullish outlook) or going short when

the price of the underlying asset is expected to go

downwards (a bearish outlook).

Inter-month spread Inter-month spreads are futures strategies that employ

futures contracts in combination with other series of

futures contracts in different maturity. Such

combinations allow futures traders to profit not only

from a bullish or bearish outlook but allow futures

traders to achieve very precise investment objectives.

Investment objectives such as locking in the price

difference between two different maturity, reaping a

risk-free arbitrage profit on futures contracts mispricing

or even profiting from an expected seasonal change in

futures contracts term structure, can be achieved using

strategic futures spreads that are calculated to produce

such a net effect.

http://www.futurestradingpedia.com/futures_arbitrage.htm

http://www.futurestradingpedia.com/futures_term_structure.htm

- 38 -

Appendix 2 Pattern of futures markets

Contango is when the futures price is above the expected futures spot price in outright

strategy. Because the futures price must converge on the expected future spot price, contango

implies that futures prices are falling over time as new information brings them into line with

the expected future spot price. In inter-month spread strategy

Normal backwardation is when the futures price is below the expected future spot price.

Appendix 3 Main features of gold futures contracts

Underlying asset Gold with purity of 96.5%

Settlement date One day before the last day of the maturity month.

Series of gold futures

10-Baht gold futures contracts: GF10/M/YY

50-Baht gold futures contracts: GF/M/YY

GF10 and GF represent 10-Baht and 50-Baht contracts.

M represents terminal month of each contract. There

are 6 even months a year such as G: February, J: April,

M: June, Q: August, V: October, and Z: December.

YY represents terminal year of each contract.

Last transaction 16:30 PM

Settlement In cash

Initial margin 10% of price of gold futures contract

Credibility Clearing house is responsible for cash settlement and

guaranteeing contractual compliance of the

counterparties of the futures markets.

- 39 -

Appendix 4 Thai gold future trading sessions

Pre-open Morning session 9:15-9:45

Morning session 9:45-12:30

Pre-open Afternoon session 14:00-14:30

Afternoon session 14:30-16:55

Night session 19:30-22:30

Appendix 5 Gold futures pricing

London Gold AM Fixing x

x

x

Appendix 5 Brokerage fees of Thai gold futures

Brokerage fees (Baht)

Trading volume per day (contract) 50-Baht gold futures 10-Baht gold futures

1-5 500 100

6-20 400 80

Over 21 300 60

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