Electronic copy available at: http://ssrn.com/abstract=1744049

Price Transmission and Effects of Exchange Rates on DomesticCommodity Prices via Offshore Hedging

Nongnuch TantisantiwongSchool of Business

University of DundeeDundee DD1 4HN

UKemail:n.tantisantiwong@dundee.ac.uk

tel: +44 1382 385838

January 20, 2011

Abstract

The framework presents how trading in the foreign commodity futures and domestic forward foreignexchange markets can affect the optimal spot positions of domestic commodity producers and traders.It generalizes the models of Kawai and Zilcha (1986) and Kofman and Viaene (1991) to allow bothintermediate and final commodities to be traded in the international and futures markets, and theexporter to face production shock, domestic factor costs and a random price. Applying the mean-varianceexpected utility, we find that a rise in exchange rate volatility can reduce both supply and demand forcommodities and increase the domestic prices if the exchange rate elasticity of supply is greater than thatof demand. Even though the forward foreign exchange market is unbiased, and there is no correlationbetween commodity prices and exchange rates, the exchange rate can affect domestic trading and pricesthrough offshore hedging and international trade if the traders are interested in their profit in domesticcurrency. It illustrates how the world prices and foreign futures prices of commodities and their volatilitycan be transmitted to the domestic market as well as the dynamic relationship between intermediateand final goods prices. The equilibrium prices reflect trader behaviour i.e. who trade or do not trade inthe foreign commodity futures and domestic forward currency markets. The empirical result applying atwo-stage-least square approach and Thai rice and rubber prices supports the theoretical result.

Keywords: offshore hedging, currency hedging, asset pricing, price transmissionJEL Classification: F1; F3; G1; Q1

1

Electronic copy available at: http://ssrn.com/abstract=1744049

Price Transmission and Effects of Exchange Rates on Domestic Commodity

Prices via Offshore Hedging

Abstract

The framework presents how trading in the foreign commodity futures and domestic forward foreignexchange markets can affect the optimal spot positions of domestic commodity producers and traders.It generalizes the models of Kawai and Zilcha (1986) and Kofman and Viaene (1991) to allow bothintermediate and final commodities to be traded in the international and futures markets, and theexporter to face production shock, domestic factor costs and a random price. Applying the mean-varianceexpected utility, we find that a rise in exchange rate volatility can reduce both supply and demand forcommodities and increase the domestic prices if the exchange rate elasticity of supply is greater than thatof demand. Even though the forward foreign exchange market is unbiased, and there is no correlationbetween commodity prices and exchange rates, the exchange rate can affect domestic trading and pricesthrough offshore hedging and international trade if the traders are interested in their profit in domesticcurrency. It illustrates how the world prices and foreign futures prices of commodities and their volatilitycan be transmitted to the domestic market as well as the dynamic relationship between intermediateand final goods prices. The equilibrium prices reflect trader behaviour i.e. who trade or do not trade inthe foreign commodity futures and domestic forward currency markets. The empirical result applying atwo-stage-least square approach and Thai rice and rubber prices supports the theoretical result.

Keywords: offshore hedging, currency hedging, asset pricing, price transmissionJEL Classification: F1; F3; G1; Q1

1 Introduction

Many frameworks try to explain the behaviour of traders and commodity prices in an economy that has

both commodity spot and futures markets. However, some small countries are the world largest exporters or

importers of commodities, and they do not have their own commodity futures market. The domestic traders

in these small countries are price takers. The world prices can therefore affect the domestic commodity

prices, and the higher volatility of world prices can have an adverse effect on these small economies. For

example, many oil importing countries suffered from the recent oil price crisis in 2008. The inflation of South

Korea, Taiwan and the Philippines rose sharply due to the rise in oil and rice prices as they are the world

largest importers of both commodities. On the other hand, the higher volatility of oil and rice prices causes

economic instability of oil and rice exporting countries. For instance, in the first half of 2008 Thai people

suffered from a continuous increase in the domestic price of rice which is main and necessary food of the

country because more rice was exported due to the higher world price, leaving the country with the lower

supply. The rise in oil price caused a higher production costs of synthetic rubber and thus increased the

demand for substitutes (e.g. natural rubber). Thailand which is the world largest exporter of milled rice

and rubber products benefited from this. That is, Thai export growth increases, so Thailand experienced a

resilient economic growth in spite of facing higher fuel import bills. Later, the commodity prices dropped

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Electronic copy available at: http://ssrn.com/abstract=1744049

following a sharp fall in oil price in July 2008. This caused a decrease in Thai export growth, farm incomes

and incomes of rice mills and rubber sheet manufacturers, leading to a reduction of private consumption

growth. As a result, the economic growth dropped from 0.8% y-o-y in the first half of 2008 to —0.7 and -4.9%

y-o-y in the third and fourth quarters of 2008, respectively.

From this, we can see that traders facing price risk are not only exporters, but also producers, processors

and storage companies. Without the domestic futures market, domestic traders can only hedge their price

risk in the foreign commodity futures markets or use the foreign futures prices as information in predicting

future commodity prices. For example, before the Agricultural Futures Exchange of Thailand (AFET)

started trading futures contracts of smoked rubber sheet in May 2004 and futures contracts of milled rice in

August 2004, Thai rubber traders hedge their price risk in the Singapore Commodity Exchange (SICOM)1

and Thai rice traders trade in the Chicago Board of Trade (CBOT)2. This raises a concern whether exchange

rates can affect domestic commodity prices also through foreign futures trading.

Kawai and Zilcha (1986) found that if the economy has only the forward foreign exchange market, exports

could be increased by the introduction of domestic commodity futures markets and decreasing exporters’

risk aversion. Many recent literatures found the optimal offshore hedging strategy for the exporters or the

importers. Kawai and Zilcha (1986) and Kofman and Viaene (1991) found the exporters’ optimal strategy in

the case of incomplete market such that there is no commodity futures market in the economy. Their models

were focused on intermediate commodity which was storable, quoted in the foreign demanding country’s

currency and traded in the international and futures markets. Yun and Kim (2010) found that Korean oil

importers’ hedging would be more effective if they hedged their price risk in the foreign futures market and

simultaneously entered into currency futures contracts. Moreover, Jin and Koo (2002) developed a theoretical

model to find a hedging strategy when the traders face hedging cost and in their empirical work they also

found the optimal hedging ratio for Japanese wheat importers who hedged their price risk in the CBOT and

hedged exchange rate risk in the Tokyo International Financial Futures Exchange (TIFFE). Unlike others,

Kofman and Viaene (1991) also found the optimal strategies of domestic producers and processors as well.

1There are more Thai traders trading the futures contract of smoked rubber sheet in the SICOM than in other futuresmarket because the Singapore is the largest port shipping smoked rubber sheet for Thailand and Malaysia, the world largestexporters of smoked rubber sheet.

2For the case of rice, there are more Thai traders trading in the CBOT than in other futures market because the US is oneof the largest importers of Thai milled rice. However, rice traded at the CBOT is rough rice, not milled rice.

2

While these models focused on optimal strategies of exporters of intermediate commodities, some small

countries allow exports of final goods only e.g. Thai rough rice and natural rubber cannot be exported due

to nature of products, much higher delivery cost, and regulations. For some commodities e.g. sugar and oil,

both intermediate and final commodity (raw sugar and refined sugar, or crude oil and refined oil) can be

exported in some countries.

Some literatures found the empirical relationship between spot exchange rates and domestic commodity

prices. Investigating the relation between Thai milled rice price and the US dollar exchange rate, Kofman

and Viaene (1991) found a positive ex-post correlation coefficient while Gilbert (1991) found the exchange

rate elasticity equal to -1. Applying Granger Causality test, Timmer (2009) found that the Euro-US Dollar

exchange rate significantly Granger caused prices of commodities e.g. rice, corn, wheat, crude oil and palm oil.

In addition, Chen, Rogoff and Rossi (2010) showed that exchange rates had significant power in forecasting

commodity prices. Apart from commodity prices, some studies currency hedging for international financial

portfolio; for example, Schmittmann (2010) found that both exchange rate volatility and the correlations of

exchange rates with bond and equity returns can increase risk exposure to investors.

An aim of this paper is to develop a framework to explain what are the effects of trading in the foreign

commodity futures and domestic currency markets on the domestic commodity market of a small country

and how exchange rates can affect domestic commodity prices through this trading. The framework here

expands the models of Kawai and Zilcha (1986) and Kofman and Viaene (1991), allowing either intermediate

commodity or final commodity to be traded in the international and futures markets. Some of their assump-

tions are also relaxed e.g. exporters face export uncertainty, domestic factor costs and domestic price of final

goods. By applying a two-period mean-variance approach, the agents’ optimal commodity spot and futures

holdings and optimal forward exchange holding in this particular case are specified. Unlike Danthine (1978),

Holthausen (1979), Feder, Just and Schmitz (1980), and Benninga and Oosterhof (2004), the degree of risk

aversion can affect all optimal spot positions. We find that relationships among optimal strategies, equilib-

rium prices, and exchange rates depend upon which product is exported, whether exports are contracted in

advance, which traders hedge their price and exchange rate risks, and whether the commodity prices and the

exchange rates are correlated. We show that even if there is no correlation between commodity prices and

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exchange rates, there are still some exchange rate effects on the commodity prices via exporting/importing

and trading in the foreign futures if the agents are interested in their profits in domestic currency. The

higher volatility of exchange rate can lower the optimal forward position, and thus the optimal futures and

spot position. The higher volatilities of spot prices and futures price will reduce both demand and supply

of the commodity, but their impacts on price depending on which between supply and demand is affected

more. IAs another aim of the paper, the framework shows how world prices are transmitted to domestic

intermediate and final commodity markets.

For empirical studies, we use the data on Thai rice and rubber prices, and the exchange rates of Thai Baht

against US Dollar and Singapore Dollar before futures contracts first traded in the AFET. The empirical

finding supports the theoretical result. That is, the contemporaneous correlations of exchange rates with

commodity prices are insignificant for the case of rice and significant for the case of rubber. This result

is different from the findings of Kofman and Viaene (1991) and Gilbert (1991); it may be due to Thailand

moving from the fix exchange rate system to the managed-float system in 1997. The forward foreign exchange

market is biased, allowing the forward exchange rate to have impacts on the optimal spot position and

commodity prices. As an advantage of this framework, the estimation result can reflect who trades in the

foreign commodity futures and forward foreign exchange markets and who does not.

The rest of paper is outlined as follows. In the next section, the theoretical framework is developed to

find the optimal strategies and equilibrium prices. The robustness of the theoretical result is also discussed.

In Section 3, the two-stage-least-square regression shows how prices of intermediate and final commodities

are related and how they are affected by world prices, foreign future prices and exchange rates. Section 4

concludes and suggests some further research.

2 Framework

2.1 Assumptions

In this framework, both intermediate and final commodities are storable and internationally tradable. Here,

we consider how offshore commodity hedging and domestic currency hedging of traders can affect the domestic

spot commodity market of a small country which does not have its own commodity futures market, but has

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Producer Processor

Primary commodity market

Storage companies Exporters

World MarketFlows of Intermediate Commodity

Flows of Final Commodity

Flows of Primary Commodity

Exported commodities

ConsumerDomestic Intermediate + Final Goods Markets

Figure 1: Flows of intermediate and final commodities within an exporting country

the forward foreign exchange market. The mean-variance expected utlity maximization is applied to find

the optimal strategies of domestic traders: producers, processors, exporters (or importers), and storage

companies. Production and trade flows among traders for the commodities that the country exports is

shown in figure (1) while flows for the commodities that the country imports is shown in figure (2)

We assume that the production process, storage and internationally delivery take one period (i.e. traders

hold the positions for a single-period horizon), and in each period both intermediate and final commodities are

traded in the domestic market. The intermediate producers choosing the optimal level of input (e.g. primary

commodity) at period t and sell their output (intermediate commodity) to processor, storage companies or

exporters at price Pt+1 at period t+1. With the optimal level of input (intermediate commodity) chosen

at period t, processors produce the final commodity and sell it to storage companies or exporters at price

Qt+1 at period t+1. Storage companies can buy either intermediate or final commodities from the domestic

markets and sell them to the domestic market in the next period to make a profit. For the exporting country,

exporters buy the commodities from the domestic market; after packing they deliver the commodities to the

foreign importers and get paid in foreign currency in the next period at the world prices (Pmt+1 and Qmt+1).

In the case that the country imports commodities, importers pay for importing commodities at the world

prices at period t. They sell the commodities to the domestic market in the next period after receiving

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Producer Processor

Primary commodity market

Storage companies Importers

World MarketFlows of Intermediate Commodity

Flows of Final Commodity

Flows of Primary Commodity

Imported commodities

ConsumerDomestic Intermediate + Final Goods Markets

Figure 2: Flows of intermediate and final commodities within an importing country

commodities.

The export/import and futures prices are quoted in the foreign demanding country’s currency. As the

country does not have a commodity futures market, domestic traders can hedge their price risk in the foreign

commodity futures market, and hedge their exchange rate risk in the domestic forward exchange market.

Either intermediate or final commodity is traded in the futures market. In addition, the maturity of the

futures and forward contracts is at time t+ 1.

Note that in period t all stochastic variables of time t + 1 are unknown. In the sequel, Xit denotes the

position of the agent of type i in the primary good at time t and similarly for Yit (intermediate good), Hit

(final good) and Y fit (futures contract for intermediate or final commodity). Πi is the profit of trader i where

i = f for the intermediate producers, i = p for the processors, i = sy for the companies storing intermediate

good, i = sh for the companies storing final good, i = ey for the firm exporting intermediate good and i = eh

for the firm exporting final good. Let Zfit denote the position of the agent of type i in the forward exchange

contract at time t. The framework also has assumptions as follows.

A1. All agents can hedge or speculate in the foreign futures market by selling or buying the futures

contract with a full margin at time t which is worth Y fitFtet in domestic currency. It follows that all

domestic traders close their futures position by the last trading day of period t+1 by a cash settlement

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because delivering to or taking delivery from the foreign futures market requires substantially additional

costs, or the commodity traded in the foreign futures market is different from the commodity of which

price is hedged. All traders transfer the cash (in foreign currency) through the foreign futures market’s

clearinghouse both at time t and t+ 1 e.g. the payment on Y fitFt is made at time t with the exchange rate

et and the payment on Y fitFt+1 is made at time t+1 to close futures position with the exchange rate et+1.

A2. Due to international trade and foreign futures trading, traders face exchange rate risk. To hedge

exchange rate risk, traders can short or long the forward exchange contract at time t, based on the expected

future payment or receipt (in foreign currency). Unlike the trade in the futures market, there is no margin

requirement in the forward market so the payment in the forward exchange market is only made at maturity

t+1. After the cash transfer, the foreign currency remaining in their hands can be sold to the spot exchange

market. If their actual payment (receipt) in foreign currency is larger (smaller) than Zfit, they can also buy

more foreign currency in the spot market.

A3. At time t, all traders choose their optimal decisions by maximising their expected utility function (V )

depending on their profit in domestic currency. Any variables such as the optimal spot and futures positions

at time t chosen by agent i at time t depend on his own information set available at time t (Iit). Eit(·)

denotes agent i’s expectation depending on Iit. V arit(·) denotes agent i’s expected variance of a variable

depending on Iit. The discount factor, ρ, is assumed to be 1/(1+ it+1) where it+1 is the interest rate at time

t+1 and perfectly foreseen at time t.

A4. Domestic traders in a commodity market are rational and are small in the international commodity

market, foreign futures market and domestic forward exchange market relatively to trading volume in the

markets. So Eit(et+1) = Et(et+1). ft = Et(et+1)+ risk premium. This risk premium can be time varying.

Unlike the assumption of Battermann, Braulke, Broll and Schimmelpfennig (2000) here the expected future

exchange rate for trader i, Eit(et+1), is not necessarily equal to the forward exchange rate, ft.

A5. Production shock, storage and export uncertainty, noise trading in the commodity futures and

forward foreign exchange markets are uncorrelated and do not have serial correlations. The domestic spot

and forward exchange markets are insignificantly affected by the uncertainty of commodity spot and futures

prices.

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2.2 Profit Functions

2.2.1 Intermediate producers

A producer buys primary commodity at time t to produce intermediate commodity and sells his output

(f(Xft, l, t+1))3 in the spot market at time t+1. We assume that the production shock, t+1 has Eft( t+1) =

0 and V arft( t+1) = σ2. The production shock is realised just before delivering the output to the spot market

at time t + 1. θX2ft is the production cost excluding the cost of seeds (θ > 0). He can hedge his price risk

by selling futures contracts maturing at time t+ 1, Y fft, at price Ft in the foreign futures market at time t.

His profit function is, therefore,

Πf = Y fftΦt − rtXft − θX2

ft + ρ(f(Xft) + t+1)Pt+1 − Y fft Φt+1 + (et+1 − ft)Z

fft. (1)

where rt is the primary commodity price and Φt (=Ftet) is the foreign futures price in domestic currency at

time t. Because of closing futures position with cash settlement, he faces exchange rate risk which he can

hedge by buying forward exchange contracts maturing at time t + 1 at the forward rate ft. He may buy

the exact amount of the foreign currency which he has to pay to the futures market from the spot exchange

market at t+1 at the rate et+1 and thus Zfft = 0. Alternatively, he may take delivery of the amount of foreign

currency Zfft from the forward exchange market. He may sell his excess foreign currency Zf

ft − Y fft Ft+1 in

the spot exchange market at t+ 1 if his actual payment (in foreign currency) to the futures market at time

t+ 1 is smaller than Zfft. On the other hand, he may buy more foreign currency from the spot exchange if

Zfft < Y f

ft Ft+1.

2.2.2 Processors

At time t a processor purchases intermediate goods to produce final goods. He sells his final goods at time

t+1 in the domestic market of final commodity at price Qt+1. At time t, he can also sell futures contracts of

the final commodity maturing at time t+1 (Y fpt) to hedge his price risk. He closes all of his futures position

at time t+1 by buying futures contracts at price Ft+1. He can hedge his exchange rate risk by buying the

forward exchange contract, Zfpt. After taking delivery of Z

fpt at the forward rate ft, he may buy the remaining

foreign currency in the spot exchange market if it turns out that he has underhedged his exchange rate risk

3Yft+1 = minbXft+1, l1/2+ t+1 where l is other inputs and 0 < b < 1. Therefore, the cost function is equal to the cost

of seeds and the other production cost which depends on the amount of input used in the production.

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i.e. Y fpt Ft+1 > Zf

pt. Alternatively, he may choose to buy this amount of the foreign currency, YfptFt+1, in

the spot exchange market at the rate et+1 at time t+1 and thus Zfpt = 0. A processor’s profit function is

Πp = Y fptΦt − PtYpt − αY 2

pt + ρ(g(Ypt) + vt+1)Qt+1 − Y fpt+1Φt+1 + (et+1 − ft)Z

fpt (2)

where g(Ypt, k, νt+1) is a production function of the final good (Hpt+1)4. The production shock, νt+1 has a

zero mean and a constant variance (σ2v). αY2pt is the other production cost which depends on the amount of

intermediate commodity.

2.2.3 Storage companies

A storage company purchases intermediate goods or final goods at time t and sells them to make a profit

at time t+1. His storage cost is (γyY2sy,t or γhH

2sh,t) where 0 < γ < 1. wy

t+1 and wht+1 denotes stor-

age uncertainty for intermediate goods and final goods with Esj,t(wjt+1) = 0, V arsj,t(w

jt+1) = σ2jw, and

Covsj,t(wyt+1,w

ht+1) = 0 where j = y and h. At time t, he can hedge his price risk by selling the futures

contract maturing at time t and close the futures position at time t+1. In addition, he can hedge his ex-

change rate risk due to the payment to the futures market at time t+1 with the forward exchange contract

(Zfsj,t) at the forward rate, ft. He may sell Z

fsj,t − Y f

sj,tFt+1 in the spot exchange market if it turns out

that he has overhedged his exchange rate risk. Instead, he may choose to buy foreign currency from the

spot exchange market at t+1 at the rate et+1 i.e. Zfsj,t = 0. The profit of the company that stores the

intermediate commodity is

Πsy = Y fsytΦt − PtYsy,t − γyY

2sy,t + ρ(Ysy,t + wy

t+1)Pt+1 − Y fsy,tΦt+1 + (et+1 − ft)Z

fsy,t. (3)

For the company that stores the final commodity, the company’s profit function is

Πsh = Y fsh,tΦt − PtHsh,t − γhH

2sh,t + ρ(Hsh,t + wh

t+1)Pt+1 − Y fsh,tΦt+1 + (et+1 − ft)Z

fsh,t. (4)

2.2.4 Exporters/Importers

An exporter commits to export intermediate goods or final goods. He purchases the commodities at time

t and export them at time t+1. Like Kawai and Zilcha (1986), we assume that export prices at time t+1

are random. His total production cost is the cost of commodity (PtYey,t or QtHeh,t) plus delivery and

4Hpt+1 = mina(Ypt), k1/2+νt+1 where k is other inputs and 0 < a < 1. Therefore, the cost function is equal to the cost ofintermediate goods and the other production cost which depends on the amount of intermediate goods used in the production.

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transaction costs (βY 2ey,t or βH

2eh,t) where 0 < βj < 1. u

yt+1 and uht+1 denotes uncertainty affecting exports

of intermediate goods and final goods with Eej,t(ujt+1) = 0, V arej,t(u

jt+1) = σ2ju and Covej,t(u

yt+1,u

ht+1) = 0

where j = y and h. At time t, he can also hedge his price risk in the foreign futures market by selling

the futures contract maturing at time t and close it at maturity. In addition, he can hedge his exchange

rate risk due to the payment to the futures market at time t+1 by purchasing the forward foreign exchange

contract (Zfej,t) at time t at the forward rate ft. He may sell Z

fej,t − Y f

ej,tFt+1 in the spot exchange market

if it turns out that he has overhedged his exchange rate risk. Or else, he may buy foreign currency from the

spot exchange market at t+1 at the rate et+1 so Zfej,t = 0.

The profit function of the intermediate goods exporter is

Πey = Y fey,tΦt+1 − PtYey,t − βY 2

ey,t + ρ(Yey,t + uyt+1)Pmt+1et+1 − Y fey,tΦt+1 + (et+1 − ft)Z

fey,t. (5)

The final goods exporter’s profit function will be

Πeh = Y feh,tΦt −QtHeh,t − βH2

eh,t + ρ(Heh,t + uht+1)Qmt+1et+1 − Y feh,tΦt+1 + (et+1 − ft)Z

feh,t. (6)

In the framework of an imported commodity, the importer’s input costs will be the world prices, Pmt and

Qmt, instead of Pt and Qt while the commodity is sold at time t+1 at the domestic price. Given that he

makes decision at time t, he faces price risk from selling the commodity to the domestic market and also

exchange rate risk from offshore hedging.

2.3 Optimal Strategies

Each trader chooses his optimal commodity spot position, commodity futures position and forward exchange

position by maximising the mean-variance expected utility depending on their profits. The decision is made

at time t, so the domestic supply of intermediate and final commodities at time t+1 depends on the input

that producers, processors and storage companies bought at time t. The objective function

Vi = Uit(Πit) + ρEitUit+1(Πit+1) (7)

is maximised with respect to the spot position (Xft for i = f , Yit for i = p, sy and ey, and Hit for i = sh

and eh), the futures position (Y fit ) and the forward position (Z

fit).

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2.3.1 The optimal spot position

The optimal spot position of the producer is X∗ft while the optimal spot position for the processor is Y∗pt.

From this, we also find the optimal output level at time t+1 regardless of production shocks i.e. f(X∗ft)

for the producer and g(Y ∗pt) for the processor. For storage companies, the optimal spot position is trading

volume, not the stock of commodity, at time t which is carried forward to the period t+1. The optimal

position at time t for the company storing intermediate goods is denoted as Y ∗sy,t and for the company storing

final goods as H∗sh,t. Y∗ey,t is the optimal position at time t for the exporter of intermediate goods and H∗eh,t

for the exporter of final goods. Let S∗it be the vector of the optimal spot positions i.e. f(X∗ft) for i = f ,

g(Y ∗pt) for i = p, Y ∗it for i = sy, ey and H∗it for i = sh, eh.

Solving the first order conditions (see Appendix A) yields the optimal position

S∗it =

¡ρEit(Mit+1)− Cit − ρAiEit(Mit+1)Covit(Mit+1, ξit+1)

¢χit

+Φt − ρEit(Φt+1)

χit

¯¯s

V arit(Mit+1)

V arit(Φt+1)

¯¯ Corrit(Mit+1,Φt+1)− Corrit(Φt+1, et+1)Corrit(Mit+1, et+1)

1− Corr2it(Φt+1, et+1)

+ρ(Eit(et+1)− ft)

χit

¯¯s

V arit(Mit+1)

V arit(et+1)

¯¯ Corrit(Φt+1, et+1)Corrit(Mit+1,Φt+1)− Corrit(Mit+1, et+1)

1− Corr2it(Φt+1, et+1)(8)

for all i where

1 > Corr2it(Φt+1, et+1) >Corrit(Φt+1, et+1)Corrit(Mit+1, et+1)

Corrit(Mit+1,Φt+1)

Mit+1 is the price of product sold by trade type i: Pt+1 for the producer and the company storing or

importing the intermediate commodity, Qt+1 for the processor and the company storing or importing the

final commodity, Pmt+1et+1 for the exporter of the intermediate commodity, and Qmt+1et+1 for the exporter

of the final commodity. Cit is the input cost: rt/b for the producer, Pt/a for the processor, Pt for the company

storing or exporting intermediate goods, Qt for the company storing or exporting final goods, Pmt+1et+1

and Qmt+1et+1 for the importers of intermediate and final commodities. ξit+1 is production shock for the

producer and the processor, storage uncertainty for storage companies, and export (import) uncertainty for

exporters (importers). We assume that Covit(Mit+1, ξit+1) < 0. This is because a decrease in the supply of

11

the commodities due to a negative shock (e.g. weather and rotting) will raises the commodity price.

χit = λi + ρAiV arit(Mit+1)1−Corr2it(Mit+1,Φt+1) + Corr2it(Mit+1, et+1)

1− Corr2it(Φt+1, et+1)

+2Corrit(Mit+1, et+1)Corrit(Φt+1, et+1)Corrit(Mit+1,Φt+1)

1− Corr2it(Φt+1, et+1)

where λi is equal to 2θb2 for the farmer,

2αa2 for the processor, 2γy or 2γh for the storage company, 2βy or 2βh

for the exporters (importers). λi = 0 if there is no other costs apart from the cost of commodity. χit > 0

implies that the second order conditions (SOCs) are satisfied.

Unlike Anderson and Danthine (1983), Antoniou (1986), and Benninga and Oosterhof (2004) in which

the country has its own futures market, the optimal spot position here depends on trading in other markets

and the degree of risk aversion; thus, the separation theorem is not applicable. When the expected gain in

the spot, futures or forward market increases, the traders tend to hold a larger spot position. Like Kawai and

Zilcha (1986), Kofman and Viaene (1986) and Schmittmann (2010), the failure of uncovered interest rate

parity (UIP) allows currency hedging to have an impact on the spot position. While the higher volatility of

domestic spot prices, world prices and foreign futures prices of commodities and exchange rate can cause a

reduction of the optimal spot positionm, the higher Corrit(Mit+1,Φt+1) reduces the optimal spot position

(See Appendix B). This is supported by the finding of Bahmani-Oskooee and Mitra (2008) that exchange

rate volatility has negative impacts on exports and imports of commodities between the US and India. The

effects on his profit are in the same direction as those on the optimal spot positions if the expected marginal

gain of trading in futures and forward markets is non-negative and that the marginal revenue product (MRP)

of input is not less than its marginal resource cost (MRC).

If there is no correlation between commodity prices and exchange rates, Corrit(Rt+1, et+1) = 0 for all i

where R = P,Q,Qm, Pm, F. For Lt+1 = Φt+1, Pmt+1et+1 and Qmt+1et+1,

Corrit(Lt+1, et+1) =Covit(Lt+1, et+1)p

V arit(Lt+1)V arit(et+1)

=Eit(Lt+1/et+1)V arit(, et+1) +Eit(et+1)Covit(Lt+1/et+1, et+1)p

V arit(Lt+1)V arit(et+1)

=Eit(Lt+1/et+1)V arit(, et+1)p

V arit(Lt+1)V arit(et+1)= Eit(

Lt+1et+1

)

sV arit(et+1)

V arit(Lt+1)

Eit(Φt+1) = Eit(Ft+1)Eit(et+1) for all i and Eit(Mit+1) for the exporters are Eey,t(Pmt+1)Eey,t(et+1) and

Eeh,t(Qmt+1)Eeh,t(et+1). Then, the optimal positions of traders are still affected by the exchange rate and

12

its volatility. If the forward market is also unbiased, or Corrit(Mit+1, et+1) = 0 and Corrit(Φt+1, et+1) = 0

for all i, the optimal position will be

Sit =

£ρEit(Mit+1)− Cit − ρAiEit(Mit+1)Covit(Mit+1, ξit+1)

¤λi + ρAiV arit(Mit+1) [1− Corr2it(Mit+1,Φt+1)]

+[Φt − ρEit(Φt+1)]Corrit(Mit+1,Φt+1)

λi + ρAiV arit(Mit+1) [1− Corr2it(Mit+1,Φt+1)]

¯¯s

V arit(Mit+1)

V arit(Φt+1)

¯¯ (9)

This optimal spot positions is not affected directly by the exchange rates but indirectly through foreign

futures trading and exports (see Appendix C). The second term of the optimal input level of (8) and (9)

is the effect of futures trading. The sum of the first two terms of (8) is larger than (9). With the effect of

speculative trading in the forward foreign exchange market on the optimal spot position, (8) À (9). (9) is

also the optimal position for the case that 1) the economy does not have a forward foreign exchange market

or 2) the trader hedges only his price risk.

If the producer does not hold futures position or if he is not allowed to trade in the foreign futures market,

he does not need to hedge exchange rate risk. In this case, the optimal spot position (8) will become

Sit =

£ρEit(Mit+1)− Cit − ρAiEit(Mit+1)Covit(Mit+1, ξt+1)

¤(ρAiV arit(Mit+1) + λi)

(10)

for all i. If the trader does not trade in the foreign futures market but use the futures price to predict the

future spot price, Eit(Pt+1), Eit(Qt+1), Eey,t(Pmt+1) and Eeh,t(Qmt+1) in (10) will be replaced by or be a

function of Ft. As the optimal spot position (10) <(9) <(8), allowing the trader to hedge his risks in the

foreign futures market and the domestic forward exchange market will raise production level and supply of

commodity in the domestic market. By how much the production level or trading volume in the spot market

for each trader increases depends on whether the commodity prices and foreign exchange rates are correlated

and whether the forward exchange market is unbiased.

If the final good production process is short, the processor can buy the intermediate commodity to

produce the final good and sell the output to the market at time t. In this case he does not face any price

risk and has no need to trade in the foreign futures and forward foreign exchange markets. His optimal spot

position is

Ypt =ρgypQt+1 − Pt+1

2α(11)

where gyp =∂g(Ypt)∂Ypt

. Unlike other trader types, exporters face exchange rate risk even though they do not

13

involve in the foreign commodity futures market. If they choose to hedge their price risk in the offshore

futures market, then they face more exchange rate risk. As can be seen from equation (8), the optimal spot

position depends on whether he also trades in the foreign futures market and the forward exchange market.

If he does not trade in the futures market, but he hedges the exchange rate risk of his export incomes,

Corrit(Φt+1, et+1) = 0 and Corrit(Mit+1,Φt+1) = 0. Thus, the second term disappear and the last term is

reduced; therefore, his optimal spot position becomes smaller than (8) but greater than (10).

Considering a case in which the exporter precommits to export intermediate (final) commodity at time t

at the preset export price Pmt+1 (Qmt+1), the preset export price can be determined by the current export

price and thus Pmt+1 (Qmt+1) are known at time t as assumed by Kofman and Viaene (1991) and Benninga

and Oosterhof (2004). The exporter has no need to hedge price risk. The optimal positions of the exporters

will be

Yey,t =[ρPmt+1ft − Pt]

2β(12)

and

Heh,t =[ρQmt+1ft −Qt]

2β(13)

2.3.2 The optimal futures position

The optimal futures position of the trader type i is

Y f∗it =

(Φt − ρEit(Φt+1))

ρAiV arit(Φt+1) ((1− Corr2it(Φt+1, et+1)))

+(Eft(et+1)− ft)Corrft(Φt+1, et+1)

Ai

¯pV arit(Φt+1)V arit(et+1)

¯(1− Corr2it(Φt+1, et+1))

+ Y Hit (14)

for all i. The optimal futures position has 2 components: speculation and hedging. The first two terms are

effects of speculation in the foreign commodity futures market and the forward foreign exchange market.

Y Hit is the hedging component:

Y Hit = S∗it

¯¯s

V arit(Mt+1)

V arit(Φt+1)

¯¯ Corrit(Mit+1,Φt+1)− Corrit(Mit+1, et+1)Corrit(Φt+1, et+1)

(1− Corr2it(Φt+1, et+1))

for all i. Y Hit is a partial hedge of the expected output level. Whether the trader will short or long the

contract depends on the expected gains in the foreign futures and forward foreign exchange markets, and his

spot position. As

Corr2it(Φt+1, et+1) >Corrit(Φt+1, et+1)Corrit(Mit+1, et+1)

Corrit(Mit+1,Φt+1),

14

if there is no correlation between commodity prices and exchange rates and the trader hedges his exchange

rate risk, the denominator increases as

V arft(Φt+1 −Eit(Ft+1)et+1) > V arft(Φt+1)(1− Corr2ft(Φt+1, et+1)) > 0.

and Covit(Φt+1, et+1) = Eit(Ft+1)V arit(et+1). Thus, the optimal futures position will be smaller than (14).

If traders do not hedge their exchange rate risk, Zf∗it is zero for all i. Then the second term disappear and

there are no Covit(Φt+1, et+1), Covit(Pmt+1et+1, et+1), Covit(Qmt+1et+1, et+1) in (14). The optimal position

is reduced to be

Y f∗it =

Φt − ρEft(Φt+1)

ρAiV arft(Φt+1)+ S∗it

Covit(Mit+1,Φt+1)

V arit(Φt+1)(15)

We find that Y Hit in (15) is greater than in (14) i.e. offshore hedging is more effective when they hedge both

price and exchange rate risks. This is supported by empirical findings of Yun and Kim (2010).

Suppose that only intermediate commodity is traded in the foreign futures market. The size of futures

position may be affected by the type of commodity traded in the foreign futures market through the futures

price and Covit(Mit+1,Φt+1). For example, the covariance between the domestic price of final (intermediate)

good and the foreign futures price of intermediate (final) good may be lower than the covariance between

the domestic prices and the foreign futures price of the same good. The optimal spot and forward positions

are also affected through the change in futures position.

2.3.3 The optimal forward position

The optimal forward position of the trader type i is

Zf∗it =

Eit(et+1)− ftAiV arit(et+1)

+ Y f∗it

Covit(Φt+1, et+1)

V arit(et+1)− S∗it

Covit(Mit+1, et+1)

V arit(et+1)(16)

Obviously, Zf∗it is composed of two components: speculation (the first term) and hedging (the last two

terms). The second term of (16) is a partial hedge of the expected payment of receipts of foreign currency

due to closing futures position at time t+1 and its last term is a partial hedge of the expected future

receipts from the spot market. If commodity prices and exchange rate are uncorrelated, the second term

will become a full hedge, Y f∗it Eit(Ft+1), and the last term will be zero for all traders except exporters. This

is because the output prices for exporters are Pmt+1et+1 and Qmt+1et+1 i.e. Covey,t(Pmt+1et+1, et+1) and

15

Coveh,t(Qmt+1et+1, et+1) in this case are equal to Eey(Pmt+1)V arey,t(et+1) and Eey(Qmt+1)V arey,t(et+1),

respectively.

In short, the optimal spot position is affected by the degree of risk aversion and thus the separation

theorem is not applicable. Without hedging price risk in the foreign futures markets or exchange rate risk in

the forward foreign exchange markets, the spot commodity markets will have both lower demand and lower

supply. For all traders, all optimal positions are affected by the type of commodity traded in the foreign

futures market only through the futures prices and covariance between output prices and foreign futures

prices. Note that by changing the subscript t to be t+1, we can get the optimal positions at time t+1 for

all traders.

2.4 Equilibrium solution

From the optimal spot positions in the previous section, the market-clearing conditions for the markets of

intermediate and final commodities in the exporting country at time t+1 are

npY∗pt+1 + neyY

∗ey,t+1 + nsyY

∗sy,t+1 = nf

£f(X∗ft) + t+1

¤+ nsy[Y

∗sy,t + wy

t+1] (17)

and

nehH∗eh,t+1 + nshH

∗sh,t+1 +H∗ct+1 = np

£aY ∗pt + νt+1

¤+ nsh

£H∗sh,t + wh

t+1

¤(18)

where H∗ct+1(Qt+1) is the demand for final goods of consumers at time t+1, assuming to be linear with

the current domestic price. ni denotes the number of the trader type i. The left-hand side represents the

demand in the spot market while the right-hand side represents the supply5. As domestic traders are small

in the international market and the foreign futures and forward foreign exchange markets, the futures price,

export prices and spot and forward exchange rates are exogenous.

With both equilibrium conditions, the domestic equilibrium spot prices of intermediate and final com-

modities at time t+1 are specified. The supply of commodites does not depend on the current domestic

spot prices. It depends on the domestic spot prices of inputs, the foreign futures price, and exchange rates

at time t, as well as price expectations of producers and storage companies perceived at time t. In contrast,

the demand for commodities depends on the current spot price. It also depends on the current futures price5For the importing country, Yey and Heh are on the supply side.

16

and exchange rates, the expected exchange rate, and the expected future prices of commodities sold at time

t+2 in the domestic market, the world market and the foreign futures commodity market. So from (17),

Pt+1 = −nf£f(X∗ft) + t+1

¤+ npY

∗pt+1,−p + neyY

∗ey,t+1,−p + nsy(Y

∗sy,t+1,−p −

£Y ∗sy,t + wy

t+1

¤) (19)

where Y ∗it+1,−p denotes the optimal position of the trader type i excluding the effect of Pt+1. This supports

the assumption given before that Covit(Pt+1, ξt+1) < 0. Moreover, storage companies or the buffer stock’s

manager can raise the current spot price by buying more of the commodity to increase their stock at time

t+1. From (18), the equilibrium price of final goods in the domestic market is

Qt+1 = −np£aY ∗pt + νt+1

¤+ neH

∗et+1,−q +H∗ct+1,−q + ns(H

∗st+1,−q −

£H∗st + wh

t+1

¤) (20)

whereH∗it+1,−q denotes the optimal position of trader type i excluding the effect ofQt+1. IfH∗ct+1 = c−dQt+1,

then H∗ct+1,−q = c.

We can also rewrite (19) as

Pt+1 = f(rt, Pt,Φt,Φt+1, ft, ft+1,Λit,Λjt+1,Ωit,Ωjt+1)− (nf t+1 + nsywyt+1) (21)

where i = f, sy and j = p, ey, sy. Λit and Λjt+1 are sets of the expected future domestic and world prices of

the intermediate commodity (Eit(Pt+1) and Eit(Pmt+1)), and the expected futures price and exchange rate

(Eit(Φt+1) and Eit(et+1)), perceived by the trader type i at time t and the trader type j at time t+1. Ωit

and Ωjt+1 are sets of expected variances and correlations, perceived by the trader type i at time t and the

trader type j at time t+1, of future prices and exchange rates. (20) can be rewritten as

Qt+1 = f(Pt, Qt,Φt,Φt+1, ft, ft+1,Λkt,Λmt+1,Ωkt,Ωmt+1)− (npvt+1 + nshwht+1) (22)

where k = p, sh and m = e, sh. Λkt = Ekt(Qt+1), Ekt(Φt+1), Eit(et+1) and Λmt = Est+1(Qt+2),

Eet+1(Qmt+2et+2), Emt+1(Φt+2), Emt(et+2). Ωkt and Ωmt+1 are sets of expected variances and covari-

ances of domestic and world prices of final goods, the futures price and exchange rate, perceived by the

trader type k at time t and the trader type m at time t+1.

If there is no correlation between prices and exchange rates, with the assumption A4 that Eit(et+1) =

Ejt(et+1) = Et(et+1)

Pt+1 = f(rt, Pt,Φt,Φt+1,Λit,Λjt+1,Ωit,Ωjt+1)− (nf t+1 + nsywyt+1) (23)

17

where Λit = Eit(Pt+1), Eit(Ft+1)ft and Λjt+1 = Est+1(Pt+2), Ept+1(Qt+2), Eet+1(Pmt+2)ft+1, Ejt+1(Ft+2)ft+1.

Qt+1 = f(Pt, Qt,Φt,Φt+1,Λkt,Λmt+1,Ωkt,Ωmt+1)− (npvt+1 + nshwht+1) (24)

where Λkt = Ekt(Qt+1), Ekt(Ft+1)ft and Λmt= Est+1(Qt+2), Eet+1(Qmt+2)ft+1, Emt+1(Ft+2)ft+1.

As can be seen in (8) and (9), the optimal spot position decreases when V arit(Φt+1) or V arit(et+1)

increases. Thus the equilibrium price are also affected by exchange rate volatility. However, whether the

effect is positive or negative depends on which traders hedge their price and exchange rate risks and the

exchange rate elasticity of supply and demand. If the elasticity of supply is greater than, less than, or equal

to the elasticity of demand, then prices will increase, decrease or remain unchanged. This is supported by

the conclusion of Chu and Morrison (1984) that one of the dominant sources of commodity price variability

was the volatility of exchange rates. An increase in the expected value of world prices and a decrease in

their volatilities will raise export volume. The increase in export volume causes the domestic demand for

commodities, which are the input, to increase; therefore, the domestic prices of commodities increase. In the

case that the country is the importer of commodities, if the current world price increases, import volume

will decrease. This lowers the domestic supply of commodities and thus increases the domestic price. So

the world price and domestic prices are positively correlated.

3 Empirical studies

Based on the theoretical result in the previous section, trading in the foreign commodity futures and domestic

forward exchange markets affects the domestic spot price through the speculative component of the traders’

optimal spot holding. In this section, the determinants of equilibrium spot prices at maturity are investigated.

The aim is to find whether the spot prices are affected by the foreign futures price and exchange rates through

foreign futures trading. This paper applies Thai rice and rubber markets as case studies. As Thailand only

exports final goods of rice and rubber (milled rice and smoked rubber sheet (RSS)), Y ∗ey,t+1 = 0 and the

domestic prices are not affected by the world price of the intermediate good. The export prices of milled

rice and RSS3 in this empirical study are Thai F.O.B. prices.

For the case of Thai rubber, the AFET has the futures contract of smoked rubber sheet, maturing in

September 2004, as the first product. Due to limitation of data available from the Thai office of the rubber

18

Table 1: The KPSS unit root test of variablesCommodity Pt Qt Qmt Qmtet Ft Ftet et ft ln(et) ln(ft)Rubber 0.139 0.131 0.155 0.144 0.151 0.142 0.061 0.142 0.061 0.061Rice 0.181 0.175 0.191 0.184 0.186 0.177 0.115 0.108 0.117 0.110Critical Values: 1% = 0.216; 5% = 0.146

replanting aid fund and exclusion of the effect of exchange rate regime switching on July 2,1997, the analysis

covers the period from January 2001 - June 2004. The domestic prices of intermediate and final goods applied

in this study are of natural rubber sheet and smoked rubber sheet no.3 (RSS3). Rubber tree takes many years

to grow, so production cost is mainly fixed cost and cost of seed is relatively small and ignorable (rt ≈ 0).

The futures price of RSS3 is the price of futures contract traded at SICOM. The contract has 12 maturity

months i.e. 12 calendar months. Spot and 1-month forward exchange rates are in Thai Baht/Singapore

Dollar. So there are totally 42 monthly observations for the case of rubber.

Regarding the case of Thai rice, the futures contract maturing in November 2004 is the first contract of

milled rice traded in the AFET. The data covers the period from July 1997 to June 2004. The domestic

prices are Thai rough rice and milled rice prices. The primary commodity of rough rice is rough rice, so

rt = Pt. The foreign futures price is U.S. rough rice futures price. The CBOT trades rough rice futures

contract with 6 maturity months: January, March, May, July, September, and November. The spot and

2-month forward exchange rates are in Thai baht/U.S. dollar. There are totally 46 observations for this case.

To simplify the solution and to allow the model to be easily estimated, we can assume that, for each

agent, conditional variances and covariances of prices and production shock are constant through time6 .

Before estimating the system of equations, the KPSS unit root test is applied to test the stationarity of the

variables. The null hypothesis of KPSS test is that the series is stationary. As shown in table 1, all variables

are stationary at 0.01 significance level. So this assumption is valid.

Table 2 shows that rubber prices are negatively correlated with the THB/SGD exchange rate while rice

prices are not significantly correlated with the THB/USD exchange rate. Thus, the optimal positions of

traders and equilibrium prices in the Thai rubber market and the Thai rice market are different. Apart

6This assumption can be justified by a rational expectations paradigm. That is, the conditional distribution for each agentcomes from distributions of production shocks and storage uncertainty as well as the market-clearing condition determiningPt+1 and Qt+1 above. Agents know that the domestic commodity spot price is a linear function of production and storageuncertainty. These variables have constant variance-covariance matrices through time so do the distributions Ωit. As Qmt+1,Pmt+1, Ft+1 and et+1 are exogenous, the covariance and variances of these variables are given and assumed to be constant.If the mean values of market prices are nonnegative, the rational agents’ expected values of future prices will also be

nonnegative..

19

Table 2: The chi-square test of correlation coefficients

Rubber RicePt Qt Qmtet Ftet et Pt Qt Qmtet Ftet et

Pt 1.00 Pt 1.00Qt 0.999

(204.596)1.00 Qt 0.911

(14.016)1.00

Qmtet 0.995(63.639)

0.994(59.958)

1.00 Qmtet 0.890(12.323)

0.98535.965

1.00

Ftet 0.988(40.854)

0.988(41.219)

0.984(34.904)

1.00 Ftet 0.721(6.588)

0.742(7.009)

0.786(8.028)

1.00

et −0.611(−4.879)

−0.604(−4.797)

−0.630(−5.137)

−0.621(−5.017)

1.00 et −0.151(−0.966)

0.008(0.048)

0.010(0.064)

−0.027(−0.173)

1.00

Note: The values in parentheses are t-statistics

Table 3: Market efficiency hypothesis testing of forward foreign exchange markets

Currency Market THB/SGD THB/USDVariable Coefficient (S.E.) Coefficient (S.E.)Constant 0.38 (0.19)* 1.87 (0.42)**ln(ft−1) 0.88 (0.06)** 0.50 (0.11)**Adj-R2 84.89% 30.24%AR Test: F-stat (Prob.) 2.18 (0.13) 0.54 (0.59)H0 : φ0 = 0, φ1 = 1;χ

2-stat (prob) 6.52 (0.038) 9.77 (0.000)Note: ** and * denote the significance of coefficients at 1% and 5% significance levels, respectively

from the correlation between commodity prices and exchange rate, the commodity equilibrium prices also

depend on the biasedness of the forward foreign exchange market. As shown in the theoretical result above

and the proposition of Kawai and Zilcha (1986) and Kofman and Viaene (1991), to be persuaded to hold

forward contracts, risk-averse traders have to receive a risk premium to compensate for the uncertainty

regarding the expected future spot rate. In other words, the forward foreign exchange market is biased i.e.

Et−1(ln(et)) 6= ln(ft−1).

The heteroscedasticity-robusted standard error ordinary least square regression of ln(et) = φ0+φ1 ln(ft−1)+

ωt in Table 3 shows that the forward exchange markets are biased and the current exchange rate depends on

the previous forward rate. So it is possible to assume that the expected future exchange rate is a function

of the current foward exchange rate. Also, trading in the forward exchange market can affect the optimal

position in the rubber market and the optimal position is (8) if traders choose to hedge their exchange rate

risk. For the rice market, the optimal position is (9). The forward exchange rate is expected to have a

significant effect on Thai rubber prices. Which between intermediate and final commodity prices is affected

by the forward exchange rates depends on who hedge their price risk in the foreign commodity futures market

and their exchange rate risk in the forward foreign exchange market.

20

Consequently, we estimate equations (21) and (22) for the Thai rubber market and equations (23) and (24)

for the Thai rice market by assuming that all the terms in a coefficient (such as the degree of risk aversion,

the number of traders and variances and covariances of prices) are constant, Et−1(Pt) = α0+

p1Xi=1

αiPt−i and

Et−1(Qt) = β0 +

p2Xi=1

βiQt−i, Et−1(Qmt) = δ0 +

p3Xi=1

δiQmt−i, and Et−1(Ft) = λ0 +

p4Xi=1

λiFt−i.

For the case of Thai rubber, commodity prices and exchange rates are correlated, so Et−1(Qmtet) =

δ0+

p5Xi=1

δiQmt−iet−i and Et−1(Ftet) = γ0+

p6Xi=1

γiFt−iet−i. Due to the limitation of data, we assume that the

numbers of lags, pi, are equal to 1. Though more lags may be included if the regressions have autocorrelation

problem. Equations (21) and (22) can be rewritten as

Pt = a0 + a1Qt + a2Pt−1 + a3Ft−1et−1 + a4Ftet + a5ft−1 + a6ft + ηpt. (25)

Qt = b0 + b1Qmtet + b2Pt−1 + b3Ft−1et−1 + b4Ftet + b5ft−1 + b6ft + b7Qt−1 + ηqt. (26)

ηpt = nf t+1 + nsywyt+1and ηqt = npvt+1 + nshw

ht+1 are the residuals. Thus, the mean values of ηpt and ηqt

are equal to zero.

For the case of Thai rice prices, Et−1(Qmtet) = Et−1(Qmt)Et−1(et) =

Ãδ0 +

p3Xi=1

δiQmt−i

!Ψ(ft−1),

Et−1(Ftet) = Et−1(Ft)Et−1(et) =

Ãλ0 +

p4Xi=1

λiFt−i

!Ψ(ft−1). To simplify the model and avoid losing the

degree of freedom, we assume Ψ(ft−1) = θft−1 and pi are equal to 1 and thus equations (23) and (24) can

be rewritten as

Pt = a0 + a1Qt + a2Pt−1 + a3Ft−1et−1 + a4Ftet + a5ft−1 + a6ft + a7Ft−1ft−1 + a8Ftft + ηpt. (27)

Qt = b0+b1Qmtft+b2Pt−1+b3Ft−1et−1+b4Ftet+b5ft−1+b6ft+b7Qt−1+b8Ft−1ft−1+b9Ftft+ηqt. (28)

a0 and b0 are the sums of the constant term in expectation functions, so they can be either positive or

negative. Based on the theoretical result, a1 and b1are expected be positive as Qt and Qmtet are used to

forecast the future prices of outputs that have input prices Pt and Qt, respectively. Pt−1 is the input cost

for farmers and storage companies selling the intermediate commodity at time t and Qt−1 is the input cost

of storage companies selling the final good at time t; both are also used to expect the future prices at time

t. Therefore, a2 and b7 can be either positive, negative or insignificant. Pt−1 is the input cost of processors,

so b2 is expected to be positive. While a3 and b3 are expected to be negative as shown in (19) and (20) if

21

Table 4: Regression result of the Thai rubber market

Equation Model RS1 Model RS2 Model System RS3Pt Constant 3.17 (7.50) -0.61 (0.62) -0.68 (0.47)

Qt 0.75 (0.23)** 0.96 (0.09)** 0.84 (0.05)**Pt−1 0.05 (0.11) 0.36 (0.11)** 0.18 (0.07)*Ft−1et−1 0.09 (0.18) -0.26 (0.15)†

Ftet 0.15 (0.23)ft−1 -0.02 (0.66)ft -0.10 (0.62)Ft−1 -4.69 (1.68)**Ft−2et−2 -0.28 (0.07)**Pt−11 -0.14 (0.08)†

Pt−12 0.27 (0.08)**Adj-R2 99.11% 99.38% 99.50%Log likelihood -50.50 -43.13 -22.61Autocorrelation: F − stat (prob.) 16.81 (0.00) 4.87 (0.01) 0.12 (0.88)Qt Constant -18.34 (8.64)* -12.54 (6.32)† -22.46 (5.93)**

Qmtet 0.73 (0.15)** 0.72 (0.12)** 0.72 (0.19)**Pt−1 -0.03 (0.48)Ft−1et−1 -0.33 (0.19)† -0.35 (0.15)* -0.45 (0.16)**Ftet 0.43 (0.12)** 0.49 (0.10)** 0.52 (0.17)**ft−1 1.03 (0.54)† 0.48 (0.24)† 0.84 (0.23)**ft -0.34 (0.53)Qt−1 0.23 (0.46) 0.61 (0.13)** 0.44 (0.13)**Qmt−1et−1 -0.48 (0.24)†

Ft−2et−2 -0.32 (0.09)**Adj-R2 99.31% 99.52% 99.48%Log likelihood -46.26 -39.18 -39.80Autocorrelation: F − stat (prob.) 8.02 (0.00) 3.71 (0.04) 2.39 (0.11)Mis-specification: LR− stat (prob.) 0.01 (0.91) 0.65 (0.42) 1.00 (0.32)Note: **, *, † denote the significance of coefficients at 1%, 5%, 10% significance levels, respectively

producers or storage companies hedge their price risks, a4 and b4 are expected to be positive if processors

or exporters hedge their price risk. If the companies storing intermediate goods (final goods) trade in the

futures market, a3 and a4 (b3 and b4) both will be significant. a7 and a8 (b8 and b9) should have the opposite

sign to a3 and a4 (b3 and b4), respectively. If the traders also hedge their exchange rate risk, then a5, a6, b5

and b6 of (25) and (26) will be significant.

Applying the two-stage-least-square estimation approach, the estimation result in Table 4 and 5 shows

that commodity prices are affected by spot and forward exchange rates through exports and offshore hedging.

For the Thai rubber market, as shown in the correlation matrix, the domestic spot price of intermediate

goods are highly correlated with the domestic and world prices of final goods. Thus, the estimators of

b2 and b7 in model RS1 are insignificant. Removing Pt−1 to correct multicollinearity problem and adding

more lags of variables to correct autocorrelation problem yield models RS2 and RS3. The most appropriate

22

Table 5: Regression result of the Thai rice market

Equation Variable Model R1 Model R2 Model R3Pt Constant 1126.48 (1183.22) 2323.54 (450.30)** 2107.48 (477.95)**

Qt 0.21 (0.07)** 0.24 (0.04)** 0.24 (0.04)**Pt−1 0.43 (0.18)* 0.31 (0.11)** 0.31 (0.09)**Ft−1et−1 -1.30 (0.72)† -1.14 (0.59)† -0.98 (0.59)†

Ftet 1.09 (0.69)ft−1 -33.05 (18.19)† -18.83 (9.18)* -14.60 (7.82)†

ft 32.13 (27.74)Ft−1ft−1 1.32 (0.71)† 1.15 (0.59)† 0.99 (0.58)†

Ftft -1.08 (0.66)Adj-R2 85.85% 86.17% 86.30%Log likelihood -289.87 -291.52 -310.78Autocorrelation: F − stat (prob.) 0.34 (0.72) 0.11 (0.90) 0.21 (0.81)Qt Constant -1142.762 (944.62) -1770.13 (260.74)* -1737.10 (1041.59)

Qmtft 0.88 (0.07)** 0.86 (0.05)** 0.91 (0.05)**Pt−1 -0.07 (0.10) 0.19 (0.10)†

Ft−1et−1 -0.81 (0.92)Ftet 3.91 (0.54)** 3.81 (0.49)* 3.87 (0.62)**ft−1 14.96 (18.62)ft 9.92 (23.37) 31.15 (16.96)* 24.51 (18.32)Ft−1ft−1 0.79 (0.90)Ftft -3.93 (0.53)** -3.85 (0.49)** -3.93 (0.62)*Qt−1 0.11 (0.07) 0.13 (0.04)**

Adj-R2 97.94% 98.05% 97.65%Log likelihood -284.35 -285.65 -289.55Autocorrelation: F − stat (prob.) 0.61 (0.55) 0.47 (0.63) 0.29 (0.75)Mis-specification: LR− stat (prob.) 0.45 (0.50) 2.37 (0.12) 2.41 (0.12)Note: **, *, † denote the significance of coefficients at 1%, 5%, 10% significance levels, respectively

model here is RS3 that does not have multicollinearity, autocorrelation and mis-specification problems. The

estimators of a1 and b1 are positive as expected. That is, both processors and exporters use the current

output price to predict their future output prices. The estimator of a6 is insignificant while the estimator

of b5 is significant; this implies that processors do not hedge their price and exchange rate risks. Thus, the

previous forward exchange rate can affect the final commodity price only through the optimal spot position

of storage companies in the previous period. The positive coefficient of b5 supports our assumption that

1 > Corr2it(Φt+1, et+1) >Corrit(Φt+1, et+1)Corrit(Mit+1, et+1)

Corrit(Mit+1,Φt+1)

and χi > 0. The result also shows that exports and storage companies in the final goods market hedge their

price and exchange rate risks; as expected the estimator of b3 is significantly negative and b4 is significantly

positive. The effects of the current forward exchange rate on the final goods price through trading by

storage companies may be offset by the effects through trading by exporters, causing the insignificance of

the estimator of b6. Unlike the smoked rubber sheet market, traders in the natural rubber sheet market do

23

Figure b: Thai rice prices

Figure a: Thai rubber prices

Rough Rice Prices

3000

4000

5000

6000

7000

8000

Sep

-97

Mar

-98

Sep

-98

Mar

-99

Sep

-99

Mar

-00

Sep

-00

Mar

-01

Sep

-01

Mar

-02

Sep

-02

Mar

-03

Sep

-03

Mar

-04

Actual FittedMilled Rice Prices

3000

6000

9000

12000

15000

Sep

-97

Mar

-98

Sep

-98

Mar

-99

Sep

-99

Mar

-00

Sep

-00

Mar

-01

Sep

-01

Mar

-02

Sep

-02

Mar

-03

Sep

-03

Mar

-04

Actual Fitted

Natural Rubber Sheet Prices

0

10

20

30

40

50

60

Jan-

02

Mar

-02

May

-02

Jul-0

2

Sep-

02

Nov

-02

Jan-

03

Mar

-03

May

-03

Jul-0

3

Sep-

03

Nov

-03

Jan-

04

Mar

-04

May

-04

Actual Fitted

Smoked Rubber Sheet Prices

0

10

20

30

40

50

60

Mar

-01

Jun-

01

Sep-

01

Dec

-01

Mar

-02

Jun-

02

Sep-

02

Dec

-02

Mar

-03

Jun-

03

Sep-

03

Dec

-03

Mar

-04

Jun-

04

Actual Fitted

Figure 3: Fitted and actual values of intermediate and final commodity prices

not hedge their risks. The negative coefficients of futures price Ft−1 and Pt−11 and the positive coefficient of

Pt−12 indicate that producers use the SICOM futures price to predict their future output price while storage

companies use the commodity price at the same period in the year before7.

For the Thai rice market, removing the insignificant coefficients we obtain models R2 and R3: one with

the first lag of intermediate goods price and another with the first lag of final goods price in (28). R2 is

chosen because all coefficients are significant, the model does not have heteroscedasticity, autocorrelation and

mis-specification problems, and it has the higher log likelihood value. The result shows that the producers

of intermediate commodity and the exporters of final commodity hedge their price risk in the CBOT. As

expected, the estimators of a1 and b1 are positive. In addition, a3 and b9 are negative while a7 and b4 are

positive. These indicate that processors and exporters of final commodity use the current prices of final

commodity to predict the future price in the domestic and international market. In addition, the significant

estimators of a5, a7, b6and b9 implies that exchange rates have effects on domestic commodity prices through

offshore hedging.

7This reflects the seasonal effect on natural rubber sheet price. The production level is lower during rainy season. Theweather causes disease to rubber tree and reduces the production of rubber latex.

24

Table 6: Descriptive statistics of estimated residuals

Statistics Rubber RicePt Qt Pt Qt

Mean −2.41× 10−15 −1.61× 10−15 1.07× 10−12 −2.66× 10−13Standard Deviation 0.523 0.674 260.063 220.17Skewness 0.785 0.471 0.061 0.313Kurtosis 3.138 3.303 2.266 2.960Jarque-Bera 3.108 1.634 1.038 0.603Prob. 0.211 0.442 0.595 0.707

The models have remarkably high explanatory power. The graphs of fitted and actual values in figure 3

show that the models fit very well. ηpt and ηqt are the estimated residual of which statistics are summarised

in Table 6. The statistics shows that the estimated residuals are normally distributed with mean values

equal to 0 as assumed in the theoretical framework.

In short, this empirical result shows that biasedness of the domestic forward exchange market allows

the spot and forward exchange rates to affect the commodity prices. This effect depends on whether the

commodity prices and exchange rates are correlated and who hedge their price risk in the foreign futures

markets and hedge their exchange rate risk in the forward foreign exchange market. Rice producers hedge

their price risk while rubber producers do not. This can relate to the commodities that the foreign futures

market trades. The CBOT trades futures contracts of rough rice (intermediate goods) while the SICOM

trades futures contracts of RSS no. 3 (final goods). The reason why processors do not hedge their risk may

be that the production process take a short period and thus they almost face no price risk; this is consistent

with the insignificant coefficient of Pt−1 in the (26) and (28). Exporters hedge their price and exchange rate

risks in both markets. Only the companies storing RSS hedge their price risk; this may be because rough

rice is stored by the government agency through price guarantee program while there is no such a program

for rubber.

4 Conclusion

In conclusion, this paper is developed to find the optimal offshore trading strategy and how it affects the

optimal spot commodity and forward foreign exchange positions. It derives equilibrium prices at maturity

in the domestic commodity markets to show how offshore trading allows the foreign exchange rates affect

the domestic commodity prices in a country without its own commodity futures markets. The framework

25

expands the models of Kawai and Zilcha (1986) to explain trading of other trader types. It relaxes the

assumptions of Kawai and Zilcha (1986) and Kofman and Viaene (1991) to allow both intermediate and

final goods to be traded in the international and futures markets. As suggested by Kawai and Zilcha (1986),

this framework allows exporters to face export shocks, factor costs and random export prices. Like other

frameworks, traders are assumed to close all of their futures position due to high delivery and transaction

costs.

Applying a two-period mean-variance approach, this framework shows that the changes in the futures

price and exchange rates and their volatility can affect the spot positions and domestic prices of internation-

ally tradable commodities in many cases. Firstly, the traders hedge their price risk in the foreign commodity

futures market and exchange rate risk in the forward foreign exchange markets which are not unbiased and

the commodity prices are correlated with the exchange rate. Second, exporters, importers and the traders

hedging their price risk in the foreign futures market are interested in the profits in domestic currency; the

effects exist even though the commodity prices and exchange rates are uncorrelated. Thirdly, the traders

use the foreign futures price as information in predicting future commodity prices.

Like Kawai and Zilcha (1986), we find that without the correlation between commodity prices and

exchange rates, the trader’s optimal position in the forward exchange market is full hedging of his expected

payment and receipt in foreign currency and the speculation in the domestic currency market. The optimal

futures position is a partial hedge of spot position, speculation in the futures market and the effect of

speculation in the forward market. We also find that the separation theorem does not apply to the optimal

spot position here. The spot position will be greater when the traders hedge their risks. Offshore hedging of

all traders will be more effective when they hedge both price and currency risks. While increases in variances

of prices and exchange rates decrease traders’ optimal spot and futures positions, a rise in the covariance

between the domestic spot price and the foreign futures price in domestic currency can increase their optimal

positions. The decreases in the difference between the expected spot exchange rate and the forward exchange

rate, the increase in exchange rate volatility, and the increase in correlations of exchange rates and domestic

commodity prices can either increase or decrease the commodity spot price; this depends on which traders

hedge their exchange rate risk and whether the effects of these changes on the supply is greater than the

26

effects on the demand in the markets.

The empirical result also supports the theoretical result. We find that Thai rice and rubber sheet prices

are affected by exchange rates though exports and offshore hedging. Offshore hedging by different trader

types leads to different impacts of foreign futures prices and foreign exchange rates on domestic commodity

prices. With the biasedness of the forward foreign exchange market, we find the effect of the forward foreign

exchange rate on domestic rubber and rice prices even though rice prices (in domestic currency) and the

exchange rate are not correlated. The model also indicates that some traders hedge their price risk in the

foreign futures market, some do not hedge their risk, and some use the futures price as information to predict

the future spot price.

Further research could compare the optimal strategy, price volatility and trader’s welfare before and after

the existence of domestic commodity futures market. The finding would guide the policy makers whether

the country should have a domestic commodity futures market. Empirical work could be done using recent

commodity prices to investigate how the prices and trader behaviour change when the domestic commodity

future market becomes available. It could also apply the prices of more commodities in different countries

to calculate the optimal hedging ratios based on the optimal strategy found in this paper.

References

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Appendix A

The profit of the traders can be rewritten in a general form as

Πi = Y fitΦt − CitSit − θS2it + ρMit+1(f(Sit) + ξit+1)

−Y fit Φt+1 + (et+1 − ft)Z

fit. (29)

He choose Sit, Yfit and Zf

it at time by maximising his expected utility

Vi = MaxY fit, Yit,Z

fit

Y fitΦt − CitSit −

λi2S2it + ρ[Eit(Π

∗it+1)−

Ai

2V arit(Π

∗it+1)]. (30)

29

where the expected future profit is

Eit(Π∗it+1) = Eit(Mt+1)f(Sit) +Eit(Mit+1ξit+1)− Y f

itEit(Φt+1)

+ [Eit(et+1)− ft]Zfit

and the variance of his expected future profit is

V arit(Π∗it+1) = V arit(Mit+1)f(Sit)

2 + V arit(Mit+1ξit+1) + V arit(Φt+1)Yf2it

+Zf2it V arit(et+1) + 2f(Sit)Covit(Mt+1,Mt+1ξit+1)

−2f(Sit)³Y fitCovit(Mit+1,Φt+1)− Zf

itCovit(Mit+1, et+1)´

−2Y fitCovit(Mit+1ξit+1,Φt+1) + 2Z

fitCovit(Mit+1ξit+1, et+1)

−2Y fitZ

fitCovit(Φt+1, et+1)

where Covit(ξit+1, et+1), Covit(Mit+1ξit+1,Φt+1) and Covit(Mit+1ξit+1, et+1) are equal to 0.

His FOC with respect to Sit is

∂Vi∂Xst

= −Ct − λiSit + ρ[Eit(Mit+1)−AifSf(Sit)V arit(Mit+1) + Covit(Mit+1ξit+1,Mit+1)

−Y fitCovit(Mit+1,Φt+1) + Zf

itCovit(Mit+1, et+1)] = 0 (31)

where fS =∂f(Sit)∂Sit

. The FOCs with respect to Y fit and Zf

it are

∂Vi

∂Y fft

= Φt − ρEit(Φt+1)− ρAiY fit V arit(Φt+1)−Eit(f(Sit))Covit(Mit+1,Φt+1)

−ZfitCovit(Φt+1, et+1)

= 0 (32)

and

∂Vi

∂Zfit

= Eit(et+1)− ft −AiZfit V arit(et+1)− Y f

it Covit(Φt+1, et+1) + SitCovit(Mit+1, et+1)

= 0. (33)

Appendix B

The effect of changes in price and exchange rate volatilities are as follows.

∂S∗it∂V arit(Mit+1)

= −S∗itχit − 2λit

2χit

¯pV ar3it(Mit+1)

¯ < 030

∂S∗it∂V arit(Φt+1)

=Φt − ρEit(Φt+1)

2χit

¯¯s

V arit(Mit+1)

V ar3it(Φt+1)

¯¯

Corrit(Mit+1,Φt+1)− Corrit(Φt+1, et+1)Corrit(Mit+1, et+1)

1− Corr2it(Φt+1, et+1)

> 0

∂S∗it∂V arit(et+1)

= −ρ(Eit(et+1)− ft)

¯qV arit(Mit+1)V ar3it(et+1)

¯2χit (1− Corr2it(Φt+1, et+1))

(Corrit(Φt+1, et+1)Corrit(Mit+1,Φt+1)− Corrit(Mit+1, et+1))

< 0

∂S∗it∂Corrit(Mit+1, et+1)

= −ρ(Eit(et+1)− ft)

¯qV arit(Mit+1)V arit(et+1)

¯χ2itV arit(et+1) (1− Corr2it(Φt+1, et+1)

3)χit + 2ρAiV arit(Mit+1)

(Corrit(Φt+1, et+1)Corrit(Mit+1,Φt+1)− Corrit(Mit+1, et+1))2

1− Corr2it(Φt+1, et+1)

< 0

∂S∗it∂Corrit(Mit+1,Φt+1)

=

¯qV arit(Mit+1)V arit(Φt+1)

¯(Φt − ρEit(Φt+1) + ρ(Eit(et+1)− ft)Corrit(Φt+1, et+1))

χit (1− Corr2it(Φt+1, et+1))

+2S∗itρAiV arit(Mit+1)

(Corrit(Mit+1,Φt+1)− Corrit(Mit+1, et+1)Corrit(Φt+1, et+1))

χit (1− Corr2it(Φt+1, et+1))

> 0

Appendix C

V ar(AB) = E [AB −E(AB)]2 (34)

where A and B are random variables. Define X = A−E(A) and Y = B −E(B). Then, A = X +E(A) and

B = Y +E(B). Therefore,

V ar(AB) = E[XY +XE(B) + Y E(A)− Cov(A,B)]2

= E[X2Y 2 + 2X2Y E(B) + 2XY 2E(A)− 2XY Cov(A,B) +X2E(B)2 + Y 2E(A)2

+2XYE(A)E(B)− 2XE(B)Cov(A,B)− 2Y E(A)Cov(A,B) + Cov2(A,B)] (35)

As

E(X2Y 2) = V ar(A)V ar(B) + 2Cov2(A,B), E(X2Y E(B)) = 0, E(XY 2E(A)) = 0,

31

V ar(AB) = V ar(A)V ar(B) + Cov2(A,B) +E(B)2V ar(A)

+E(A)2V ar(B) + 2Cov(A,B)E(A)E(B) (36)

V ar(Lt+1) = V ar(Lt+1et+1

)V ar(et+1) + Cov2(Lt+1et+1

, et+1) +E(et+1)2V ar(

Lt+1et+1

)

+E(Lt+1et+1

)2V ar(et+1) + 2Cov(Lt+1et+1

, et+1)E(Lt+1et+1

)E(et+1) (37)

if Cov(Lt+1et+1, et+1) = 0,

V ar(Lt+1) = V ar(Lt+1et+1

)V ar(et+1) +E(et+1)2V ar(

Lt+1et+1

) +E(Lt+1et+1

)2V ar(et+1) (38)

32