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:[email protected]
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
3
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
4
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
5
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
6
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.
7
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.
8
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.
9
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).
10
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.
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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