Offshore hedging strategy of Japan-based wheat traders under multiple sources of risk and hedging costs

Journal of International Money and Finance 25 (2006) 220e236 www.elsevier.com/locate/econbase

Offshore hedging strategy of Japan-based wheat traders under multiple sources of risk and hedging costs Hyun J. Jin a,*, Won W. Koo b a

Department of Industrial Economics, College of Industrial Science, Chung-Ang University, South Korea, 456-756 b Center for Agricultural Policy and Trade Studies, Department of Ag-Business and Applied Economics, The North Dakota State University, Fargo, ND 58105-5636, USA

Abstract Japan-based international wheat traders face multiple risks from the changes in wheat prices and exchange rates. This study shows that Japanese wheat importers would employ futures hedging in the CBOT and/or TIFFE to reduce the risks, although there is no wheat futures trading in Japan. For the importers, hedging in the CBOT and TIFFE might accompany some costs in addition to transaction and opportunity costs, such as additional transaction cost as a foreign trader and a relatively higher bid-ask spread due to a large volume of trade. Thus, introducing hedging costs in an offshore hedging model for the traders is necessary, and it may change optimal hedging ratios in both futures markets. Empirical results show that costs in the hedging activities are at play in determining optimal hedging positions in the markets. Ó 2005 Elsevier Ltd. All rights reserved. JEL classification: C30; F30; G10 Keywords: Japan-based wheat importers; Risk management; Offshore futures hedging; Hedging cost

1. Introduction Wheat is one of the most important sources of food for Japanese consumers, and domestic consumption has been continuously increasing since 1960. In the year 2000, Japan consumed * Corresponding author. Tel.: þ82 31 670 3045; fax: þ82 31 675 1381. E-mail address: [email protected] (H.J. Jin). 0261-5606/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jimonfin.2005.11.005

H.J. Jin, W.W. Koo / Journal of International Money and Finance 25 (2006) 220e236

221

5824 thousand metric tons of wheat, while its domestic production was just 3.76 thousand metric tons. Thus, to fill the gap between the demand for domestic consumption and the domestic production of wheat, Japan imports more than 99% of her wheat consumption. According to the production, supply, and distribution database (PS&D) of the Economic Research Service (ERS) of the U.S. Department of Agriculture (USDA), Japan imported 5911 thousand metric tons of wheat in fiscal-year 2000, of which 51.4% was from the United States. The U.S. market share of wheat in Japan has been constant at around 50% during the last four decades. Since Japanese traders import a huge volume of wheat from the United States, small risks in the U.S. wheat prices and exchange rates between Japanese yen and the U.S. dollar may result in large losses in the trade. Japan-based wheat importers, who face the multiple risks from wheat price and exchange rate changes, need to have proper risk management tools. Futures contracts may provide such tools. However, there is no futures trading for wheat in Japan, and the trading volume of exchange rate futures at the Tokyo International Financial Futures Exchange (TIFFE) is smaller compared to that at the International Monetary Market (IMM) of the Chicago Mercantile Exchange (CME). This study is initialized to show that Japan-based wheat importers would employ wheat and exchange rate futures contracts using an offshore hedging strategy that comprises underlying commodity futures contracts at the Chicago Board of Trade (CBOT) and additional currency futures contracts at the TIFFE. For a representative Japan-based wheat importer, hedging in the CBOT and TIFFE might incur extra costs in addition to usual transaction and opportunity costs. Unless he uses an electronic hedging method, additional transaction and management costs may be imputed to the trader. For the trader, the bid-ask spread will be substantial in both futures markets because of the large volume of futures contracts they might need to purchase and because of the low liquidity in the TIFFE due to the small trading volume. Almost 100% of U.S. wheat exported to Japan is shipped from Pacific North West (PNW) because the cleaning facilities in PNW meet Japanese dockage specification. The average shipment of wheat carried by a vessel from PNW to Japan is approximately 20,000 metric tons. Japan Food Agency (JFA) does not allow to load wheat with other grains, although it occasionally allows a combination of two different classes of the wheat.1 The amount of wheat imported on each vessel is about 928,592 bushels, an extraordinary quantity, and thus the volume of futures contracts to be purchased in both markets will be large. Therefore, the bid-ask spread will be relatively large compared to those of other hedgers in the futures markets. This suggests that hedging costs will be substantial and at play in determining optimal hedging positions for the Japan-based wheat importers. If hedging with commodity futures contracts at the CBOT costs more than hedging for an equivalent unit with currency futures contracts at the TIFFE, importers may assign more importance to currency hedging than commodity hedging. Introducing hedging costs in an offshore hedging model is therefore necessary and may change hedge ratios in both futures markets. In order to construct an offshore hedging model for the representative wheat importer, this study utilizes two lines of hedging literature. One of these lines deals with hedging costs in commodity futures markets (Hirshleifer, 1988; Simman, 1993; Lence, 1995, 1996; Locke and Venkatesh, 1997; Wang et al., 1997; Frechette, 2000, 2001). Lence and Frechette found that transaction costs and opportunity costs are important factors that drive hedgers from the

1 The information about the typical shipment from the Pacific North West to Japan was provided by the branch office in Japan of U.S. wheat association.

222

H.J. Jin, W.W. Koo / Journal of International Money and Finance 25 (2006) 220e236

market and reduce optimal hedge ratios. Their main conclusion is that optimal hedge ratios vary with hedging costs. Frechette (2001) included hedging costs in his study of commodity futures and options for corn buyers involved in dairy production and concluded that the hedging cost in each market affects the demand for both hedging goods. The other line consists of offshore hedging studies for international traders (Thompson and Bond, 1987; Fung and Lai, 1991; Kroner and Sultan, 1993; Hauser and Neff, 1993; Haigh and Holt, 2000, 2002). While other offshore hedging studies have not paid attention to hedging costs, the studies by Kroner and Sultan, and Haigh and Holt considered the commission fees associated with hedging into a mean-variance framework; however, they did not explicitly include it in the hedge ratio estimation. Following these two lines of research, we construct an offshore hedging demand model that accounts explicitly for hedging costs for Japan-based wheat importers. This study estimates optimal hedge ratios for Japan-based wheat traders in both commodity and currency futures markets, the CBOT and TIFFE, and evaluates the effects of hedging costs on the offshore hedging strategy. One contribution of this study is applying the offshore hedging demand model to data relevant for Japan-based wheat importers. Another contribution may be combining a model of price and exchange rate risk with hedging costs to show the relationship between optimal offshore hedge ratios and hedging costs. The remainder of the paper is organized as follows. A hedging demand model for both commodity and currency futures hedging is developed and the effects of hedging costs on the demand system are analyzed in Section 2. The hedging model is applied to the case of a representative Japan-based wheat importer in Section 3. Demands for commodity and currency futures are estimated under different levels of hedging costs. A short summary and conclusion follow in Section 4. 2. An offshore hedging demand model Consider two countries: an exporting country (A) and an importing country (B). Assume that country A exports wheat and has a commodity futures market and a commodity cash market. Also assume that country B has wheat importers with risk-averse utility and that the country has a currency cash market and a currency futures market. The importers in country B can access both the commodity futures market in country A and the currency futures market in their own country in order to avoid risks from export price and exchange rate variations. It is also assumed that there are only two time periods: time t and time t þ 1. Hedgers place hedging at time t and lift or revise it at time t þ 1. For the Japan-based traders, the unit of time will be months since it typically takes months to negotiate and consummate a contract.2 There is no multi-period trading; therefore, hedgers buy contracts that are the closest to their desired hedging date. The hedgers’ only purpose is to reduce risks from price and exchange rate variations from time t to time t þ 1. 2 The JFA purchases more than 90% of wheat imported by Japan. The JFA has a weekly tender through the year. On Tuesdays of every week, the commodity and quantity are announced. The registered wheat importers begin to check the wheat prices, freight rates, and yen exchange rates against exporting countries’ currency values. On Thursday, the JFA selects an offer with the lowest price at the Japanese port delivery in Japanese yen. Once the tender is awarded to an importer, he makes contacts with wheat exporters and shipping brokers. Considering time for transportation of heavy grain, it usually takes several months for the importers from receiving the tender to completing the contract with the JFA.

H.J. Jin, W.W. Koo / Journal of International Money and Finance 25 (2006) 220e236

223

In this study, the marginal hedging costs serve as prices for hedging. Traders might face a downward demand curve for hedging because of the hedging cost. Assume that hedging costs are constant, thus the costs are both marginal and average costs. The costs may include transaction costs, brokers’ fees, opportunity costs, learning costs, bid-ask spread, etc. With the hedging costs, a Marshallian type of demand for offshore hedging can be derived with the assumption of mean-variance utility. In the hedging demand model, hedging products are treated as goods and the hedging costs as prices of the goods. Suppose there is a representative grain importer in country B who needs to buy wheat from country A at period t þ 1. His expected profits on the hedged portfolio at time t can be written as follows: etþ1 R etþ1 þ Ht ðF etþ1  Ft Rt  ct Rt Þ þ Gt ðe etþ1 R Et ½Ptþ1
¼ Xtþ1 P Stþ1  St  tt Þ;

ð1Þ

where Et denotes the mathematical expectation operator for period t þ 1 at period t, Xtþ1 represents the amount of the grain to be purchased at time t þ 1, Pt represents the commodity export price in the exporting country A at time t, Ft represents the commodity futures price in the exporting country A at time t, Rt denotes the exchange rate of the importing country’s currency against the exporting country’s currency at time t, St denotes the currency futures price in the importing country B at time t, c denotes the price of commodity hedging, i.e., hedging cost faced by the trader in the commodity futures market, t denotes the price of currency hedging, i.e., hedging cost faced by the trader in the currency futures market, Ht denotes the amount of futures contracts to be bought in the commodity futures market, and Gt denotes the amount of futures contract to be purchased in the currency futures market. The first term on the right-hand side is the total cost for purchasing grain from the export country at time t þ 1; therefore, a minus sign is added to the term. Xtþ1 can be considered to be given since our objective is to estimate optimal hedge ratios for a specific amount of wheat. The second term is the return from engaging in the commodity futures market. As commodity futures contracts are denominated in U.S. dollars, the spot exchange rates are multiplied by the futures prices and commodity hedging cost. The trader needs a long hedging, thus the sign of Ht is positive. The trader lifts the futures contracts and converts into the trader’s home currency at etþ1 > Ft Rt þ ct Rt ; the trader would make money on the transaction. Alteretþ1 R time t þ 1. If F e e natively, if Ftþ1 Rtþ1 < Ft Rt þ ct Rt ; the trader would lose on the transaction. The last term is the gain from purchasing currency hedging. The trader also needs a long hedging in the currency futures market, thus the sign of Gt is positive. Again, if e Stþ1 > St þ tt ; the trader would make money on the transaction. Alternatively, if e Stþ1 < St þ tt ; the trader would lose on the transaction. Prices denoted with a t subscript are known at time t, whereas prices denoted with a t þ 1 subscript are unknown, and thus Ptþ1, Ftþ1, Rtþ1, and Stþ1 are treated as random variables and denoted by the w symbol. Following Hauser and Neff (1993) and Haigh and Holt (2002), the currency futures prices in the last term of Eq. (1) are multiplied by the grain export prices to make the currency futures hedge ratio an equivalent unit to the commodity futures hedge ratio. After this multiplication, dividing Eq. (1) by Xtþ1 yields etþ1 þ ht ðF etþ1  Ft Rt  ct Rt Þ þ gt ðe etþ1  St Pt  tt Pt Þ; etþ1 R etþ1 R Stþ1 P Et ½ptþ1
¼ P

ð2Þ

where h ¼ H/X and g ¼ G/(XP), which are hedge ratios in the commodity and currency futures markets, respectively. The dimension of g is the amount of currency futures contracts divided

224

H.J. Jin, W.W. Koo / Journal of International Money and Finance 25 (2006) 220e236

by the values of wheat, not by the physical quantity of wheat. The objective of the importer is changed to a maximization of per unit expected profits, and the choice variable is hedge ratios rather than quantities hedged. The na€ıve hedging strategy has been used because it is a simple method to reduce price risks. If the respective cash and futures prices are perfectly and positively correlated, any loss (gain) in the cash position will be offset by the gain (loss) in the futures position. In this case, the hedger’s net position will be unchanged, and the na€ıve hedging strategy will be a perfectly suitable hedging method. However, since the spot and futures prices typically do not move together, other strategies have been proposed and used to determine the ‘optimal’ hedge ratio. The mean-variance framework is one of the strategies, and this study adopts the framework. Previous hedging studies, such as those by Kroner and Sultan (1993), Gagnon et al. (1998), and Frechette (2000) have argued that the transaction costs can be easily incorporated into the mean-variance framework, in which the objective of the decision maker is to maximize expected per-unit profit with respect to h and g, subject to the variance of the profit. An expression of the objective function of the representative trader is r Ut ¼ Et ½ptþ1 jUt
 Vt ðptþ1 jUt Þ; 2

ð3Þ

where Vt($) represents a volatility measure of risk which accompanies the returns; it is specifically the one-period-forward estimate of variance of returns. Ut denotes the information set available at time t. r represents the coefficient of absolute risk aversion, which is derived by U$/U#. r is supposed to have a positive sign and be fixed at a specific level. It is assumed that the utility function of the representative grain importer is continuous, monotonic increasing, and strictly concave. Corresponding to the objective function (2), the estimated variance of returns for the period t þ 1 is eRÞ e þ h2 Vt ðF eRÞ e þ g2 Vt ðe e  2hCVt ðP eR; e F eRÞ e  2gCVt ðP eR; e e e Vt ðptþ1 Þ ¼ Vt ðP SPÞ SPÞ eR; e e e þ 2hgCVt ðF SPÞ;

ð4Þ

where CVt($) is the covariance operator. After substituting Eq. (4) into the mean-variance framework (3), maximizing the mean-variance utility function with respect to h and g generates first order conditions. The second order condition is satisfied by the assumption of strict concavity of the utility function U($). If we solve the first order conditions with respect to h and g, the optimal hedge ratios for commodity and currency futures are obtained and the equations for the hedge ratios are presented in Appendix A. In the equations, both hedging costs (c and t) as well as two variance terms, three covariance terms, and four speculative component terms are at play in determining optimal hedge positions for the trader. The effects of hedging costs on the optimal commodity and currency hedging positions would be clarified by identifying the sign of partial derivatives of the optimal hedge ratios with respect to the hedging costs. The partial derivatives are ! e vh Rt Vt ðe SPÞ ¼ ; eRÞV e t ðe e  CVt ðF eR; e e e 2Þ vc SPÞ SPÞ 2rðVt ðF

ð5aÞ

H.J. Jin, W.W. Koo / Journal of International Money and Finance 25 (2006) 220e236

225

! eR; e e e vh Pt CVt ðF SPÞ ¼ ; eRÞV e t ðe e  CVt ðF eR; e e e 2Þ vt SPÞ SPÞ 2rðVt ðF

ð5bÞ

! eR; e e e vg Rt CVt ðF SPÞ ¼ ; eR; e e e 2  V t ðF eRÞV e t ðe e vc SPÞ SPÞÞ 2rðCVt ðF

ð5cÞ

! eRÞ e vg Pt Vt ðF ¼ : eR; e e e 2  V t ðF eRÞV e t ðe e vt SPÞ SPÞÞ 2rðCVt ðF

ð5dÞ

and

To define expected signs of the derivatives, one needs to know expected signs of eR; e e e and Vt ðF eRÞV e t ðP eRÞ e  CVt ðF eR; e e e 2 . Details for defining the signs are presented CVt ðF SPÞ SPÞ in Appendix B, which show that expected signs of both terms are positive. Note that the coefficient of risk aversion is positive. Thus, denominators in the partial derivatives (5a) and (5b) would be positive, while those of (5c) and (5d) would be negative. Therefore, the expected signs of the partial derivatives are as follows: vh vh vg vg  0;  0;  0;  0: vc vt vc vt

ð6Þ

The inequalities show that the own-price effects would be negative and cross-price effects would be positive. There are two implications that can be drawn from the terms (Eq. (6)). First, hedging cost might not be a negligible factor in determining optimal hedging positions for the wheat importers, albeit hedging costs are not large relative to the value of the shipment. The costs will play a significant role as the price for hedging goods. This implies that the amount hedged will decrease as the marginal hedging cost increases. Therefore, reducing hedging costs would be an effective way to stimulate offshore hedging activities in the futures markets. The reduced cost of commodity futures hedging in the CBOT could induce more offshore hedgers into the market, resulting in reduced risk for wheat importers. Reduction of hedging costs can be accomplished, e.g., by introducing them to electronic trading. This might help hedgers reduce commission fees or other fees especially relevant for foreign traders. Second, positive cross-price effects imply that the hedging costs are at play in making commodity futures and currency futures substitute goods for each other, ceteris paribus. The amount hedged with one futures product will increase when the marginal cost of the other futures market rises. However, the substitutability between the two markets is expected to be relatively low because of small hedging costs compared to the value of the shipment. Note that the signs of the cross-price effects are equal, but the sizes are not the same because of the multiplication by Rt and Pt. This implies that the demand system for offshore hedging would satisfy the symmetry condition without the multiplication of commodity hedging cost by spot exchange rate and the multiplication of currency hedging cost by spot grain price in Eqs. (1) and (2). The question of which futures demand is more sensitive to its own-cost changes remains obscure, depending on eRÞ e and Rt Vt ðe e the size of Pt Vt ðF SPÞ:

226

H.J. Jin, W.W. Koo / Journal of International Money and Finance 25 (2006) 220e236

3. Application to Japanese wheat importers The hedging demand model developed in the previous section is applied to Japan-based wheat importers. These traders need a risk management tool to avoid risks from variations in both wheat prices and exchange rates.3 Hedgers maximize their mean-variance utility with respect to both hedge ratios. In this empirical analysis, the exporting country is the United States and the importing country is Japan. The central commodity export market is Portland, and the central commodity futures market is the CBOT. The CBOT is selected as a representative grain futures market in the United States due to its relative importance in the international grain market and because there is no futures trading for wheat in Japan. This study chooses the TIFFE as the currency futures market. If we choose the CME instead of the TIFFE as a financial futures market, the results will be differently quantified, but implications of hedging costs to optimal hedging positions would be the same. 3.1. Data The data set consists of wheat export prices in Portland, the nearby wheat futures prices in the CBOT, the exchange rates of the Japanese yen against the U.S. dollar, and the nearby U.S. dollar currency futures prices in the TIFFE. When a futures contract comes close to maturity, the nearby contract was used to compile the data because an increased volume of trading may induce larger volatility of the prices. A jump is made to the prices of the successive contract before the month of the prior contract’s maturity. Thus, this study implicitly assumes that hedgers roll over into the next nearest contract before the current contract expires. The wheat export prices are acquired from the ERS/USDA; the nearby wheat futures prices are provided by the Great Pacific Trading Company; the exchange rates are furnished by ERS/USDA and the International Monetary Fund; and the U.S. dollar currency futures prices are provided by the TIFFE. The unit for the commodity prices is cents per bushel, and the unit for the currency prices is yen per dollar. These data are available from January 1991 to February 2001. Summary statistics are presented in Table 1 and plots of the data are displayed in Fig. 1. The data are monthly and thus, this empirical analysis implicitly assumes that the importers make their decisions monthly, which matches with real-world observations for trading horizons of Japan-based wheat importers. Augmented DickeyeFuller (1981) (ADF) test was performed on the series to check existence of a unit-root. The ADF test results indicate that all series are nonstationary. When the same test was applied to the first differenced series, the null of a unit-root was clearly rejected at all conventional significance levels. Preliminary conditional mean analysis on each differenced series was completed using autoregressive (AR) models. The lags, p, in the AR models were chosen by the Akaike information criteria (AIC). For the prediction error on chosen AR( p) model for each series, the autoregressive conditional heteroskedasticity-Lagrange multiplier (ARCH-LM) test 3 Japan-based wheat importers have the firm offer of the freight rates from the shipping brokers before the tender award. It is not popular that U.S. exporters sell wheat on cost and freight (C&F) basis due to many problems in the unloading ports of Japan. U.S. exporters usually do not handle the matters well. The registered importers negotiate the freights with the shipping brokers in Japan. Freight is settled between an agreed charterer and an agreed owner via a shipping broker. There is no open market like a CBOT but the interested parties create the market of the freight among the professionals. The risk from transportation cost changes goes to Japan-based importers. However, the importers can have a firm offer of the freight before the tender and they can fix the freight rate to a level with the owner after the award is given by the JFA. Therefore, the Japan-based wheat importers face no substantial risk from changes in transportation costs.

H.J. Jin, W.W. Koo / Journal of International Money and Finance 25 (2006) 220e236

227

Table 1 Descriptive statistics of the cash and futures price series Series

Mean

Standard deviation

Skewness

Kurtosis

Normality test

Wheat prices Wheat futures prices Exchange rates Currency futures prices

384.28 342.81 115.09 114.83

77.51 74.71 13.51 12.96

0.563 0.895 0.057 0.242

2.646 3.585 2.469 2.243

7.10 18.06 1.49 4.09

(0.028) (0.000) (0.473) (0.128)

Notes: Positive skewness means that the distribution has a long right tail and vice versa. The kurtosis of the normal distribution is 3. If the kurtosis exceeds 3, the distribution is peaked and has a thicker tail relative to the normal. Otherwise, the distribution is flat and has a thinner tail relative to the normal. The normality test was completed using the JarqueeBera statistic where the null hypothesis is that series follows a normal distribution and the values in the parenthesis are p-values.

and the BreuscheGodfrey LM (BGLM) test were performed to check remaining ARCH effects and serial correlations.4 The results show that the conditional mean model does a good job of explaining the variation of each series. The null hypotheses of no ARCH effect and no serial correlation were not rejected for all residual series at the conventional levels.5 The ADF test results indicate that the process of each series is I(1) in the sense of Engle and Granger (1987). Therefore, cointegration between cash and futures prices was tested using the Johansen’s (1991) procedure. The results, shown in Table 2, indicate that cash and futures price pairs are found to be cointegrated and the number of cointegrating vectors is one for both cases. Existence of cointegrating relationship suggests that an error correction term (ECT) should be included in a vector autoregressive (VAR) model to forecast the expected values of cash and futures price changes. For the price pairs, a vector error correction (VEC) model is constructed as follows: DPt ¼ a0 þ

p X

ai DPti þ

i¼1

DFt ¼ b0 þ

p X

q X

q X i¼1

ð7aÞ

biþp DFti þ f2 ECTPFt1 þ 3Ft ;

ð7bÞ

qiþq DSti þ f3 ECTRSt1 þ 3Rt ;

ð7cÞ

p X

bi DPti þ

i¼1

qi DRti þ

q X

i¼1

DSt ¼ u0 þ

aiþp DFti þ f1 ECTPFt1 þ 3Pt ;

i¼1

i¼1

DRt ¼ q0 þ

p X

i¼1

ui DRti þ

q X

uiþq DSti þ f4 ECTRSt1 þ 3St ;

ð7dÞ

i¼1

4 The null hypothesis of the ARCH-LM test is that there is no ARCH in errors, and the null hypothesis of the BGLM test is that there is no serial correlation up to lag order p in errors. The test statistic of ARCH-LM is calculated by TR2, the statistic is distributed with c2p, where T is the number of observations, R2 is the coefficient of determination from the auxiliary regression, and p is the number of variables in the right-hand side of the auxiliary equation. The test was completed by collecting the residuals from a chosen model, AR( p), and performing regression between squared residual and laggedsquared residuals. The test statistic of the BGLM test is calculated in a similar step as the ARCH-LM, except that R2 is the coefficient of determination from the auxiliary regression of the residual on the first lag of series and lagged residuals. 5 The results of AR( p) model estimation are not presented in the text for the reason of space. They are obtainable from the authors upon request.

H.J. Jin, W.W. Koo / Journal of International Money and Finance 25 (2006) 220e236

228

600

500

Yen (currency), Cent (wheat)

Wheat Prices 400

Wheat Futures Prices

300

200

Exchange Rates

100 Currency Futures Prices

0

01

l-0

n-

Ju

Ja

9

00

l-9

n-

Ju

Ja

8

99

l-9

n-

Ju

Ja

7

98

l-9

n-

Ju

Ja

6

97

l-9

n-

Ju

Ja

5

96

l-9

n-

Ju

Ja

4

95

l-9

n-

Ju

Ja

3

94

l-9

n-

Ju

Ja

2

93 n-

l-9 Ju

Ja

1

92 n-

l-9 Ju

Ja

Ja

n-

91

0

Month

Fig. 1. Cash and futures price series: Pt, Ft, Rt, and St.

where ECTPF and ECTRS denote normalized cointegrating vector for each cash and futures price pair, and the truncation lag, p and q, is selected based on the AIC statistics: p is equal to one and q is equal to four. Estimates and diagnostic statistics of the VEC models are presented in Table 2. 3.2. Empirical results The expected values of cash and futures prices are calculated through the VEC, an adaptive expectation model. The varianceecovariance matrix is calculated based on the expected wheat and currency prices. Using the varianceecovariance matrix, we estimated the optimal hedge ratios. Note that there are variances of two random variables and covariances of four random eRÞ e and CVt ðF eR; e e e and devariables in the equations of the optimal hedge ratios, e.g., Vt ðF SPÞ, compositions of the variance and covariance of multi-variables are explained in Appendix C. The model is re-estimated with a new observation added for each month. The first estimation starts from January 1993, not from January 1991, in order to have some observations for obtaining the expected values, and the last one ends in February 2001. Here, a GARCH type approach is not adopted in calculating the varianceecovariance matrix because the ARCH-LM statistics in both univariate AR( p) and VEC models show no significant ARCH effects. However, using such a model may provide a slightly different performance in offshore hedging as Haigh and Holt (2000) suggested. Using the hedging demand functions (A1) and (A2), the optimal hedge ratios were estimated. Since pinpointing exact costs of hedging activities is difficult and is also beyond the scope of

H.J. Jin, W.W. Koo / Journal of International Money and Finance 25 (2006) 220e236

229

Table 2 Cointegration test and VEC conditional mean models Variable

P

F

Variable

Constant DP1 DP2 DP3 DP4 DF1 DF2 DF3 DF4 ECTPF

0.031 (0.02) 0.040 (0.32) e e e 0.287 (2.48) e e e 0.032 (0.40)

0.036 (0.02) 0.092 (0.61) e e e 0.241 (1.75) e e e 0.228 (2.42)

Constant DR1 DR2 DR3 DR4 DS1 DS2 DS3 DS4 ECTRS

R

S

AIC Log likelihood

8.694 517.68

9.037 538.23

e e

5.618 318.67

4.765 268.81

b3 b4 Q6 Q12 ARCH-LM6 ARCH-LM12

0.051 3.541 5.413 7.468 3.756 13.222

0.760 6.296 6.153 10.977 6.977 8.477

e e e e e e

0.714 5.489 1.308 6.028 3.509 4.319

1.038 5.656 1.988 5.348 9.883 17.899

0.189 0.055 0.028 0.136 0.187 0.162 0.036 0.323 0.136 0.163

(0.53) (0.20) (0.11) (0.59) (1.03) (0.55) (0.14) (1.34) (0.85) (0.61)

0.177 0.199 0.059 0.027 0.120 0.044 0.158 0.271 0.146 0.532

(0.76) (1.13) (0.35) (0.18) (1.01) (0.23) (0.92) (1.72) (1.40) (3.04)

Cointegration test

P and F

R and S

H0: r ¼ 0; HA: r > 0 H0: r  1; HA: r > 1 ECT

19.10** 3.45 ECTPF ¼ P1.062F

21.96** 6.01 ECTRS ¼ R1.048S þ 5.190

Notes: Optimal lag in the VEC models was chosen based on AIC value. The values in the parentheses are t-statistics. The skewness and kurtosis for the residuals are b3 and b4. The Qk are LjungeBox Q-statistics at lag k, which test the null hypothesis of no autocorrelation up to lag k. The null was not rejected for all residual series at the 5% significance level. The null hypothesis of ARCH-LM test is that there is no ARCH in the residuals. The null was not rejected for all residual series at the 5% level. r denotes the number of cointegrating relations and ECT denotes normalized cointegrating vector. The cointegration test statistics are from trace test and the superscript. **Denotes a rejection of the null at the 5% level.

this study, cost ranges were instead used for the hedging activities. Frechette (2000, 2001) stated that a reasonable value for the hedging cost could be $25 per contract of 5000 bushels of corn. If we consider the margin accounts, bid-ask spread, and other costs for offshore hedgers, the cost could be higher than $25 per contract. Thus, a cost range for wheat futures hedging could run from 0.5 to 2.5 cents per bushel. For each trader, the realized hedging cost in the commodity futures market would be somewhere in this range, depending on his knowledge of the market, hedging procedure, and his discount rate. U.S. dollareJapanese yen currency futures in the TIFFE was downsized to one-fifth of its value on November 2000; i.e., the contract size was changed from US$50,000 to US$10,000. Calculation of a reasonable value of hedging cost in the TIFFE is also difficult. Thus, in the same context as the commodity hedging cost, a cost range for currency futures hedging is selected as approximately 0.057e1.425 yen per dollar, considering that the average exchange ratio between yen and U.S. dollar for the sample period is 114. When we consider the former contract size in the TIFFE, the hedging cost could be as low as 0.057 yen per dollar; when using the later contract size, the cost could be as high as 1.425 yen per dollar. Converting

230

H.J. Jin, W.W. Koo / Journal of International Money and Finance 25 (2006) 220e236

Table 3 Average optimal hedge ratios, h* and g* using CBOT and TIFFE c

t 0.00

0.05

0.35

0.65

0.95

1.25

0.00

0.4880 0.5028

0.4886 0.5000

0.4927 0.4831

0.4967 0.4662

0.5008 0.4494

0.5048 0.4325

0.50

0.4828 0.5046

0.4834 0.5018

0.4875 0.4849

0.4916 0.4680

0.4956 0.4511

0.4996 0.4342

1.00

0.4776 0.5063

0.4783 0.5035

0.4823 0.4866

0.4863 0.4698

0.4904 0.4529

0.4944 0.4360

1.50

0.4724 0.5081

0.4731 0.5053

0.4771 0.4884

0.4811 0.4715

0.4852 0.4546

0.4892 0.4377

2.00

0.4672 0.5098

0.4679 0.5070

0.4719 0.4901

0.4759 0.4733

0.4798 0.4564

0.4840 0.4395

2.50

0.4620 0.5116

0.4626 0.5088

0.4667 0.4919

0.4707 0.4750

0.4748 0.4581

0.4788 0.4412

Notes: In each cell, the upper number represents optimal commodity futures hedge ratios, h*, and the lower number denotes the optimal currency futures hedge ratios, g*. Column labels denote changes of the currency hedging costs, ranging from 0.05 to 1.25 cents per dollar. Row labels represent changes of the commodity hedging costs, ranging from 0.50 to 2.50 cents per bushel.

yen into cents yields a range running from 0.05 to 1.25 cents per dollar. For each trader, his realized hedging cost in the currency futures market would be somewhere in this range. One needs to set the coefficient of absolute risk aversion, r, to cover a range of possible risk preferences. In past studies regarding offshore hedging, defining the value of r has been elusive. Kroner and Sultan (1993) and Gagnon et al. (1998) have used a value of 4.0, based on empirical studies for stock market volatility (e.g., Grossman and Shillers, 1981; Poterba and Summers, 1986) without any adjustment for offshore hedging. In this study, Lapan and Moschini (1994), Lence (1995) and Frechette (2000) are used as guides in selecting values of the coefficient. We adjusted the values of absolute risk aversion from these studies by considering data frequency, monetary unit, and import-based quantity. We select a value of absolute risk aversion at 0.2 per each cent. This value can be considered as a moderate risk aversion.6 The coefficient of risk aversion can be increased or decreased to cover other possible ranges of risk preference. Expanding this analysis to other risk aversions and broader cost ranges is straightforward. Higher hedge ratios in both futures markets are expected when the value of the risk aversion coefficient is increased and hedging costs are lowered, and vice versa. The results of average optimal hedge ratios are displayed in Table 3. The optimal hedge ratios change with different hedging costs. As hedging costs increase, optimal hedge ratios decrease. Although dramatic changes in the hedge ratios are not observed, the results suggest 6 Lapan and Moschini (1994) and Lence (1995) suggested that risk aversion ranges from 0 to 20 per year for a soybean farmer. To adjust the risk aversion coefficient for the case of international wheat traders, we considered the following three factors: (1) converting an annual value to a monthly value, (2) in cents, and (3) on an assumption that import-based quantity for the representative trader is at least one hundred times larger than an output-based quantity for a farmer. A final scaling factor of roughly 0.1 is produced by (1) dividing by 12, (2) dividing by 100, and (3) multiplying by 100. Thus, the range of r runs approximately from 0 to 2 and reasonable values for low, moderate, and high risk aversions are 0.02, 0.20, and 2.00, respectively.

H.J. Jin, W.W. Koo / Journal of International Money and Finance 25 (2006) 220e236

231

that both hedging costs are at play in changing optimal offshore hedging positions. When we consider that Japanese grain traders import 3 million metric tons from the United States each year, small changes in the optimal hedge ratio could result in large differences in the amount hedged and hedging performance. This suggests that the role of hedging costs cannot be ignored in the estimation of optimal offshore hedge ratios for Japan-based wheat importers. When we assume zero hedging costs in both futures markets, the wheat trader would have hedging positions composed of a 0.4880 commodity hedge ratio and a 0.5028 currency hedge ratio. Under the assumption of no hedging cost, hedge ratios are higher in the currency futures market than in the commodity futures market, implying that in recent years basis risk may be slightly lower in the currency market than in the wheat market. Assume that the realized currency hedging cost is fixed at 0.35 cents per dollar. Then, when we increase the commodity hedging cost from 0.0 to 2.5 cents per bushel, the optimal commodity hedge ratio decreases from 0.4927 to 0.4667 and the optimal currency hedge ratio increases from 0.4831 to 0.4919. Conversely, assume that the realized commodity hedging cost is fixed at 0.5. When we increase the currency hedging cost from 0.00 to 1.25, the optimal commodity hedge ratio rises from 0.4828 to 0.4996 and the optimal currency hedge ratio is lowered from 0.5046 to 0.4342. These results show negative own-price effects and positive cross-price effects on the hedging demand system. This confirms the substitute relationship between the two futures hedging methods under positive hedging costs in both markets and a non-zero covariance relationship between them. Hedging costs could actually differ for each offshore trader. A sophisticated offshore hedger may pay a relatively low hedging cost and thus his schedule of hedging costs will be somewhere in the higher left corner of Table 3. On the other hand, the costs for a novice may be in the lower right corner. Fig. 2 shows optimal commodity hedge ratios for corresponding own-costs. As the commodity hedging cost increases, the optimal commodity hedge ratio decreases, ceteris paribus. Since we set the hedging cost as the price of the hedging goods, the curve can be interpreted as a Marshallian-type demand curve. The demand curve is linear due to the

3

Commodity Hedging Costs

2.5

2

1.5

1

0.5

0 0.425

0.45

0.475

0.5

0.525

Optimal Commodity Hedge Ratios

Fig. 2. Demand curves for commodity hedging and cross-price effect. Notes: The arrow indicates the shift in the commodity hedging demand curve as we increase the hedging cost in the currency futures market. The linearity of the curves is due to the mean-variance approach.

232

H.J. Jin, W.W. Koo / Journal of International Money and Finance 25 (2006) 220e236

Table 4 Average optimal hedge ratios, h* and g* using CBOT and CME c

t 0.00

0.05

0.35

0.65

0.95

1.25

0.00

0.4625 0.4946

0.4632 0.4918

0.4672 0.4749

0.4713 0.4580

0.4753 0.4411

0.4793 0.4242

0.50

0.4573 0.4964

0.4580 0.4936

0.4620 0.4767

0.4661 0.4598

0.4701 0.4429

0.4741 0.4260

1.00

0.4521 0.4981

0.4528 0.4953

0.4568 0.4784

0.4609 0.4615

0.4649 0.4447

0.4689 0.4278

1.50

0.4469 0.4999

0.4476 0.4971

0.4516 0.4802

0.4556 0.4633

0.4597 0.4464

0.4637 0.4295

2.00

0.4417 0.5017

0.4424 0.4988

0.4464 0.4819

0.4505 0.4651

0.4545 0.4482

0.4585 0.4313

2.50

0.4365 0.5034

0.4371 0.5006

0.4412 0.4837

0.4452 0.4668

0.4493 0.4499

0.4533 0.4330

Notes: Formats of cells and labels are the same as those in Table 3.

mean-variance utility. It has a negative slope, suggesting that the willingness to hedge is lowered as the cost increases. Further, if we increase the currency hedging cost, the commodity hedging demand curve moves outward, implying cross-price effect through a substitute relationship between the two futures hedging. The five different curves represent commodity hedging demand curves when fixing currency hedging costs at five different levels, ranging from 0.05 to 1.25 cents per dollar. The demand curve for currency hedging was also drawn, and it has a similar shape as the commodity hedging demand curve. The currency demand curve also has a negative slope, but it is slightly more sensitive to its own-price changes than the commodity hedging demand curve. The figure is obtainable from the authors upon request. A noticeable result is that when we increase both hedging costs simultaneously from 0.0 to 2.5 in the commodity futures market and from 0.0 to 1.25 in the currency futures market, the optimal wheat hedge ratio decreases from 0.4880 to 0.4788, and the optimal currency hedge ratio decreases from 0.5028 to 0.4412, showing that the currency hedge ratio decreases more than the commodity hedge ratio does. The results can be explained by the fact that the currency hedging demand has a larger own-price elasticity than cross-price elasticity. In this study, the coefficient of absolute risk aversion, r, is set at 0.2 per cent. However, changing the value of risk aversion might result in substantial changes of the optimal hedge ratios in both markets. We proceeded further to expand the empirical analysis to other risk aversions. When value of the risk aversion coefficient increases, higher hedge ratios are obtained in both futures markets, and vice versa. Optimal hedge ratios were also estimated on the assumption that one of the markets could have an infinite hedging cost in order to check if there are kinks in the hedging demand curves. In this demand system, no kinks are found. As mentioned in Section 1, the trading volume of currency futures at the TIFFE is smaller compared to that at the CME. We further analyzed the hedging model by replacing currency futures prices (Rt) from the TIFFE with that from the CME for comparison of optimal hedging positions between the two cases. Currency futures contracts in the CME is for yen, while those in the TIFFE for U.S. dollar, suggesting that Japan-based wheat importers who want to use the CME futures contracts need different hedging positions from the position using the TIFFE

H.J. Jin, W.W. Koo / Journal of International Money and Finance 25 (2006) 220e236

233

etþ1 and StPt on the third term in futures contracts. Thus, one needs to reverse the signs of e Stþ1 P Eq. (2). The optimal hedge ratios were estimated through the same steps and results are presented in Table 4.7 Hedge ratios are slightly smaller in both the wheat and currency futures markets, compared to results in the case of using the TIFFE. Commodity futures hedge ratios decreased more than currency futures hedge ratios did. However, economic conclusions remain the same although we changed currency futures contract from the TIFFE to the CME. 4. Conclusions This study indicates that Japan-based wheat importers would employ futures contracts in the CBOT and/or TIFFE to avoid multiple risks from wheat price and exchange rate changes. Also, it shows that the role of hedging costs cannot be ignored in both futures markets. The demands for hedging increase when the hedging costs are reduced, confirming negative own-price effects. Both hedge ratios show positive cross-price effects, suggesting that the two futures hedging methods have a substitute relationship with a small marginal rate of substitution. The results have several implications. First, Japan-based wheat importers who face risks from changes in both wheat prices and exchange rates may be able to reduce the risks by hedging in the CBOT and/or TIFFE, although there is no wheat futures trading in Japan. The empirical results show that the prescriptive hedge ratios are slightly higher in the currency futures market than in the commodity futures market when no hedging costs are involved, suggesting that in recent years, basis risk might be smaller in the currency market than in the wheat market. Second, an opportunity to capitalize on reduced hedging costs could stimulate offshore grain importers to increase hedging demand and therefore increased import demand for the U.S. grains. Third, the substitution effect of the hedging demand implies that when the importer faces a high cost in the commodity futures market, his hedging position might give more weight to the currency futures than the commodity futures, and if the condition is reversed, the weight on his hedging positions will be changed. However, the marginal rate of substitution seems to be small. There are some limits to this study. Attention was not given to estimating pointed hedging costs for the trader. Instead, we set up a range for each hedging cost. Future research for deriving hedging costs for different groups of hedgers (by risk preference, by level of experience in futures trading, and by agents’ discount rate) would contribute more detailed analysis of the implications of hedging costs to optimal hedging positions. Another limit of this study is that other risk management tools are not considered; it is likely that offshore traders may use other risk management tools, such as commodity options or currency options, in addition to the two futures hedging methods. Future research including other risk management tools may contribute to more effective strategies for international traders.

Acknowledgments The author wishes to thank two anonymous reviewers and the editor of the Journal for their useful comments and insights. Any errors are the authors’ own. 7 Hedging costs for using the CME contracts may be slightly different from the costs in the TIFFE when we consider different contract sizes, locations, and hedging positions between the two markets. However, for the purpose of comparison with the case of using the TIFFE, the cost range for the CME futures hedging was set identical to the range for the TIFFE futures hedging.

H.J. Jin, W.W. Koo / Journal of International Money and Finance 25 (2006) 220e236

234

Appendix A. The optimal hedge ratios for commodity and currency futures 

h ¼

! n

1 eRÞV e t ðe e  CVt ðF eR; e e e Þ SPÞ SPÞ rðVt ðF 2

etþ1 eR; e e ee SPÞ Stþ1 P CVt ðF

ee ee eR; e e e e e ee e e ee e e þ rCVt ðP SPÞCV t ðFR; SPÞ  CVt ðFR; SPÞPt St þ cRt Vt ðSPÞ  Ftþ1 Rtþ1 Vt ðSPÞ o eR; e F eRÞV e t ðe e þ Ft Rt Vt ðe e  tPt CVt ðF eR; e e e SPÞ SPÞ SPÞ ðA1Þ  rCVt ðP and 

g ¼

1 eR; e e e 2  Vt ðF eRÞV e t ðe e SPÞ SPÞÞ rðCVt ðF

! n

etþ1 eR; e e e F etþ1 R SPÞ  CVt ðF

e e eR; e F eRÞCV e e e ee e e ee ee ee  rCVt ðP t ðFR; SPÞ þ CVt ðFR; SPÞFt Rt  tVt ðFRÞPt þ Stþ1 Ptþ1 Vt ðFRÞ o eR; e e e t ðF eRÞ e  Pt St Vt ðF eRÞ e þ cRt CVt ðF eR; e e e : SPÞV SPÞ ðA2Þ þ rCVt ðP

e SePÞ e and 2r½Vt ðFeRÞV e t ðPeRÞLCV e e e ee 2 Appendix B. Defining the signs of CVt ðFeR; t ðFR; SPÞ
eR; e e e produces the following equation: Decomposing CVt ðF SPÞ eR; e e e ¼ E½F eR; e e e  E½F eR
E½ e e e CVt ðF SPÞ SP
SP
;

ðB1Þ

e RÞ e þ E½F
E½ e R
e and E½e e comprises similar components. Substituting eR
e ¼ CVt ðF; SP
where E½F the relations into Eq. (B1) yields e e e e eR; e e e ¼ E½F eR ee e  ðCVt ðF; e RÞ e þ E½F
E½ e R
ÞðCV e CVt ðF SPÞ SP
t ðS; PÞ þ E½S
E½P
Þ;

ðB2Þ

e RÞ e and CVt ðe e are expected to be negative, based on the studies S; PÞ where the signs of CVt ðF; for the relationship between commodity prices and exchange rates (e.g., Lucas, 1980; Frankel, 1981; Chambers, 1984; Thompson and Bond, 1987). The absolute value of the covariance cane R
e and E½e e because the expected values of the products, not exceed the magnitude of E½F
E½ S
E½P
eR
e and E½e e are larger than or equal to zero. The sign of CVt ðF eR; e e e is therefore expected E½F SP
, SPÞ to be positive. Through the statistical relationship between covariance and correlation, we can define the eRÞV e t ðP eRÞ e  CVt ðF eR; e e e 2
. The covariance between F eR e and e e is expressed sign of 2r½Vt ðF SPÞ SP as follows: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiqffiffiffiffiffiffiffiffiffiffiffiffiffiffi eR; e e e ¼ rFR;SP Vt ðF eRÞ e Vt ðe e ; SPÞ SPÞ ðB3Þ CVt ðF eR e and e e The following relation holds unwhere rFR;SP is the correlation coefficient between F SP. less rFR;SP ¼ 1, which would lead to corner solutions. e e ee 2 eRÞV e t ðP eRÞ e  CVt ðF eR; e e e 2 ¼ CVt ðFR; SPÞ  CVt ðF eR; e e e 2 > 0: SPÞ SPÞ Vt ðF r2FR;SP

ðB4Þ

H.J. Jin, W.W. Koo / Journal of International Money and Finance 25 (2006) 220e236

235

However, a contemporaneous covariance between commodity prices and foreign exchange rates may not be negative due to the time lags between the time of contract and the time of delivery of grain. If we estimate the covariance using a time-varying conditional volatility model, we may see some positive signs of the covariances. Therefore, the sign of the covariance should be empirically checked.

Appendix C. Decomposition of variance and covariance of multi-variables The variances of two random variables are calculated using the following interaction terms: VðxyÞ ¼ E½x2
E½y2
þ CVðx2 ; y2 Þ þ fE½x
E½y
þ CVðx; yÞg2 ; where x and y are random variables with a bivariate normal distribution. The covariances of four random variables are calculated through the equation as follows: CVðxy; uvÞ ¼ E½x
E½u
CVðy; vÞ þ E½x
E½v
CVðy; uÞ þ E½y
E½u
CVðx; vÞ þ E½y
E½v
CVðx; uÞ þ CVðx; uÞCVðy; vÞ þ CVðx; vÞCVðy; uÞ; where x, y, u, and v are jointly distributed random variables. For details of the covariance decomposition under multivariate normality, see Haigh and Holt (2002).

References Chambers, R.G., 1984. Agricultural and financial market interdependence in the short run. American Journal of Agricultural Economics 66, 12e24. Dickey, D.A., Fuller, W., 1981. Likelihood ratio tests for autoregressive time series with a unit root. Econometrica 49, 1057e1072. Engle, R.F., Granger, C.W.J., 1987. Co-integration and error correction: representation, estimation, and testing. Econometrica 55, 251e276. Frankel, J.A., 1981. Flexible exchange rates, prices and the role of news: lessons from the 1970s. Journal of Political Economics 89, 665e705. Frechette, D.L., 2000. The demand for hedging and the value of hedging opportunities. American Journal of Agricultural Economics 82 (4), 897e907. Frechette, D.L., 2001. The demand for hedging with futures and options. The Journal of Futures Markets 21 (8), 693e712. Fung, H.G., Lai, G.C., 1991. Forward market and international trade. Southern Economic Journal 57, 982e992. Gagnon, L., Lypny, G.J., McCurdy, T.H., 1998. Hedging foreign currency portfolios. Journal of Empirical Finance 5, 197e220. Grossman, S.J., Shillers, R.J., 1981. The determinants of the variability of stock market prices. American Economic Review 71, 222e227. Haigh, M.S., Holt, M.T., 2000. Hedging multiple price uncertainty in international grain trade. American Journal of Agricultural Economics 82 (4), 881e896. Haigh, M.S., Holt, M.T., 2002. Hedging foreign currency, freight and commodity futures portfolios. The Journal of Futures Markets 22, 1205e1221. Hauser, R.J., Neff, D., 1993. Export/import risks at alternative stages of U.S. grain export trade. The Journal of Futures Markets 13, 579e595. Hirshleifer, D., 1988. Risk, futures pricing, and the organization of production in commodity markets. Journal of Political Economics 96, 1206e1220.

236

H.J. Jin, W.W. Koo / Journal of International Money and Finance 25 (2006) 220e236

Johansen, S., 1991. Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica 59, 1551e1580. Kroner, K.F., Sultan, J., 1993. Time-varying distributions and dynamic hedging with foreign currency futures. Journal of Financial and Quantitative Analysis 28 (4), 535e551. Lapan, H., Moschini, G., 1994. Futures hedging under price, basis, and production risk. American Journal of Agricultural Economics 76, 465e477. Lence, S.H., 1995. The economic value of minimum-variance hedges. American Journal of Agricultural Economics 77 (2), 353e364. Lence, S.H., 1996. Relaxing the assumptions of minimum-variance hedging. Journal of Agricultural and Resource Economics 21 (1), 39e55. Locke, P.R., Venkatesh, P.C., 1997. Futures market transaction costs. The Journal of Futures Markets 17 (2), 229e245. Lucas, R.F., 1980. Tariffs, nontraded goods and the optimal stabilization policy. American Economic Review 70, 611e625. Poterba, J., Summers, L., 1986. The persistence of volatility and stock market fluctuations. American Economic Review 76, 1142e1151. Simman, Y., 1993. What is the opportunity cost of mean-variance investment strategies? Management Science 39 (5), 578e587. Thompson, S.R., Bond, G.E., 1987. Offshore commodity hedging under floating exchange rates. American Journal of Agricultural Economics 69, 46e55. Wang, G.H.K., Yau, J., Baptiste, T., 1997. Trading volume and transaction costs in futures markets. The Journal of Futures Markets 17 (7), 757e780.