Exchange Rate Risk Sharing Contract with Risk-averse Firms

Transcription

1 03 International Conference on Avances in Social Science, Humanities, an anagement ASSH 03 Exchange ate isk Sharing Contract with isk-averse Firms LIU Yang, A Yong-kai, FU Hong School of anagement an Economics, University of Electronic Science an Technology of China, Chengu, Sichuan 60054, P.. China Abstract In this paper, we consier a global supply chain moel which inclues a retailer an a manufacturer from ifferent countries. We use a mean-variance moel to stuy how the foreign exchange transaction exposure affects this global supply chain. Furthermore, we esign a risk sharing contract to improve the expecte utilities of both the noe enterprises. Base on our analysis, we fin this risk sharing contract can realize the Pareto improvements in this global supply chain when the firms risk aversion coefficients satisfy some conitions. Keywors: risk-averse; mean-variance moel; exchange rate risk; global supply chain.. Introuction As a unique risk in the global supply chain, exchange rate risk is one of the most important risks in the global supply chain management []. Generally, exchange rate risk can be ivie into three types, which are the transaction exposure, the account exposure an the operation exposure. However, to the best of our knowlege, stuies on exchange rate risk in the global supply chain are relatively rare. The existing stuies on account exposure are mainly focus on firms themselves instea of the global supply chain []-[4]. The existing literatures has been concerne with operation exposure are mainly aime at the configuration of the global supply chain networks, but has neglecte ealing with the coorination of the global supply chain [5]-[0]. The existing stuies on transaction exposure in the global supply chain are even rarer. Arcelus stuies the newsvenor moel []. Besies, anuj an entzer buil a supply chain exchange rate risk frame inclues 5 steps []. Compare with above stuies, our innovations are mainly reflecte in the following aspects: We use a supply chain contract instea of financial metho or programming to manage the exchange rate risk. Our analysis is base on the 03. The authors - Publishe by Atlantis Press 500

2 expecte utility, while the existing researches are base on the expecte profits. This paper procees as follows: First we set out the assumptions an introuce the basic moels. After that, we stuy the Stackelberg game with risk-averse players. Finally, we esign a risk sharing contract to improve this global supply chain.. oel We consier a global supply chain inclues a retailer in country an a manufacturer in country. The manufacturer only supplies one kin of prouct. The retailer imports this prouct from the manufacturer at time T 0 an pays at time T. Here we use a two-stage game to analyze each player's ecision. The manufacturer is the leaer of this Stackelberg game, while the retailer is the follower. The eman function is q a bp, in which ab, 0,an the prouction cost c is constant. For simplicity's sake, let us suppose the exchange rate of country s currency relative to the country s currency is x. It means x units of country s currency equal to unit of country s currency. x is a ranom variable with probability ensity function f x on the support x [ A, B], in which 0 A B. B an A represent the upper an lower limits of x. The stanar eviations of x is an the variance of x is. Normally, foreign exchange transaction exposure means uncertain profits. As we assume above, the manufacturer is ominate in this global supply chain. In orer to iminish its transaction exposure, the manufacturer will require the retailer to pay in the currency of country. So the retailer will inevitably meet the foreign exchange transaction exposure. In orer to analyze the influence of foreign exchange transaction exposure, let us suppose both the retailer an the manufacturer are risk-averse players,an their risk aversion coefficients are an. Base on pervious stuies [3]-[5], we use the mean-variance moel to escribe their utilities. Their expecte utilities can be represente as: E U a bp p we Var E U a bp w c The optimal wholesale price of this Stackelberg Game is: a bc x w bx The optimal wholesale price is: 3 a bc x p 3 4b The optimal sale quantity is: a bc x q 4 4 An their optimal expecte profits are: 50

3 a bc E 6b a bc E 8 be 5 Theorem : When the variation of exchange rate is constant, there is a negative correlation between the expecte utilities of both firms an the risk aversion coefficient of the retailer. When the risk aversion coefficient of the retailer is constant, there is a negative correlation between the expecte utilities of both firms an the variation of exchange rate. Proof: In orer to facilitate the calculation, we assume k E. Then we have: contract that only require the retailer to pay part of the total settlement in the currency of country, an settle the rest part in the currency of country. In this situation, their expecte utilities can be represente as: E Uc a bp p E E w E Uc a bp E w c In which, E B f x x A x 7, stans for the expecte exchange rate in manufacturer s realization. Base on the efinition of E an E, it is easy to know that EE. An Var, x EU c a bck k 8 a b c k k 8bk 6 Base on Eq. 6, it is easy to know that the expecte utilities of both firms an k are negative correlate. Which means both the risk aversion coefficient of the retailer an the variation of foreign exchange are negative correlate with the expecte utilities of both firms. 3. isk sharing contract From Eq. 4 we know, consier the retailer s risk aversion preference will lea to a reuction in the sale quantity. Here we esign a risk sharing contract to increase the sale quantity, thus increasing the expecte utilities of both firms. Consier a 50 stans for the stanar eviations of x. In orer to facilitate the calculation, we assume that: y E E 8 z E Substituting Eq. 8 into Eq. 7, then we have: EU EU c c az bcy 6bz az bcy 8byz 9 Theorem : This risk sharing contract can lea to a Pareto improvement in the performance of this supply chain if E is satisfie. E Proof: Base on Eq. 5 an Eq. 9, after

4 the use of this risk sharing contract, the is a negative correlation between the incremental part of their expecte utilities expecte utilities of both firms an the risk can be represente as: aversion coefficient of the retailer when the variation of exchange rate is constant; az bcy bcz E bc z E y i 6bz z E y a z b c y E i 8 byz E Base on Eq. 4, it is easy to know the pre-conition for this eal is a bc E. At least one firm will have a negative utility if this conition cannot be satisfie. Hence, the Pareto improvement conition of the supply chain can be transforme into z E y 0. Substituting Eq. 8 into z E y, then we have: which focuse on the risk preferences in the global supply chain are even rarer. For z E y E E E E E 4. Conclusion 0 an a negative correlation between the expecte utilities of both firms an the variation of the exchange rate when the retailer s risk aversion coefficient is constant. With this risk sharing contract, Pareto improvements can be achieve when their risk aversion coefficients satisfy some conitions. So far, base on our knowlege, only a few existing stuies have investigate the foreign exchange transaction exposure in the global supply chain. An the stuies future research, there are some interesting topics. Examples inclue the coorination of the global supply chain, the risk Base on Eq., the improvement propensities of firms in the global supply conition of the supply chain can be chain. represente as: Acknowlegments: We woul like to acknowlege the financial support, from the Key Project of the Natural Sciences Founation NSF of china In this paper, we esign a risk sharing contract to improve the global supply eferences chain uner the foreign exchange [] Z. Liu, A. Nagurney, Supply Chain transaction exposure. By examining the Outsourcing uner Exchange ate influences of risk aversion preferences, we isk an Competition, Omega, 395, raw the following conclusions: There pp ,

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