VALIDATING A MODEL OF CURRENCY VALUATION Developments in Business Simulation and Experiential Learning, Volume 27, 2000 VALIDATING A MODEL OF CURRENCY VALUATION Precha Thavikulwat, Towson University ABSTRACT An empirical study of the foreign-holdings model of currency valuation is conducted with 116 undergraduates taking part in an interna- tional-business gaming simulation. Results are consistent with current understanding of ex- change rates. In the very long term, currency values of the model move in rough correspon- dence with monetary theory. In the short term, a high degree of uncertainty, with no repeating pattern, is evident. Uncertainty rose with the elapse of time between observations at the rate of about 1% per period. INTRODUCTION A computerized international business gaming simulation cannot be complete without incorpo- rating currency exchange rates. For this pur- pose, Thavikulwat (1999) has proposed a for- eign-holdings model that he proved to be self- limiting, volume-independent, and risk- compensating. The model values currencies relative to each other in direct proportion to the foreign holdings of each, that is, (1) where XA,B: Currency value of Nation A’s currency with respect to Nation B’s FA: Quantity of A’s money owned without en- cumbrance by foreigners FB: Quantity of B’s money owned without en- cumbrance by foreigners In turn, foreign holdings are determined as fol- lows: )()( )()( VSFIVBIA FLLAFDDACBIBF −−−+ +−++−= (2) where IB: Initial balance CB: Current account balance DA: Deposits placed abroad by our nationals in foreign currencies FD: Foreigner’s deposits in our nation’s cur- rency LA: Loans from abroad, denominated in for- eign currency FL: Foreigner’s loans, issued in our nation’s currency IA: Investments abroad VB: Value bought with investments abroad FI: Foreigner’s investments VS: Value sold for foreigner’s investments Thavikulwat’s analysis was entirely mathemati- cal. He presented no empirical data showing that the currency value resulting from the model was valid, in the sense that it would correctly guide student analysis in a business gaming simulation. B A BA F FX =, The problem of validating a model for student analysis of a theoretical construct is different from the problem of validating a model for ex- pert analysis of an everyday-world reality. In the latter case, the model can be said to be valid to the extent of its correspondence with its eve- ryday-world counterpart (Peters, Vissers, & Heijne, 1998; Stanislaw, 1986). In the former case, however, the theoretical construct that the model attempts to replicate is observable in the everyday world only under exacting conditions 132 Developments in Business Simulation and Experiential Learning, Volume 27, 2000 that rarely occur. Thus, one generally observes that heavy objects fall faster than lighter ones, except under controlled experimental condi- tions. Thavikulwat’s foreign holdings model attempts to replicate the pricing behavior of perfectly knowledgeable international bankers operating in a crime-free world of zero transaction costs and completely rational governments. That world is idealized and nonexistent. The ration- ale for modeling it is the same as that for developing laws of motion for bodies in a vacuum. The vacuum does not exist, but the forces that operate in a vacuum also operate without a vacuum. The difference is that under everyday-world conditions, their effects can be confounded by situational factors. Thus, Thavikulwat’s foreign holdings model cannot be validated against the behavior of the U.S. dollar, the German mark, or the Mexican peso of the everyday world, for these currencies operate in a messy world that the model does not attempt to replicate. The model must be validated against our understanding of the forces underlying exchange rate movements. Unfortunately, those who study currency ex- change rates have been notably unsuccessful in putting forth theories that have withstood the test of time. Thus, De Grauwe, Dewachter, and Embrechts (1993) noted the “situation where theories are developed to fit the exchange rate cycle in which we live, [so that] a different the- ory seems to be needed for every different cy- cle,” a sentiment echoed also by Copeland (1994). Even so, monetary theory is generally accepted as the standard for explaining currency ex- change rates over the very long run of 15 or more years. The central idea of this theory is that currency is simply a medium of exchange. Its value should therefore reflect the prices of the goods and services it can buy, and these prices vary directly with the supply of money and inversely with the quantity of goods and services that can be bought. Thus: b BA BA BA Y MaX      = , , , (3) where MA,B: Money supply of Nation A relative to Na- tion B YA,B: Quantity goods and services that can be bought in Nation A relative to those quan- tities in Nation B a, b: Relational parameters More recent theories take the position that cur- rency is not just a medium of exchange, but an asset that has a place in a balanced investment portfolio. Uncertainty is emphasized, as well as the possibility that exchange rates may be inher- ently unpredictable in the short-term even in the absence of chance. Although all of these recent theories remain unsettled, they do suggest char- acteristics that can be examined to assess the validity of models. The task in validating a model for a gaming simulation is to show that the results of the model are not aberrant when compared to what is known about the subject. For a model of cur- rency values, one needs to show that within the very long run interval of a gaming simulation, however that might be defined operationally in the particular implementation, the movement of currency values corresponds roughly with monetary theory. In this test, both extremes of an exact fit and a complete absence of fit would undermine validity. Moreover, one must show that within the short term currency values move in a manner consistent with a high degree of un- certainty, that no repeating pattern is evident, and that the uncertainty rises with the elapse of time between observations. The study reported here attempts to validate Thavikulwat’s foreign holdings model through those considerations. Data was obtain from a gaming simulation wherein participants were 133 Developments in Business Simulation and Experiential Learning, Volume 27, 2000 divided into three nations and allowed to trade, invest, and move short-term funds internation- ally, based on exchanged rates set computation- ally by the model. Although the behavior of the banking system in setting exchange rates was completely determined by the model, simulation participants were free to act in their own self- interest as they saw fit. Moreover, because par- ticipants were fully informed about the mathe- matics of the model, they were collectively in full control of its results. Thus, to the extent the model is valid, it is valid because it fits the hu- man nature of the participants, and not because of the mathematics alone. METHODOLOGY Participants Participants were 116 undergraduates enrolled in three sections of an international-business course at a comprehensive university. Each sec- tion constituted a nation. The nations were named North, South, and East, with participant populations of 40, 37, and 39, respectively. Gaming Simulation The gaming simulation, GEO III, was computer- assisted, as defined by Crookall, Martin, Saun- ders, and Coote (1986). It scored participants on a consumption-based scheme (Thavikulwat, 1990). Thus, each individual received a periodic income from his or her government, supple- mented with salaries and dividends from com- panies and capital gains from trading stocks, and each was scored based on the points re- ceived when the individual expended monies to purchase products produced by companies that the participants themselves founded. In all, the participants founded 161 companies, of which 88 had become insolvent by the conclusion of the semester-long exercise. Time in the gaming simulation was activity driven, advancing automatically whenever a preset count of participants had gained access to the computer system. Over the course of the semester, it advanced through 1,042 periods over 13 active weeks. Decisions were entered asynchronously, and could be executed when- ever the participants got access to the local area network on which the simulation was installed. Access was usually available some time every day of the weeks. Model Thavikulwat’s foreign-holdings model was used to determine currency values. The currency ex- change rates themselves were adjustably-pegged with an incremental parameter of 0.2 in accor- dance with the geometrically-centered method suggested by Thavikulwat. Thus, exchanges rates moved in discontinuous steps by a factor of 1.2 (i.e., 1.2-n, …, 1.2-2, 1.2-1, 1, 1.2, 1.22, …, 1.2n). Moreover, foreign-holdings computation was simplified by assuming that the value of every investment was identical to the payment made to acquire it. Thus, Equation 2 was simpli- fied to the following: )()( FLLAFDDACBIBF +−++−= (4) Data Data files of the gaming simulation were ar- chived every day that the gaming simulation was active. Because time in the gaming simula- tion was activity driven, the number of periods between archived data ranged from 0 to 69. Eliminating data of the early periods when ac- tivity was minimal and keeping only the most recent data set of those from the same period, 66 data sets were selected for this study. The mean number of periods between data sets was 15.8 (SD = 19.9). Besides foreign holdings, the data included a measure of each nation’s money supply (M1), gross domestic income (GDP), and consumer price index (CPI). M1 was computed by adding together the cash balances of individuals and 134 Developments in Business Simulation and Experiential Learning, Volume 27, 2000 companies. It was a snapshot of the simulation’s economy at the time each data set was archived. The CPI was an average of consumer payments for products on a payment-per-point basis. It and the GDP were aggregated from the begin- ning of the exercise to the current period of each data set. Results The full monetary model of Equation 3 requires both M and Y on its right-hand side. For Y, economists commonly use the annual GDP of the preceding year, adjusted for inflation by a price index taken over the same interval. With that approach, the inflation-adjusted GDP is a proxy for the desired measure, which is the quantity of goods and services that can be bought with M. The proxy is convenient, con- sidering especially the impossibility of directly measuring things that can be bought. Neverthe- less, it introduces error that may be worse than simply dropping Y from the formulation, equivalent to assuming that relative changes in Y are negligible when compared to relative changes in M. To test the fit of monetary theory to the model- derived currency values of the gaming simula- tion, Equation 3 was transformed logarithmi- cally as follows: (5) Data from the gaming simulation were then fit- ted to the model by regression in two trials. Trial 1 included Y adjusted for inflation using the CPI; Trial 2 omitted Y. The results are pre- sented in Table 1, for North Nation with respect to South Nation, and Table 2, for North Nation with respect to East Nation. As Tables 1 and 2 show, the full monetary model, with Y, is not a statistically significant fit for the currency values of the gaming simulation in both cases, but the simplified model, exclud- ing Y, is a statistically significant fit in the case of North vs. South, but not in the case of North vs. East. Nevertheless, the sign of the b parame- ter is positive in all instances, as required by monetary theory. Thus, the data may be said to correspond roughly with monetary theory. As for the uncertainty and possible pattern in the movements of currency values, Figure 1 plots currency value and money supply for North Nation with respect to South Nation over the course of the exercise, and Figure 2 plots the corresponding values for North Nation with re- spect to East Nation over the same interval. Consistent with theory, the plots evidence a high degree of uncertainty, with no obvious re- peating pattern to currency values. A measure of the increase in uncertainty that rises with the elapse of time between observations can be ob- tained by fitting the data to the following equa- tion: ( ) ( ) b ntt ntt an XX XX = − − ,min ,max (6) where Xt, Xt-n: Currency values observed at times t and t-n, respectively n: Number of periods between two observa- tions of currency values a, b: Relational parameters ( ) ( )      += BA BA BA Y MbaX , , , lnlnln Transforming Equation 6 logarithmically results in: ( ) ( ) ( ) ( )nbaXX ntt lnlnlnln +=− − (7) TABLE 1 REGRESSION OF NORTH NATION WITH RE- SPECT TO SOUTH NATION Trial ln(a) b r2 1 (with Y) 0.244 (t = 1.27) 0.211 (t = 0.89) 0.01 2 (without Y) -0.206 (t = -1.91) 0.681*** (t = 4.00) 0.20 ***p < .001 135 Developments in Business Simulation and Experiential Learning, Volume 27, 2000 TABLE 2 REGRESSION OF NORTH NATION WITH RESPECT TO EAST NATION Trial ln(a) b r2 1 (with Y) 0.546*** (t = 4.70) 0.199 (t = 1.39) 0.03 2 (without Y) 0.416** (t = 3.30) 0.309 (t = 1.67) 0.04 **p < .01, ***p < .001 FIGURE 1 PLOT OF NORTH NATION’S CURRENCY VALUE AND MONEY SUPPLY RELA- TIVE TO SOUTH’S FIGURE 2 PLOT OF NORTH NATION’S CURRENCY VALUE AND MONEY SUPPLY RELA- TIVE TO EAST’S Fitting Equation 7 to the data by regression gave rise to the results of Table 3. The fit is remarka- bly strong. Considering that the b parameter is within one standard error of 1.0 (SE = 0.125 for North vs. South; SE = 0.156 for North vs. East) and that the regression estimated value of a av- erages to 0.01 (e-4.522 = 0.0109 and e-4.731 = 0.0088), the data may be said to be consistent with the following result: ( ) ( ) n XX XX ntt ntt 01.0 ,min ,max = − − (8) TABLE 3 REGRESSION OF CHANGES IN CURRENCY VALUES OVER TIME 0 1 2 3 4 5 6 7 8 9 0 200 400 600 800 1000 1200 Period R at io o f N or th to S ou th Currency Value Money Supply Series ln(a) b r2 North vs. South -4.522*** (t = -15.53) 0.882*** (t = 7.03) 0.44 North vs. East -4.731*** (t = -13.04) 0.960*** (t = 6.14) 0.37 ***p < .001 Thus, currency values in the gaming simulation diverge at the rate of about 1% per period. This is a measure of the time-dependent risk of hold- ing foreign currencies in the gaming simulation. 0 2 4 6 8 10 12 14 0 200 400 600 800 1000 1200 Period R at io o f N or th to E as t Currency Value Money Supply 136 Developments in Business Simulation and Experiential Learning, Volume 27, 2000 CONCLUSION This study shows that a simplified version of the foreign holdings model performed in a manner consistent what is know about currency ex- change rates. The data roughly fits monetary theory, as would be expected from a sufficiently valid model. Currency values move in a manner consistent with a high degree of uncertainty, with no evident repeating pattern, and with an uncertainty that increased at the approximate rate of 1% per period. The degree to which uncertainty increases with elapsed time depends upon the initial-balance value of the model. Thavikulwat (1999) did not suggest an initial-balance value. By the logic of the mathematics, however, larger initial-balance values must give rise to lower time-dependent risks of holding foreign currencies, but addi- tional studies will be needed to determine the precise relationship. When understanding of a subject is weak, as it clearly is in the subject of currency valuation, any model of that subject area is likely to be somewhat incorrect. Thus, Thavikulwat’s for- eign-holdings model is probably incorrect in some degree. It may have few applications in everyday-world settings. Applied to gaming simulation, however, this study shows that any incorrectness it may have is not evident. The consideration that participants may be forgiving even if an algorithm should be incorrect in some way, as Wolfe and Jackson (1989) has demon- strated, adds another level of comfort to its use. REFERENCES Copeland, L. (1994). Exchange Rates and International Finance, 2nd Ed. Workingham, England: Addison-Wesley. Crookall, D., Martin, A., Saunders, D., & Coote, A. (1986). Human and computer involvement in simulation. Simulation & Games, 17, 345- 375. De Grauwe, P., Dewachter, H., & Embrechts, M. (1993). Exchange Rate Theory. Oxford, U.K.: Blackwell. GEO III: An international-business gaming simulation. Thavikulwat, P. (1997-1999). Towson, MD: Towson University (Dept. of Management, Towson University, Towson, MD 21252, USA). Peters, V., Vissers, G., & Heijne, G. (1998). The validity of games. Simulation & Gaming: An International Journal, 29, 20-30. Stanislaw, H. (1986). Tests of computer simulation validity. Simulation & Games: An International Journal, 17, 173-191. Thavikulwat, P. (1990). Consumption as the objective in -computer-scored total enterprise simulations. Developments in Business Simulation & Experiential Exercises, 17, 167- 169. Thavikulwat, P. (1999). A model of currency exchange rates. Developments in Business Simulation and Experiential Learning, 26, 200-208. Wolfe, J. A., & Jackson, R. (1989). An investigation of the need for algorithmic validity. Simulation & Games, 20, 272-291. 137 Table of Contents Volume 27, 2000 Internet International: A Simulation Exercise for Understanding Technological Innovation and customer Service In a Rapidly Growing Internet Server Company Simulations and Learning: Dialog and Directions Endnote Activity: A Tool for Integration of Course Content and Communication Skill Practice Incorporating Video as a Teaching Strategy in Interpersonal Communication Vision Quest: An Alternative Approach to Industry Analysis for MBA Courses in Strategic Strategic Management: An Evaluation of the Use of Three Learning Methods Trainer, Mentor, Educator: What Role for the College Business Instructor in the Next Century? Using the Internet and Shareware to Facilitate Computer Simulation in Distance Learning Classes Visual Modeling of Business Simulations Teaching about Information with Management Games A Self-Evaluation Based on the Discussion and Decision in Experts' Business Gaming The Restaurant Game Using Journals to Enhance Computer Simulation Based Learning Exercises to Facilitate Better Student Writing in the Undergraduate Strategy Class Identifying, Resolving, and Managing Common Ethical Dilemmas in the Workplace: An Experiential Approach Integrating the Digital Revolution into the Classroom The Wheel of Learning: An Integrative Business Curriculum Experiment The Changing Nature of Simulation Research: A Brief ABSEL History Perspectives on Simulation & Gaming's Review Process Experiential Learning Across Disciplines: Mixing International Business and Accounting Simulating Governmental Effects on Economic Development Internationalizing the Introduction to Business Course Using an International Text and Domestic Simulation with a Twist Using Stock Value as the Performance Measure in a Business Simulation Game Introducing Cross-Elasticities in Demand Algorithms Validating a Model of Currency Valuation An Exercise for Exploring the Relationship between Jungian Psychological Types and Organizational Politics Exercise: Preparing Financial Reports Using the Group Categorizing Technique Effect of Trust and Cultural Beliefs on Negotiation Processes: Data from an Experiential Role Play Experiential Learning Gets Stamp of Approval From the Boyer Commission Talent Search 2000 - An Experiential Activity to Help Strengthen Skills in Employee Recruitment and Selection Clemson University's Collaborative Learning Environment Initial Data on a Test Bank Assessing Total Enterprise Simulation Learning Changing the Assessment Paradigm: Using Student Portfolios To Assess Learning from Simulations How We Learn and Why We Don't: The Cognitive Profile Model: A Workshop in Teaching to Reach Your Students Knowing Thyself: A Portfolio Approach to Student Self-Assessment Collaborative Learning and Web-Based Instruction in a Cognitive Apprenticeship Model Teamwork Attributes in a Classroom Simulation Virtual Teams: Meeting the Next Challenge for Experiential Education New Age Learning: Nuance or Nonsense Developing Charisma: An Experiential Exercise in Leadership Problems and Solutions in Going Web-based with an Agribusiness Simulation Creating a Comprehensive Web-Enhanced Classroom Your Class is in Session, Now What? The Challenges of Teaching On-line An Application of Process Control Charts for Attributes as a Form of Classroom Assessment for Experiential Learning Work Goals and Life Aspirations: Do You Have What it Takes to be an Entrepreneur An Exercise to Develop Initiative: Possible Dream? The Ball Point Pen Assembly Company Management Game Review System Development Total Enterprise Simulations and Optimizing the Decision Set: Assessing Student Learning Across Decision Periods Facilitating Learning in the New Millennium with the Complete Online Decision Entry, System (CODES) The Marketing Management Experience The Right Venue for Your Simulation One More Time: Overall Dominance in Total Enterprise Simulation Performance A Profile of ABSEL Conference Attendees Learning Readiness: An Underappreciated Yet Vital Dimension in Experiential Learning Active Learning in a Professional Undergraduate Curriculum The Problem Is - They Think Differently! Cultures Integration in Mergers and Acquisitions: Putting Managers Together in a Business Simulation The Global Business Game: A Strategic Management and International Business Simulation