Play it Forward - The Design and Development of a Forward Contract Simulation Page 92 - Developments in Business Simulation and Experiential Learning, volume 39, 2012 ABSTRACT A game simulating commodity market prices from the per- spective of an energy firm selling propane to end users. This paper describes the expectation of the sponsoring firm, includes a brief literature review and identifies 2 pop- ular commodity futures models. A methodolgy is selected and the model is verified and tested. Screen shots of the finished simulation are displayed. The paper concludes with expected results, initial reactions of the players, facili- tator, and the sponser. Lastly, the author suggests possible research extensions for this INTRODUCTION An energy trading firm contacted me in March 2011 and inquired if I could make a simulation / training game for their professional development program that explained the mechanics and business benefits of using future Pro- pane contracts to hedge the riskiness of their business given the volatility of commodity prices. An additional benefit to the client is the possibility of developing a trading rule that produces an expected trading profit in addition to reducing risk. They had contracted me in 2010 to build a simula- tion / training game to better understand the financial im- pact of managing their product mix, production capacity and distribution options. Being familiar with the firm’s operations and management philosophy plus having access to financial data and their management is crucial in devel- oping an effective simulation. The firm enters into a forward contract with a producer at a current price (Fo) for delivery of an asset in the future that it plans to use or sell. The futures price is derivative of the expected future spot price. The payoff to the buyer in a future contract is the difference between the future spot price (St) and the agreed upon contract price. The option to enter the contract at a price believed to be favorable cur- rently reduces risk by identifying future cost. The hedge being modeled is not intended to be a riskless hedge at the request of the client. In accepting the contract to build a simulation, I identified the following expectations: Develop a simulation model that employs methods that represent actual price paths for the commodity. Develop a tool that allows a player to experiment with hedging in a safe environment and discover the importance of forecasting and understand that hedging strategies and use of derivatives in gen- eral can both reduce risk (volatility) and improve profitability. Develop a decision rule that if employed is more likely than not to yield higher profits (a positive ex- pected value. This tool is primarily a teaching and learning instru- ment and it is not my intention to develop new theory or create an optimal closed from solution. BRIEF LITERATURE REVIEW Prior to beginning the construction of this simulation I explored and drew on several excellent published sources. My search encompassed three themes; the practice of using derivatives as a risk management strategy, how can com- modity price paths be modeled, and the use of simulation as a teaching, learning, and perhaps as a decision tool. Ben- hamou & Mamalis (2002) identified three primary reasons that a firm uses derivatives. They are to hedge against price fluctuations, speculation and arbitrage. Peterson & Thiaga- rajan (2000) compared two firms using different approach- es to managing risk. One, American Barrick aggressively used derivatives to manage risk and the second, Homestake Mining did not. They found the volatility of earnings and the return to equity falls by 2%, the probability of financial distress lessens with the use of derivatives and there is an increase in expected profits. Non hedging firms are more likely to experience unexpected cash flow fluctuations. Hedging firms are able to remain more competitive than non hedging firms in they are able to maintain more stable prices for their customers than firms that are required to pass on input price increases. Schwartz in 1997 published a much cited paper in the Journal of Finance. He presented three models of commod- ity price behavior that he tested against a set of actively traded commodities. All models incorporate the Wiener process for incorporating the Brownian motion attribute of price paths through time. A single factor model was based on the log of the spot price following a mean reverting pro- cess and including a speed of adjustment factor specified as PLAY IT FORWARD – THE DESIGN AND DEVELOPMENT OF A FORWARD CONTRACT SIMULATION Craig Miller Normandale Community College craig.miller@normandale.edu mailto:craig.miller@normandale.edu Page 93 - Developments in Business Simulation and Experiential Learning, volume 39, 2012 k. A two factor model included a convenience yield factor and a third model added interest rates. He found that over a long term (in excess of two years) models two and three demonstrated less error and more accurately captures actual volatility with model one showing less long term volatility. Over short periods of time, such as the six month window the simulation covers, it is not clear that any one of the three models is dominant. Gamerman (1997) defined simulation as “a treatment of a real world problem through reproduction in a computer environment.” Generally, it will be a smaller scale replica of the system under study. He argued that it is an appropri- ate tool when some components of the system are subject to random fluctuation that can only be described by proba- bility distributions. A Markov Chain (Markov chains were introduced by Andre Andreevich Markov. Markov was led to develop Markov chains as a natural extension of se- quences of independent random variables) process is an effective addition to a simulation model when successive results depend on all their predecessors only through their immediate predecessors as in a price path with a random- ness term such as a Wiener Process. M. Miller (2001) cited simulation as a beneficial risk management tool enabled by computer technology in his paper surveying financial innovations since 1960’s. Both Hull and Benninga recognize that Monte Carlo Simulation (a simulation of a stochastic process sampling random out- comes) can be used to price derivatives though Benninga does assert that simulation is really an experimental tech- nique and in general should be avoided if another closed form solution is available. Miller and Nentl (2003) defined simulation as a replica or model designed to represent an actual or theoretical real- ity. They reported simulation use in business education and training increases involvement and motivation and results in deeper comprehension, better retention, and students are more self- directed. Cheng (2009) created and tested a simulation designed to teach option trading practices to novices. They modeled commodity prices as a mean reverting process (converging on marginal cost of production) and using a Wiener Process simulating movement. Cheng found his subjects did poorly on their initial trials but improved significantly with prac- tice and repetition. He concluded that simulation is an ef- fective training tool if there is an opportunity to experiment with alternative scenarios, play multiple times, and a knowledgeable facilitator debriefs the players by helping them to understand and analyze results. METHODOLOGY Price data was collected over a 20 year period (Appendix 1) and to mirror the simulation period, from November 2009 to October 2010 (Appendix 2). It was the latter data set that was used to calculate the estimated mean and standard deviation. Three models of commodity price behavior were con- sidered. A standard one factor model found in Hull, and a one and two factor model presented and studied by Schwartz. Upon reflection the Schwartz two factor model was abandoned for this project and for the time being. This choice will be addressed in the paper’s closing comments. The two models selected for testing are presented in Figure 1 below. The models are developed using math techniques that are expected to be beyond the technical capabilities of play- ers / traders and likely a workshop facilitator (and possibly readers of this paper). My expectation is users of this game will accept the model embedded under the covers to be externally valid. This paper does present the math for read- ers interested in evaluating the model’s fidelity. Professors teaching Finance at the graduate level will recognize these models to be variations of the Black Sholes Options Pricing Model – a standard valuation technique for several decades now and centerpiece of a Nobel Prize award. The models are more similar than different. Model 2 includes a constant k that reflects the magnitude of the speed of adjustment of the log of the spot price reversion to the mean. The value 1.5 was selected for k based on per- sonal experimentation using the empirical range in the Schwartz data set. Model 2 also assumes a lognormal dis- tribution. For both models 1 and 2 were derived from the Figure 1 Models of commodity price behavior Model 1: St = ((– r) * St-1 * dt) + (* St-1 * dz)) + St-1 Notation: St = Predicted spot price = .1619 r = opportunity cost of capital = .06 drift = .10219 St-1 = Predicted spot price dt = time increment  = daily  * 252.5 = .28 dz = normsinv (rand ()) * dt.5 Model 2: St = (k * ( – ( 2 / 2k)) +  * dt.5 * dz)) + St-1 Notation: St = Predicted spot price k = 1.5  = .1619  = daily  * 252.5 = .28 drift = .10339 dt = time increment dz = normsinv (rand ()) * dt.5 Page 94 - Developments in Business Simulation and Experiential Learning, volume 39, 2012 November 2009 – October 2010 data set presented as Ap- pendix 2. Both models are stochastic (probability driven rather than deterministic) Markov Process incorporating Wiener’s mathematical representation of Brownian motion. Both models also include an Ito process (dx = *dt + *dz) in which variable  (the drift) and  (the variance) are func- tions of underlying data – in this case historical propane prices. It is assumed the drift rate is constant over the mod- el period. The uncertainty however increases over time as a square root function of time. Each model will be tested over a three month period (November 2010 to January 2011). The time period of 252 days is a common interval when evaluating options as it covers a complete year of variance that considers systemat- ic cycles. Appendix 3 lists the actual spot price each day, the predicted spot price, and the error term. The Appendix also includes a graph of three predicted and actual prices over the 3 month period and a summary statistic – the Mean Absolute Deviation. METHODOLOGY – TEST OF MODEL Appendix 3 contains for both model 1 and model 2 a summary of the actual spot price during the modeling peri- od along with the prediction and error. Each table con- cludes with summary statistics for actual mean, predicted mean, their respective sample standard deviations, and a mean average deviation. Model 2 appears to be a better predictor using this short term data set. While the 90 day mean was price was $1.298, the average price predicted by model 1’s price path is only $1.175 compared to model 2’s $1.293. Models 2’s mean average deviation was also closer to 0 (.0047 vs. .123) which is the expected MAD for an unbiased model. A useful and often insightful evaluation of a model is a visual inspection. Again, turning to Appendix 3 a plot of predicted vs. actual spot prices over the model period shows model 2 tracks the price path better than model 1. The scatter plots of error terms appear to indicate a system bias for model 1 whereas model 2 seems to be closer to the ideal pattern of randomness. Based on the summary statistics cited above and the derived scatter plots of model 1 and 2’s respective perfor- mance, model 2 was selected as the engine for the simula- tion. THE SIMULATION – OVERVIEW The Story: A simulated firm, “PropaneCo” is a distributer of pro- pane fuel to residential and commercial markets. In 6 months they will need to take delivery of enough of the commodity to meet customer demand. They face the option of buying the propane as needed on the spot market, enter- ing into a forward contract to purchase the commodity, or some combination of both. Data Sources: Using historical demand, price, and interest rate data a probability distribution of demand will be developed with a mean of 1,000,000 gallons and variability modeled as a function of the actual variance. Spot and forward prices over the course of the simulation will be determined using a Monte Carlo process derived from actual price data over the past 1 year or 252 trading days. Spot prices and daily variability are displayed in Figure 2. Decision Points: At t-6 (6 months before delivery) the players will make a demand estimate. Figure 2 Spot prices and daily variability Page 95 - Developments in Business Simulation and Experiential Learning, volume 39, 2012 At t-6 the players will have an opportunity to accept or not accept a forward contract for X gallons at a price to be determined using a Monte Carlo simu- lated future price. Their decisions will range from contracting for enough to cover expected demand to rejecting the offer. If rejected, they can make a contract at t-5, t-4, or settle at t0 at the spot price. Of course, the players will not know at this point what the forward price will be at t-5, t-4, or the spot price at t0 At t-5, they face the same choice as above – but only can defer to period t-4. At t-4, they again have a similar decision, but if the forward contract is not accepted, they will need to buy at the spot price at t0. Results: At the delivery date (t0), a simulated sales price and “actual” demand will be generated – again using a Monte Carlo process as derived from historical data. The product of “actual” price times “actual” demand will be used to determine sales revenue. Cost of Goods Sold will be calculated using the input prices determined by the con- tracting decisions described above. If demand exceeds con- tracted supply at t0 the excess will be filled at the t0 spot price. Should demand be less than supply, the firm will accept delivery and incur storage and holding costs. Expected Outcomes: The practice and consequences of accurate forecasting will be reinforced. Players will better understand the mechanics of a for- ward contract. Using forward contracts (or other derivative instru- ments for that matter) need not be a speculative activity but an effective tool for managing risk. Players will experience the sensitivity of demand, pricing, and input costs on the firm’s financial results. THE SIMULATION – DETAILS The look and feel and navigation for the simulation named Play it Forward can be found as Appendix 5. To better understand this section my recommendation is for the reader to view Appendix 5, view the PowerPoint named Play it Forward, or better yet, experiment with the actual simulation file Play it Forward. (available from the author at craig.miller@normandale.edu) The simulation is based on an Excel platform and includes Visual Basic for Appli- cations Code. For each decision period the player checks the spot price St and the simulation will generate a price using model 2 (presented in the methodology section). Be- cause this model is a stochastic process, St will be unknown and vary as a function of a normal distribution represented by dz or N * t^.5. The assumed forward price, F0, will be computed as Ste r t and will converge to the spot price as time approaches the contract settlement date. The assigned value of r is 6% based on the reported short term borrowing rate of the client firm. In addition, the transaction cost of the forward contract was reported by the client firm as low – estimated at about 2 cents per gallon. The expected value of a spot price at t0 (six months hence) equals the current spot price plus the expected drift over the contract period. The annual drift using model 2 has been calculated to be .10339 which makes the expected spot price at t0 = (1 + (.10339/2) = $1.3672. From this in- formation, I am recommending hedging with a forward contract if Fot < $1.3672. Using the optimal hedge formula from financial theory (H* = (actual / predict) * ), the rec- ommended hedge ratio is .82 (from (.0475 / .0473) * .81.) The standard deviations and correlation coefficient for model 2 data is derived and presented in Appendix 3. After the player has made their hedging decisions at t-6, t-5, and t-4, they game concludes by clicking the results but- ton. A spot price for t0 is derived from the simulation mod- el as well as actual demand. Demand is derived in the sim- ulation using Excel’s normsinv (rand ()) function with  and  set to 1,000,000 and 200,000 respectively. These parameters were estimated by management of the client firm based on historical experience and future expectations. Contribution margin is the sales revenue (final price is based on a 50 cent markup, per client direction) less cost of goods sold using a First in First out inventory flow model. Any inventory deficits will be remedied by purchasing at the T0 spot price and excess inventory will be carried. For this game client management requested no holding costs be assessed as they would be negligible. Finally the game compares the contribution income based on player decisions and that of an unhedged play. My hypothesis is if a player follows the suggested decision rule using the recommended hedge ratio of .82, more often than not they will experience a greater contribution margin. This hypothesis was tested and results are reported in Appendix 4. Based on 60 plays, the average gain for a hedging strategy was $40,049. This difference was signifi- cant at a t score of 3.67. In addition, the proportion of “gains” vs. “losses” was 75% and was significant at a t score of 4.47. RESULTS, CONCLUSIONS, AND REFLECTIONS Generally, I am pleased with the project and feel the time invested will be valuable to my client and the learning I experienced is of great value to me. It is my belief that over repeated play (as is the pedagogy of a teaching and learning game/simulation) players will discover that com- bining a hedging strategy employing decision rules such as those advocated here will be profitable more often than not. mailto:craig.miller@normandale.edu Page 96 - Developments in Business Simulation and Experiential Learning, volume 39, 2012 In addition, I feel this project will satisfy the objectives presented earlier: The practice and consequences of accurate forecasting will be reinforced. Players will better understand the mechanics of a for- ward contract. Using forward contracts (or other derivative instru- ments for that matter) need not be a speculative activity but an effective tool for managing risk. Players will experience the sensitivity of demand, pricing, and input costs on the firm’s financial results. In my future work I plan to examine, better under- stand, test, and perhaps deploy three other models. One is the Schwartz two-factor model incorporating the conven- ience yield. A second model that I read about that I find intriguing is a Gabillon Markovian two factor model using two Wiener Processes; the first a short term mean reversion factor and the second is a slower long term mean reversion factor. A third area of exploration is the family of jump- diffusion models first introduced by Merton and now being more rigorously developed in response to the extreme price behavior experienced recently in some of the security mar- kets. As I understand it, this addition of low probability extreme events suits the types of simulations I create. With the elimination time constraints and the limits of my current technical abilities (I plan to continue working on my math), I expect to be able to able to assess and pro- duce more sophisticated models. A big step is to know what you don’t know. The tool was employed several times in a workshop setting during the summer of 2011. Comments by both the facitiator, the participants, and sponsor were positive. To me, that suggests the game was fun and made a cplocated environment more understandable. The players that used the suggested trading rules did aceive results similar to the expected values presented earlier. The actual data was not collected, the sample size was small (approximately 30 players), andthu the extent of followup analysis is limited. An opportunity does exist to create a better controlled de- sign making a richer statisitical analysis possible. REFERENCES Benhamou, E., & Mamalis, G. (2002). Commodity Markets (overview. White Paper published by Goldman Sachs, Deutsche Bank and Elf Trading SA, #, 1-20. Benninga, S. (2008). Financial Modeling (Third ed.). Cam- bridge, MA: MIT Press. Cheng, S., & Lim, Y. P. (2009). An Agent-Based Com- modity Trading Simulation. Proceedings of the Twenty -First Innovative Applications of Artificial Intelligence Conference (2009), 2009, 72-78. Gamerman, D. (1997). Markov Chain Monte Carlo Sto- chastic Simulation for Baysian Inference. Boca Raton, FL: Chapman & Hall. (Original work published 1997) Hull, J. (2009). Weiner Processes and Ito's Lemma. Op- tions, Futures and Other Derivatives (Seventh ed., pp. 259-272). Upper Saddle River, NJ: Pearson. Law, S. (2009). ON THE MODELLING, DESIGN AND. Doctoral Thesis, #, 22-73. Miller, M. (2001). Financial Innovation: Achievments and Prospects. The New Corporate Finance - where theory meets practice (pp. 385-392). Burr Ridge, IL: McGraw -Hill Irwin. Nentl, N., & Miller, C. (2002). Learning by Playing: Teaching Business Learners Using Computer Simula- tion. Proceedings: Conference on Emerging Issues in Business and Technology, #, 1-8. Peterson, M., & Thiagarajan, R. (2000). Risk Measurement and Hedging: with and without derivatives. Financial Management, Winter 2000, 5-30. Schwartz, E. (1997). Stochastic Behavior of Commodity Prices: Implications for Valuation and Pricing. The Journal of Finance, 52(3), 923-973. Weekly Indiana Propane Wholesale/Resale Price (Dollars per Gallon). (n.d.). infoctr@eia.doe.gov. Retrieved March 21, 2011, from http://tonto.eia.gov/dnav/pet/ hist/LeafHandler.ashx? n=PET&s=W_EPLLPA_PWR_SIN_DPG Page 97 - Developments in Business Simulation and Experiential Learning, volume 39, 2012 Appendix 1 Wholesale Prices – 20 years Page 98 - Developments in Business Simulation and Experiential Learning, volume 39, 2012 Appendix 2 Spot Prices – November 2009 – October 2010 Page 99 - Developments in Business Simulation and Experiential Learning, volume 39, 2012 Data Spot Price Data Spot Price 2-Nov 1.0540 1-Mar 1.1790 3-Nov 1.0550 2-Mar 1.1740 4-Nov 1.0800 3-Mar 1.1950 5-Nov 1.0830 4-Mar 1.1790 6-Nov 1.0590 5-Mar 1.1970 9-Nov 1.0800 8-Mar 1.1800 10-Nov 1.0690 9-Mar 1.1650 11-Nov 1.0630 10-Mar 1.1530 12-Nov 1.0630 11-Mar 1.1330 13-Nov 1.0330 12-Mar 1.0880 16-Nov 1.0530 15-Mar 1.0950 17-Nov 1.0530 16-Mar 1.1310 18-Nov 1.0850 17-Mar 1.1270 19-Nov 1.0830 18-Mar 1.1210 20-Nov 1.0750 19-Mar 1.1300 23-Nov 1.0950 22-Mar 1.1350 24-Nov 1.0930 23-Mar 1.1340 25-Nov 1.1080 24-Mar 1.1150 27-Nov 1.1080 25-Mar 1.1040 30-Nov 1.1310 26-Mar 1.0830 1-Dec 1.1650 29-Mar 1.0950 2-Dec 1.1610 30-Mar 1.1050 3-Dec 1.1610 31-Mar 1.1130 4-Dec 1.1550 1-Apr 1.1300 7-Dec 1.1550 5-Apr 1.1540 8-Dec 1.1550 6-Apr 1.1600 9-Dec 1.1400 7-Apr 1.1580 10-Dec 1.1280 8-Apr 1.1500 11-Dec 1.1150 9-Apr 1.1460 14-Dec 1.1190 12-Apr 1.1370 15-Dec 1.1190 13-Apr 1.1340 16-Dec 1.1290 14-Apr 1.1390 17-Dec 1.1610 15-Apr 1.1390 18-Dec 1.1810 16-Apr 1.1290 21-Dec 1.1850 19-Apr 1.1090 22-Dec 1.1850 20-Apr 1.1260 23-Dec 1.2550 21-Apr 1.1260 24-Dec 1.2650 22-Apr 1.1190 28-Dec 1.3090 23-Apr 1.1380 29-Dec 1.3200 26-Apr 1.1380 30-Dec 1.3100 27-Apr 1.1360 31-Dec 1.3160 28-Apr 1.1340 4-Jan 1.3730 29-Apr 1.1430 5-Jan 1.3890 30-Apr 1.1370 6-Jan 1.4450 3-May 1.1560 7-Jan 1.4340 4-May 1.1380 Page 100 - Developments in Business Simulation and Experiential Learning, volume 39, 2012 Data Spot Price Data Spot Price Data 5-Jan 1.3890 30-Apr 1.1370 1-Sep 6-Jan 1.4450 3-May 1.1560 2-Sep 7-Jan 1.4340 4-May 1.1380 3-Sep 8-Jan 1.4000 5-May 1.1210 7-Sep 11-Jan 1.3300 6-May 1.0950 8-Sep 12-Jan 1.2740 7-May 1.0850 9-Sep 13-Jan 1.2350 10-May 1.1220 10-Sep 14-Jan 1.1750 11-May 1.1240 13-Sep 15-Jan 1.2150 12-May 1.1300 14-Sep 19-Jan 1.2700 13-May 1.1290 15-Sep 20-Jan 1.2700 14-May 1.1160 16-Sep 21-Jan 1.2800 17-May 1.0720 17-Sep 22-Jan 1.2740 18-May 1.0670 20-Sep 25-Jan 1.2900 19-May 1.0670 21-Sep 26-Jan 1.3350 20-May 1.0140 22-Sep 27-Jan 1.3310 21-May 1.0090 23-Sep 28-Jan 1.3030 24-May 1.0100 24-Sep 29-Jan 1.3150 25-May 0.9950 27-Sep 1-Feb 1.3680 26-May 1.0200 28-Sep 2-Feb 1.3680 27-May 1.0800 29-Sep 3-Feb 1.3900 28-May 1.0860 30-Sep 4-Feb 1.3380 1-Jun 1.0930 1-Oct 5-Feb 1.3300 2-Jun 1.0990 4-Oct 8-Feb 1.3300 3-Jun 1.1050 5-Oct 9-Feb 1.3450 4-Jun 1.0630 6-Oct 10-Feb 1.2950 7-Jun 1.0630 7-Oct 11-Feb 1.2600 8-Jun 1.0540 8-Oct 12-Feb 1.2250 9-Jun 1.0600 11-Oct 16-Feb 1.2550 10-Jun 1.0700 12-Oct 17-Feb 1.2140 11-Jun 1.0470 13-Oct 18-Feb 1.2250 14-Jun 1.0500 14-Oct 19-Feb 1.2440 15-Jun 1.0460 15-Oct 22-Feb 1.2490 16-Jun 1.0380 18-Oct 23-Feb 1.2530 17-Jun 1.0130 19-Oct 24-Feb 1.2670 18-Jun 1.0180 20-Oct 25-Feb 1.2250 21-Jun 1.0180 21-Oct 26-Feb 1.2150 22-Jun 1.0030 22-Oct 23-Jun 0.9850 25-Oct 24-Jun 0.9840 26-Oct 25-Jun 1.0230 27-Oct 28-Jun 1.0120 28-Oct 29-Jun 0.9860 29-Oct 30-Jun 0.9900 Page 101 - Developments in Business Simulation and Experiential Learning, volume 39, 2012 Appendix 3 Tests of Models Test of Model 1 Date Actual mean predict Error Date Actual 11/1/2010 1.266 1.1804 0.0856 12/15/2010 1.309 11/2/2010 1.278 1.1794 0.0986 12/16/2010 1.303 11/3/2010 1.275 1.1797 0.0953 12/17/2010 1.311 11/4/2010 1.278 1.1807 0.0973 12/20/2010 1.320 11/5/2010 1.281 1.1815 0.0995 12/21/2010 1.321 11/8/2010 1.280 1.1822 0.0978 12/22/2010 1.328 11/9/2010 1.280 1.1768 0.1032 12/23/2010 1.338 11/10/2010 1.283 1.1774 0.1056 12/27/2010 1.339 11/11/2010 1.280 1.1694 0.1106 12/28/2010 1.339 11/12/2010 1.258 1.1688 0.0892 12/29/2010 1.338 11/15/2010 1.254 1.1692 0.0848 12/30/2010 1.321 11/16/2010 1.220 1.1720 0.0480 12/31/2010 1.329 11/17/2010 1.173 1.1752 (0.0022) 1/3/2011 1.344 11/18/2010 1.199 1.1774 0.0216 1/4/2011 1.324 11/19/2010 1.214 1.1796 0.0344 1/5/2011 1.324 11/22/2010 1.225 1.1793 0.0457 1/6/2011 1.316 11/23/2010 1.228 1.1762 0.0518 1/7/2011 1.328 11/24/2010 1.260 1.1783 0.0817 1/10/2011 1.348 11/26/2010 1.260 1.1787 0.0813 1/11/2011 1.366 11/29/2010 1.269 1.1781 0.0909 1/12/2011 1.370 11/30/2010 1.269 1.1774 0.0916 1/13/2011 1.350 12/1/2010 1.253 1.1780 0.0750 1/14/2011 1.358 12/2/2010 1.251 1.1776 0.0734 1/18/2011 1.359 12/3/2010 1.249 1.1765 0.0725 1/19/2011 1.361 12/6/2010 1.253 1.1766 0.0764 1/20/2011 1.355 12/7/2010 1.251 1.1751 0.0759 1/21/2011 1.364 12/8/2010 1.259 1.1756 0.0834 1/24/2011 1.363 12/9/2010 1.258 1.1731 0.0849 1/25/2011 1.340 12/10/2010 1.263 1.1741 0.0889 1/26/2011 1.358 Page 102 - Developments in Business Simulation and Experiential Learning, volume 39, 2012 Page 103 - Developments in Business Simulation and Experiential Learning, volume 39, 2012 Test of Model 2 Date Actual mean predict Error Date Actual mean predict 11/1/2010 1.2660 1.2021 0.0639 12/15/2010 1.3090 1.2921 11/2/2010 1.2780 1.2197 0.0583 12/16/2010 1.3030 1.2963 11/3/2010 1.2750 1.2446 0.0304 12/17/2010 1.3110 1.2915 11/4/2010 1.2780 1.2493 0.0287 12/20/2010 1.3200 1.2993 11/5/2010 1.2810 1.2338 0.0472 12/21/2010 1.3210 1.3160 11/8/2010 1.2800 1.2474 0.0326 12/22/2010 1.3280 1.3091 11/9/2010 1.2800 1.2582 0.0218 12/23/2010 1.3380 1.3131 11/10/2010 1.2830 1.2740 0.0090 12/27/2010 1.3390 1.2903 11/11/2010 1.2800 1.2628 0.0172 12/28/2010 1.3390 1.2659 11/12/2010 1.2580 1.2925 (0.0345) 12/29/2010 1.3380 1.2789 11/15/2010 1.2540 1.2707 (0.0167) 12/30/2010 1.3210 1.2846 11/16/2010 1.2200 1.2628 (0.0428) 12/31/2010 1.3290 1.3007 11/17/2010 1.1730 1.2385 (0.0655) 1/3/2011 1.3440 1.3188 11/18/2010 1.1990 1.2270 (0.0280) 1/4/2011 1.3240 1.3344 11/19/2010 1.2140 1.2377 (0.0237) 1/5/2011 1.3240 1.3565 11/22/2010 1.2250 1.2469 (0.0219) 1/6/2011 1.3160 1.3621 11/23/2010 1.2280 1.2521 (0.0241) 1/7/2011 1.3280 1.3715 11/24/2010 1.2600 1.2771 (0.0171) 1/10/2011 1.3480 1.3701 11/26/2010 1.2600 1.2700 (0.0100) 1/11/2011 1.3660 1.3687 11/29/2010 1.2690 1.2838 (0.0148) 1/12/2011 1.3700 1.3760 11/30/2010 1.2690 1.2890 (0.0200) 1/13/2011 1.3500 1.3714 12/1/2010 1.2530 1.2720 (0.0190) 1/14/2011 1.3580 1.3716 12/2/2010 1.2510 1.2515 (0.0005) 1/18/2011 1.3590 1.3476 12/3/2010 1.2490 1.2427 0.0063 1/19/2011 1.3610 1.3531 12/6/2010 1.2530 1.2554 (0.0024) 1/20/2011 1.3550 1.3628 12/7/2010 1.2510 1.2527 (0.0017) 1/21/2011 1.3640 1.3480 12/8/2010 1.2590 1.2595 (0.0005) 1/24/2011 1.3630 1.3406 12/9/2010 1.2580 1.2549 0.0031 1/25/2011 1.3400 1.3530 12/10/2010 1.2630 1.2523 0.0107 1/26/2011 1.3580 1.3673 12/13/2010 1.2820 1.2476 0.0344 1/27/2011 1.3340 1.3382 12/14/2010 1.3040 1.2775 0.0265 1/28/2011 1.3350 1.3254 Page 104 - Developments in Business Simulation and Experiential Learning, volume 39, 2012 Page 105 - Developments in Business Simulation and Experiential Learning, volume 39, 2012 Appendix 4 Tests of Models 12,716 (70,548) (70,548) 61,433 Test of mean: (98,120) 73,195 1,709 60,017 sample mean: 40,049 217,144 (97,572) sample std: 84,613 120,287 43,053 std error: 10,923 110,366 20,183 89,553 (71,986) t stat 3.67 97,555 69,036 187,922 54,487 100,879 (66,227) Test of proportion: (50,825) 234,210 27,143 8,640 sample proportion: 0.25 3,232 26,303 110,647 (32,438) std error: 0.0559 117,459 124,305 107,626 (8,839) tstat: 4.47 6,953 45,790 85,452 80,228 229,879 (31,979) (114,875) 45,821 101,284 34,394 (88,092) 104,979 130,603 34,073 (116,888) 157,161 103,122 45,279 (21,355) (58,147) (9,020) (69,309) 40,294 34,338 17,406 103,554 Test of Mean and Proportion when applying a decision rule to the simulation null hypothesis: mean = 0, proportion = .5 Page 106 - Developments in Business Simulation and Experiential Learning, volume 39, 2012 Appendix 5 Model Screen Shots Page 107 - Developments in Business Simulation and Experiential Learning, volume 39, 2012 Page 108 - Developments in Business Simulation and Experiential Learning, volume 39, 2012 Click to see price history Forecast = expected demand Page 109 - Developments in Business Simulation and Experiential Learning, volume 39, 2012 Decision rule: if the forward price of time t-6 < expected price at t0 (approximately $1.36 based on periodic drift in the model), enter a forward contract. Using model forecast and historical data the optimal hedge ratio = .82 (using  actual /  forecast) *  Decision rule: if the forward price of time t-6 < expected price at t0 (approximately $1.36 based on periodic drift in the model), enter a forward contract. A judgment here was made not to contract at this price. Page 110 - Developments in Business Simulation and Experiential Learning, volume 39, 2012 Decision rule: if the forward price of time t-6 < expected price at t0 (approximately $1.36 based on periodic drift in the model), enter a forward contract. In this case, the price dropped dramatically – as sometimes happens in life and simulation. It appears to be a valuable contract to enter. The game ends with a final spot price less than the expected value. Even so, in this case the hedging strategy was profitable. It should be noted that actual demand was greater than forecasted. In this game, the deficit will be covered by purchases in the spot market. Table of Contents Volume 39, 2012 Designing the Training Challenge Follow The Leader: Are we Teaching our Students to be Thinkers or Followers? Two Free-Rider-Accepting Methods of Organizing Groups for a Business Game Additional Benefit Through Competency Models Assessing Brand Portfolio Normative Consistency & Trends With The Normative Position of Brands & Trends Package Modeling the Impact of Marketing Mix on the Diffusion of Innovation in the Generalized Bass Model of Firm Demand Play it Forward! The Design and Development of a Forward Contract Simulation Positioning the Company: Increasing Profits in Social Networks Merger of Companies in Business Game Exercise Towards a Knowledge-Based Approach for Autonomouse Trading Agent An Exploratory Study of the Impact of a Simulation Exercise on the Managerial and Personality Traits and the Decision Making Styles of Marketing Students Should the Concept of Potential Customers be the Foundation of Demand Theory in Business Simulations? Teaching Sustainability Experientially Drawing Upon Experience and Research to Improve Future Communications Improving Assessments of Student Learning Outcomes (SLO) Over Time The Effect of Affective Domain Characteristics on Behavioral or Psychomotor Outcomes Gossip? No, Not Me! An Experiential Exercise Student Advisement Using Gantt Charts: An Experiential Exercise in Management Theory Practicing Teachers as Digital Game Creators: A Study of the Design Considerations Designing and Solving Crossword Puzzles: Examining Efficacy in a Classroom Exercise Difficult Times Call for Innovative Measures: Microfinance as Experiential Learning in Higher Education Catalysts, Client Services, and Community Change: Interdisciplinary Collaboration in a Nascent Microfinance Initiative Build A Business . . . In An Hour or Less: Getting Closer to Reality into the Classroom Smart Goals: How the Application of SMART Goals can contribute to achievement of Student Learning Outcomes The Use of Data in "Live" Cases to Encourage Systems Thinking and Integrative Analysis: An Exercise Linking Human Resource Programs and Financial Outcomes in Real Organizations Experiential Education as a Process of Changing Mental Frames by Inducing Insight Learning Process and Content Integration in an Experiential Learning Guided Internship Program Good-bye Discussion Thread: Creating a Community of Inquiry in an Online Master's Program Fiction as a Constructivist Tool for Learning Process Consultation in an Online Environment: Shaping the Context, Introducing the Dialogue Can Simulations Provide a Better Experience? A Capstone Application Modeling a Modest Proposal for Increasing the Efficiency of Academic Reserarch Dissemination Experience GEO: A Massively Multiplayer Game SysTeamsGames Three Games for Management Simulation SimVenture - A Start-Up Business Simulation Stellarbucks Simulation Developing Games Using Strategy Maps and Balanced Scorecards Strategy Dynamics Models - Powerful But Simple In-Class Games Simulating Scenarios for Financial Statement Analysis A Valuation Model of the Simulated Firm Writing the Land: An Interdisciplinary Experiential Approach On the Estimation of the Probability of Meeting Financial Commitments: A Behavioraial Finance Perspective Using Business Simulations