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Optimal risk management strategies for a cattle backgrounding operation in the Peace River area Klee, Felix Wilhem Peter 1996

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OPTIMAL RISK MANAGEMENT STRATEGIES FOR A CATTLE BACKGROUNDING OPERATION IN THE PEACE RIVER AREA by Felix Wilhem Peter Klee Dipl. Ing. Agr. ETH, Swiss Federal Institute of Technology, 1993 A THESIS SUBMITTED LN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department of Agricultural Economics) We accept this thesis as conforming to the required standards THE UNIVERSITY OF BRITISH COLUMBIA March 1996 © Felix W. P. Klee, 1996 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of AcjT. HAAAVATCVI V-COWOWW C <> The University of British Columbia Vancouver, Canada 2 ? DE-6 (2/88) 11 Abstract Backgrounding cattle is risky. Large amounts of short-term capital are required to buy feeders and feedstuffs, and a ten month cost-revenue gap makes financial planning difficult. In addition, finished cattle prices are volatile and, frankly, unknown at the time the management places its feeders. Income risk and financial risk must be addressed by the management. Several strategies are available to reduce return risk, including anticipatory hedging with cattle futures contracts, placing custom feeders, placing feeders at different months and investing off-farm. This study developed a shot-term decision making model for a backgrounding operation that addresses the interaction between feeder ownership options, the feeder placement month, cash flow requirements, hedging alternatives, off-farm investments, the line of credit and the management's degree of risk-aversity. The following backgrounding issues were examined: (1) whether participation in a classical hedging program with Feeder and Live Cattle contracts would result in lower farm return variability and would increase owned feeder placements, (2) whether managements would be deterred from using hedging strategies if a gradually increasing downward BIAS was introduced, (3) whether managements would be deterred from using hedging strategies if margin calls had to be deposited during the hedging period and (4) to what extent cash flow constraints would affect the management's decision set. The literature of decision making under uncertainty was reviewed to determine the approach which would best accommodate the backgrounding management's risk concerns. Ill The Expected Value-Variance analysis was identified to formulate these management concerns in a mathematical programming context. A quadratic programming model was chosen to derive the expected return and return standard deviation frontiers (risk-efficient frontiers). The participation in an anticipatory hedging program provided a compelling risk management tool for reducing the backgrounding operation's return variability. Compared to the no-hedging case, the standard deviation of returns was almost cut by half for the hedging case. The introduction of a downward BIAS reduced hedging ratios drastically, whereas margin calls hardly effected the use of hedging. Custom feeders proved themselves essential in closing the typical cost-revenue gap in backgrounding and, despite offering the lowest returns, enabled the backgrounder to engage in more risky activities. iv TABLE OF CONTENTS ABSTRACT ii TABLE OF CONTENTS iv LIST OF TABLES viii LIST OF FIGURES ix CHAPTER 1 1 1. INTRODUCTION 1 1.1 PROBLEM SETTING 1 1.2 PROBLEM STATEMENT 3 1.3 PROCEDURE 4 1.4 THESIS OVERVIEW 6 CHAPTER 2 8 2. OVERVIEW OF BACKGROUNDING CATTLE FN THE PEACE RIVER AREA 8 2.1 CONCEPT OF CATTLE BACKGROUNDING 9 2.2 STRUCTURE OF THE BEEF CATTLE INDUSTRY IN BRITISH COLUMBIA 12 2.3 REGIONAL COMPETITIVENESS OF BACKGROUNDING FN B.C. 15 2.4 THE CATTLE CYCLE 20 2.4.1 What is the Cattle Cycle ? 21 2.4.2 The Cattle Cycle and its Impact on Cattle Management 23 2.4.3 Cattle Backgrounding and the Cattle Cycle 24 2.5 PRODUCTION CHARACTERISTICS FOR THE CASE STUDY BACKGROUNDING OPERATION IN THE PEACE RIVER AREA 25 2.5.1 Peace River Backgrounding 26 2.5.2 The B ackgrounding Operation 27 2.5.3 Production Decisions in a Risky Environment 30 2.6 BACKGROUNDING OPERATION CHARACTERISTICS FN THE PEACE RIVER AREA -- SUMMARY 36 V CHAPTER 3 39 3. INCORPORATING RISK CONCERNS INTO THE DECISION MAKING PROCESS OF A BACKGROUNDING OPERATION 39 3.1 UNCERTAINTY VERSUS RISK 39 3.2 MODELING TECHNIQUES FOR RISK ANALYSIS 42 3.2.1 Dynamic Programming 42 3.2.2 Linear Risk Programming - MOT AD 45 3.3 EXPECTED UTILITY APPROACH 47 3.3.1 Theory of Expected Utility (EU) 48 3.3.2 Expected Value-Variance Analysis: (E-V) Criterion 49 3.3.3 Quadratic Programming 51 3.4 HEDGFNG WITH FUTURES MARKETS 56 3.4.1 The Principles of Hedging 56 3.4.2 Theory of the Optimal Hedge 62 3.4.3 Review of Hedging Literature Relating to Feedlot Management 67 3.5 SUMMARY 70 CHAPTER 4 71 4. EMPIRICAL MODEL 71 4.1 ACTIVITY ALTERNATIVES 71 4.1.1 Animal Placements 71 4.1.2 Hedging with Futures Contracts 74 4.1.3 Off-Farm Investment, Outside Financing and Structural Costs 77 4.2 THE BACKGROUNDING OPERATION QUADRATIC RISK PROGRAMMING MODEL 78 4.2.1 General Statement of the Problem 79 4.2.2 Using the Forecast Error Method to Obtain Parameter Estimates 80 4.2.3 The Objective Function and Subsequent Constraints 86 4.3 DERIVING THE CASH FLOW CONSTRAINTS SET 93 4.3.1 Income and Cost Structure for Cattle Placements 93 4.3.2 Hedge Activities Cash Flow Requirements 97 4.3.3 Off-Farm Investments, Monthly Borrowing Activities, Structural Costs, Transfers 98 4.4 SUMMARY 99 vi CHAPTER 5 100 5. DATA AND DATA DEVELOPMENT 100 5.1 MAIN DATA SOURCES 100 5.2 SELECTION OF SAMPLE SIZE (TIME FRAME) 101 5.3 GROSS MARGIN CALCULATIONS 102 5.3.1 Cattle Placement Activities 103 5.3.2 Hedging Activities 105 5.3.3 Remaining Lambda Constraint Parameters 107 5.4 SOFTWARE APPLICATION 108 CHAPTER 6 109 6. RESULTS AND SENSITIVITY ANALYSES 109 6.1 SOLVING PROCEDURE 110 6.2 BASE CASE 111 6.2.1 Optimal Farm Plans 113 6.2.2 Principles in the Base Case Risk Minimizing Strategy 120 6.2.3 General Intuition of the Base Case Results 122 6.2.4 Some Subtle Aspects of the Base Case Results 122 6.3 SENSITIVITY ANALYSIS: RESULTS OF THE SCENARIO GROUPS 124 6.3.1 1. Scenario Group: Base Case, No hedging, Anticipatory Hedging 126 6.3.2 2. Scenario Group: Changing the BIAS 130 6.3.3 3. Scenario Group: Margin Calls ' 137 6.4 SUMMARY 142 CHAPTER 7 143 7. SUMMARY AND CONCLUSIONS 143 7.1 THESIS SUMMARY 143 7.1.1 Problem 143 7.1.2 Study Approach 143 7.2 CONCLUSIONS 148 7.3 LIMITATIONS AND AREAS FOR FURTHER RESEARCH 151 7.3.1 Limitations 151 7.3.2 Areas for Further Research 154 7.4 KEY CONCLUSIONS 155 vii BIBLIOGRAPHY 157 APPENDIX 4 162 APPENDIX 5 167 APPENDIX 6 179 viii LIST OF TABLES Table 2.1: Number of Beef Cow Farms and Cows on Farm, 1991, British Columbia 12 Table 2.2: Regional Cost Difference in B.C. Backgrounding 18 Table 2.3: Backgrounding Cattle is a Risky Business 20 Table 3.1: Short Hedge Scenario Under Constant Basis and Exchange Rate 59 Table 3.2: Short Hedge Scenario Under Widening Basis and Constant Exchange Rate 59 Table 4.1: Cattle Futures Contracts in the Backgrounding Operation Model 75 Table 4.2: Data Requirements for Rolfo Forecast Errors 81 Table 4.3: Monthly Income and Expenditure Distribution for Cattle Placement 94 Table 4.4: Cash Flow Requirements for Hedging Activities 97 Table 6.1: Selection of Base Case E- V Combinations 116 Table 6.2: Comparison of Largest Monthly Cash Flow Positions Following the November Cash Flow Budget in the 95,000-Farm Plan 123 Table 6.3: Selection of Base Case and Scenario E-V Combinations 125 Table 6.4: Combined Hedging Ratios for the BIAS Scenario Group 133 Table 6.5: Percentage of Owned Animals to Custom Fed for the BIAS Scenario Group 134 Table 6.6: Estimate for the November Borrowing Activity of the 100%-Scenario 142 ix LIST OF FIGURES Figure 2.1: Typical Beef Cattle Production Stages in B.C. 9 Figure 2.2: The Backgrounding Operation Flow Chart 28 Figure 3.1: Utility Function Representation 48 Figure 3.2: The Optimal E-VFarm Plan Set 53 Figure 6.1: Expected Return and Return Standard Deviation Frontiers: Base Case and Changing Hedging Strategy 114 Figure 6.2: Expected Return and Return Standard Deviation Frontiers: Changing BIAS 132 Figure 6.3: Expected Return and Return Standard Deviation Frontiers: Margin Calls 139 Figure 6.4: Development of the Combined Hedging Ratio for the Margin Call Scenario Group 140 X 1 CHAPTER 1 1. Introduction 1.1 Problem Setting Operating a farm enterprise in the Peace River area of British Columbia is a challenging business. Harsh and persistent winters followed by short summers limit the variety of possible agricultural activities. Feed grain production, forage production and subsequent cow-calf and cattle backgrounding operations are the more prominent agricultural activities suited to the Peace River country land base on a large scale. Most farms usually specialize in one of these production types and keep the others as sideline activities. Only a few farms engage in all common Peace River production types in equal proportions. Farms that are committed to cattle backgrounding must do so on Peace River terms: placing feeders, at the time when cow-calf operations wean their calves, and bringing them through the winter by keeping them on a non-fattening feed ration and trying to get them as early as possible on well established extensive pastures, to take advantage of the lower production costs during the short summer period. Forced to rely on local feedstuffs such as grass silage, hay and barley, it takes ten months to background a 450 lbs. steer to 950 pounds of finished weight. This is a long time period! Backgrounding cattle is a risky business. Large amounts of short-term capital are required to buy feeder cattle and feedstuffs, and a carefully planned monthly cash flow budget is essential for the backgrounding operation to pass the ten month cost-revenue gap that accompanies each owned feeder placement. If this was not enough, finished cattle prices at local auction markets are volatile and, frankly, unknown at the time when Chapter 1 2 the backgrounding management reaches the decision to place its feeders. However, in a short-term decision-making process, where structures and financial commitments of a backgrounding operation do not change, successful managers must address and assess these potential business risks. The backgrounding management must pay careful attention to markets, feedstuffs and the health of animals. Feeding of certain breeds, sex of animals and administering health risk-reducing inputs may be employed to reduce output variability. Use of the futures markets, forward contracting with feedlots and participation in a government stabilization plan may be valuable means of reducing finishing price risk. If the backgrounding management is shy of taking the ownership risk attached to backgrounding operation owned feeder placements, placing custom feeders might be the best option to reduce financial risk, because then the market risk is totally transferred to the feeder's owner, whereas only a part of the production risk remains with the backgrounder. However, the backgrounding management must also address financial risk on a daily basis, which is created by the possibility of not having enough liquidity to meet all financial obligations. Typically, backgrounding managers acknowledge this necessity by establishing monthly cash flow budgets for one production year. Cash flow budgets, not only visualizing cash flow requirements of potential production activities but also of fixed and quasi-fixed costs, e.g., labour, underline the utmost importance of a backgrounding operation's liquidity. Thus, the backgrounding management might reduce financial risk by optimizing the type and the placement time of feeders, and by arranging for outside financing if it becomes necessary to bridge a temporary cash flow shortage. It is important Chapter 1 3 to realize that a backgrounding activity with a high volatility in its returns might jeopardize a well balanced monthly cash flow budget. Of course, employment of a combination of the above risk reducing means might be the best risk-minimizing strategy of the backgrounding management. The cattle backgrounding management's attempt to accommodate these factors in its short-term decision making process leads to the problem addressed in this study. 1.2 Problem Statement In this study a short-term economic optimization model is developed to help reveal the risk and return trade-off in cattle backgrounding and to assist in the formation of specific management strategies for the backgrounding operation. The model is calibrated using data from a specific ranch in the Peace River area. Thus, on one side the results of the analysis will be highly applicable to the owners of this specific ranch; however, the model and its subsequent results are also generic enough to be relevant to backgrounding operations throughout North-Western Canada. The main variables in the model are how many feeder calves to place in the backgrounding system, when (i.e., what fall months to place the calves), what fraction of the calves are owned versus custom fed, how many of the calves to hedge, using cattle futures contracts, and when to place a hedge. In addition, the backgrounding management's decision set is extended by off-farm investment alternatives. Each variable impacts the backgrounding operation's expected net return and the variability of net return. These variables also jointly affect the backgrounding operation's monthly cash Chapter 1 4 flows throughout the planning horizon of one year and, hence, are jointly constraint because of restrictions placed on bank balances and loan amounts. It is assumed that the management's main objective is to minimize the variability of the farm's net revenues subject to earning a specific level of expected net revenues to cover costs including living and new investment expenses. An assumed downward BIAS for hedging activities, that is the expected loss on entering into a futures contract because of futures market imperfection, compromises this level of expected net revenues. The desired level of expected net revenues is treated as a parameter within the model. Specifically, the results are in the form of a risk-efficient frontier that explicitly shows the minimum variability of net revenues for each level of expected net revenues. In the portion of the frontier that is of interest, the relationship between risk and return is positive: higher levels of expected net revenues require the backgrounding management to accept higher variability of net revenues. The decision as to where on the risk-efficient frontier the ranch should be located is left to the backgrounding management, since this decision depends on the management's degree of risk-aversity. The results of this study identify the precise combination of choice variables necessary to achieve a specific point on the risk-efficient frontier. 1.3 Procedure The backgrounding management shall be in a position to alter its individual risk exposure on a group of animals by engaging in the traditional strategies of hedging and custom feeding and by optimizing the feeder placement dates, since, for the latter one, expected returns of a feeder placed in September might involve less volatile market Chapter 1 5 conditions than the ones of the same type of feeder placed in November. Besides placement capacity constraints, monthly cash flow constraints will ensure that in the attempt of minimizing the overall backgrounding net revenue variance, the essential backgrounding operation's liquidity will not be left behind. A monthly credit line shall be on hand to ease possible cost revenue gaps. Monthly structural cash flow requirements and off-farm investment opportunities shall complete the backgrounding management's decision set. Having developed such a short-term decision making model, the study will then address the interaction between ownership options of cattle placements, the cattle placement month, the monthly cash flow requirements, the hedging alternatives and the backgrounding operation management's degree of risk-aversity. Further, by changing hedging options, by widening the BIAS between relevant futures prices for the hedging activities, and by increasing the cash flow burden caused by hedging activities, this study attempts to reveal the expected changes in optimal backgrounding plans that the management would consider in its short-term decision making process in order to minimize overall return risk. Theoretically, participation in hedging or custom feeding should reduce financial risk in cattle backgrounding. In addition, with different feeder placement dates, a combination of these risk managing strategies might be the most appropriate response to reduce the overall variation in the backgrounding operation's return. In the context of deriving the risk-efficient frontiers, the following issues, hypotheses, are examined: Chapter 1 6 1. Determine if participation in a "classical" hedging program with Feeder Cattle and Live Cattle contracts will result in a lower overall return variability than in the no hedging scenario and will increase the number of owned feeder placements. Further investigate, by allowing cross hedging, if risk reduction can be improved (base case). 2. Determine, the extent to which the backgrounding management will be deterred from using hedging alternatives as a means of reducing return risk if the BIAS of underlying futures prices gradually increases, causing a downward BIAS of the hedge position. 3. Determine, the extent to which the backgrounding management will be deterred from using hedging alternatives as a means of reducing return risk if margin calls must be deposited during the hedge period. 4. Demonstrate the impact of cash flow constraints on the backgrounding management's decision set, especially on hedge placements, owned and custom feeder placements and borrowing activities 1.4 Thesis Overview Chapter 2 introduces the reader to the production characteristics of cattle backgrounding in the Peace River area and sensitizes the reader towards short term cattle backgrounding management concerns. Chapter 3 reviews the theoretical approach of how to incorporate risk concerns into the decision making process of farm management, thus, backgrounding management. The modeling technique will be specified. Chapter 3 concludes with an explanation of how hedging with cattle futures markets works. Chapter Chapter 1 7 4 outlines the activities in the backgrounding management's decision set and develops the planning model used to determine the risk-efficient frontiers for the backgrounding management. Hedging costs, expected gross margin data and other cost parameters for the activity alternatives in the management's decision set are developed in Chapter 5. Features of the software used are presented also in Chapter 5. Chapter 6 presents and discusses the risk-efficient backgrounding plans for the base case and the scenarios. Chapter 7 summarizes the analysis, draws final conclusions and discusses the implications of the study for backgrounding management and for further research. 8 CHAPTER 2 2. Overview of Backgrounding Cattle in the Peace River Area Since recent studies regarding backgrounding cattle in the Peace River area are not available, this chapter shall familiarize the reader with this type of cattle production system. First, the term of "backgrounding" will be clarified. The general definition of backgrounding cattle does not come without its limitations, because, it is rather difficult to draw a definitive line between cattle production systems. Some backgrounding operations overlap as well with cow-calf producers as with finishers. Second, in an attempt to shed some further light on the characteristics of backgrounding cattle, some of the recent structures of B.C. cattle operations will be presented, followed by a literature review of the B.C. regional competitiveness to illustrade the long term production characteristics of backgrounding cattle in the Peace River area. By doing so, a more defined concept of the production characteristics for backgrounding operations in the Peace River area will evolve. Third, the cattle cycle is presented and discussed in relation to the beef industry, and its impact on cattle backgrounding is evaluated. Fourth, having described the general cattle backgrounding environment in the Peace River area, this section will turn to the more specific production settings for the \ backgrounding operation to be modeled. The majority of these production settings draw * on the authors own knowledge of backgrounding operations in the Peace River area. Chapter 2 9 At the end of the chapter, the reader will be sensitized towards running a cattle backgrounding operation in the Peace River area, and short-term cattle backgrounding management concerns will be obvious. 2.1 Concept of Cattle Backgrounding1 By way of a general definition, backgrounding might be satisfactorily described as the second stage of cattle production, wherein calves mature into cattle and are brought up to a suitable weight for either the final stage of high energy grain finishing or else for replacement in breeding stock (see figure 2.1). The weight that a backgrounding cattle producer decides to put on an animal depends on a variety of factors, including access to range, availability of forage, and expected prices. Figure 2.1: Typical Beef Cattle Production Stages in B.C. Typical Beef Cattle Production Stages in B.C. Slaughter 21-23 1 Acknowledging spring calving as the most common practice, most calves become available for backgrounding in the fall: Historically, 70% of calves are marketed in Section 2.1 relies strongly on the following report: British Columbia Beef Industry Review, SCI Sparks Companies, Inc., April 1992. Weaned Calf Backgrounding -Normal Growth -Higher Energy -Pasluri1 Replacement Heifer Feed lot Summer/Fall IWinter/Sorins ISummer J m i H me friionrhO Chapter 2 10 October and November (Rogers and Osborn, 1979). Such calves enter the backgrounding operation at a weight of 400 to 550 pounds, where they are over wintered for about 150 to 200 days. The set-up of a backgrounding operation might comprise a feedlot such as winter confinement (corrals), or it may take place in fields with windbreaks and some feeding facilities. In general, we can identify backgrounding operations that feed medium energy rations and others that feed lower energy rations. Backgrounding operations that follow a low energy feeding regime are often referred to as Grassers. The term "Grassers" depicts the practice of taking the calf off range in the fall, feeding it on a forage-based low-cost ration through the winter (locally grown forage, some grain plus minerals and occasionally protein supplements), and placing it back on the range during the next summer to go to the feedlot at about 16-18 months of age for finishing at 1,100 to 1,300 lbs. During the backgrounding period weight gains of about one and a half pounds a day are realized. On the other hand, we have medium energy ration backgrounding operations. As the "Grassers" they take the calf off range in the fall at an average weight of 500 lbs., however, then they feed it semi-intensively enough to bring it to 750 to 800 lbs. at 12 to 15 months of age. Under such a regime, one-and-a-half to two pounds of gain are achieved on a daily average. The feeder is then either shipped to another feedlot or kept for finishing to 1000 to 1,300 lbs. These backgrounding operations are referred as Drylot Backgrounding. However, rules for backgrounding are not hard and fast. Variations on these two regimes exist that do differ in the sought after backgrounding products (finished weight, Chapter 2 11 age), in time-tables and feeding regimes. For example, exotic cross-breeds require a different backgrounding attention than domestic cross-breeds. Exotic cross-breeds, e.g., Hereford-Simmental or Hereford-Simmental, etc., tend to be larger framed and later maturing cattle types. Because of the heavier finished weight of exotic cross-breeds, it is important to provide them with higher quality feedstuffs during their backgrounding period. Feed rations established for domestic-breeds might not be sufficient to cover their energy and nutritional requirements. However, the general idea of backgrounding applies also to the larger framed exotic breeds. Finally, to establish some common understanding of backgrounding, it might be said that backgrounding comprises both a lower or medium energy feeding stage that might be finalized with a grazing stage (see figure 2.1). Besides different backgrounding regimes there are also different ownership arrangements for backgrounding cattle. Some cow-calf operators prefer to retain ownership. Such operators, facing surplus forage, may keep lighter calves as grassers and send the heavier portion of their calf-crop (600-700 lbs.) directly to a custom feedlot, where they are drylot backgrounded. Others, such as specialized drylot backgrounding operators, might enter ownership of calves to feed them to 750 to 800 lbs., provided that they have access to abundant forage and cheap grain sources. However, as previously stated, a typical backgrounding strategy cannot be identified, because each backgrounding operation follows its own specific backgrounding strategy. Chapter 2 12 2.2 Structure of the Beef Cattle Industry in British Columbia Cattle backgrounding is found in all sorts of cattle operations. The combination of factors involving heavier weaning weights, feeding younger and lighter cattle, and regimes such as drylot backgrounding, has led to a situation where backgrounded cattle blend into other forms of beef production. Some backgrounding operations overlap as well with cow-calf producers that keep calves until they are ready to go into feedlots, as with finishers which acquire calves and keep them on medium energy rations until they are placed in feedlots. This has led to a situation where neither precise nor specific statistics, that might report numbers and development of backgrounding operations in British Columbia, are available. Nonetheless, to illustrate the dimension of backgrounding in the beef production chain, the number of cow-calf operations and their development in B.C. are presented at this point (table 2.1). Table 2.1: Number of Beef Cow Farms and Cows on Farm, 1991, British Columbia Groups Average (Herd #of Cumulative # of Beef Cumulative #of Size) Farms % % of Farms Cows % % of Cows Cows 1-17 3358 57.38 57.38 19982 8.23 8.23 6 18-47 1203 20.56 77.94 35276 14.53 22.76 29 48-122 814 13.91 91.85 60600 24.96 47.73 74 123-177 209 3.57 95.42 30717 12.65 60.38 147 178-272 165 2.82 98.24 35609 14.67 75.05 216 273-527 64 1.09 99.33 22917 9.44 84.49 358 528+ 39 0.67 100.00 37641 15.51 100.00 965 Total 5852 100 242742 100 41 Source: Agricultural Profile of British Columbia -Part 2, Statistics Canada, Table: 2, p: 15, Cat. 95-394 Chapter 2 13 It is assumed that backgrounding operations are more likely to be reported under cow-calf operations than feedlots, because backgrounding tends to be undertaken in areas of marginal land qualities but in proximity to abundant forage and feed grain resources. In the 1991 Census, British Columbia had 5,852 farms that reported beef cows. These farms managed a cow herd of 242,742 head. Compared to previous census data (1976: 223,384; 1981: 233,911; 1986: 214,670) this figure has not changed much. Despite the fact that the number of beef cow operations is continuously declining (1976: 7,366; 1981: 6,613 1986: 5,868), a restructuring process faced by all participants in the agricultural sector, there was still a very large number of farms (over 4,500) with herds less than 48 cows and a small number of operations (39) with herds of more than 528 cows. The vast majority of feeder calves (75%) is produced on ranches with herd sizes less than 272 head. These figures suggest that B.C.'s cow-calf operations, in terms of herd size and numbers of operations, do not show the same degree of specialization as it is found in other areas of farming. In estimating the magnitude of backgrounding in British Columbia, we have to rely on loose estimates. In a study by Equus Consulting (1990) the authors tried to estimate the number of head backgrounded in B.C. as follows: They argued that 93,000 head of cattle had been slaughtered in B.C. in 1989. Of these, 2,417 had been imported, leaving 91,500 head that were most likely backgrounded in British Columbia. They further assumed that all feeders exported in 1989, 173,500, had been backgrounded in B.C. as well. Summing up these numbers provided an estimated total amount of backgrounding in B.C. of 265,000 head. The authors acknowledged, however, that this number is a very Chapter 2 14 loose estimate. Because hard numbers of total backgrounding activity are still not available, this matter is not pursued further. As for backgrounding marketing alternatives, we encounter selling cattle at auction markets away from the backgounding operation, or direct selling off the backgrounding operation, which usually applies to bigger and established operations, and contract feeding where a backgounding ranch receives a monthly payment for services provided as outlined in a contract or is paid through a crop sharing agreement. In some cases, multimedia auctions are conducted, where cattle lots are filmed on the backgrounding operation and are than broadcast all over North America to be auctioned through the means of TV sets. Interested buyers can make their bid by calling a displayed phone number. In other instances, electronic auctions are deployed to avoid unnecessary hauling of animals to auction markets. In case of an electronic auction an auctioneer visits ranches and describes the lots of finished feeders to be sold (three weight classes). The lot characteristics are then faxed to a stockyard, where long and short listings of this information is compiled, which is then made available on-line. In weekly auctions, registered buyers can then make bids for certain lots by using their personal office-based computers. Prices paid are for fob. ranch or fob. scale subject to a 3% shrinkage. In 1995, e.g., Williams Lake and Vanderhoof area, 25,000 head2 were sold through electronic auctions. In any marketing case, typical feeder cattle buyers are either feedlots or cattle trading agents. Phone conversation with B.C. Livestock, April 3, 1996 Chapter 2 15 2.3 Regional Competitiveness of Backgrounding in B.C. In 1992, KenAgra Management Services conducted a study to review the beef industry in British Columbia. This study attempts to assess the regional competitiveness of backgrounding in British Columbia from a long-term point of view. In the process of which the study also identifies technical characteristics for backgrounding cattle in the Peace River area. The study's findings to that extent are presented here to broaden the understanding of backgrounding cattle in the Peace River area. The study considers large volumes of high quality forage as vital for a winter feeding program of backgrounded cattle. Typically, animals that are meant to be put on grass in the following Spring (Grassers) should gain 1.50 to 1.75 lbs. average gain per day. As an alternative, if they are destined to be sent to a finishing feedlot in the following Spring, cattle might be put on a ration designed to produce 2.00 to 2.50 lbs. average gain per day (Drylot-backgrounding). Note that the latter alternative demands more forage and higher energy feeds with the prospect of capitalizing on likely higher prices for finished cattle in the upcoming spring months. Abundant and high quality range is a must to ensure a continuous maturing of grassers in the Spring. Otherwise the yearlings will gain only a fraction of the expected average daily gain. Pastures should be seeded to suitable domestic forages, and the grazing system should be intensified through fencing (sub-fencing) and/or pasture riding, where applicable. Chapter 2 16 Another characteristic, although not binding in terms of regional competitiveness, is access to enough working capital3. Backgrounding requires at least 5 to 10 months of short-term capital, because as soon as an animal is placed the backgrounding operation must face costs such as initial costs, processing expenditures, medication costs, miscellaneous cost positions and grazing fees over the production period. In the worst case, the operation must even sustain the death loss of a placed animal. Revenues are only received at the selling date of the animal. Hence, in order to endure this cost revenue gap, a sustainable cash flow is important. A monthly cash flow budget for the whole production period is the best way to monitor a smoothly run operation. Many established backgrounding operations prefer silage (grain- or grass-silage) rather than hay as the main forage source in their feeding regime. Silage combines several advantages. First, the preparation of silage is fully mechanized and its harvest is less dependent on weather conditions. Good silage is nutritious and palatable. Due to its 12 to 20% crude protein content, grass and legume silage require less protein supplementation. The bulk and moisture content of silage limit dry matter intake as well as the distance that it can be transported. As long as silage is high in digestible dry matter and nutritious elements, it is preferred as the main forage source in the backgrounding feeding system. This preference is also due to the lower production costs than for hay. Feeding silage reduces mainly production risk, but also financial risk. High-quality hay on the other side, despite being an excellent source of protein, calcium, and vitamins, makes Working capital = current assets minus current liabilities Chapter 2 17 up less than 25% of feed rations on a dry matter basis. This is due to its lower energy content in comparison to cereal grains, and to the bulky nature of hay, which limits dry matter intake. However, to produce silage requires the operation to be large enough to economically support the full ownership of the equipment needed. In light of relatively dry B.C. summers, the decision on which forage system to rely on and/or to which extent to depend on any forage system must be carefully evaluated. Some backgrounding operations (Southern B.C.) are able to extend their fall grazing period by extra irrigating forage. In the latter case, calves are grazed through December 1st. The KenAgra study concludes that the technical factors most required to support successful backgrounding include: a. ) Abundant low cost grazing areas and forage for wintering b. ) Proper management dedicated to the care of cattle c. ) Water of good quality for drinking available at reasonable cost d. ) Location where access to markets is not a problem e. ) Financial backing to ensure that working capital requirements are met. The authors determined that all reviewed regions, Fraser Valley, Thompson-Okanagan, Kootenay, Bulkley-Nechako, Peace River, Pacific North West (USA) and Alberta, could obtain above mentioned resources, except equal availability of feed for backgrounding. Based on their evaluation, the northern regions of B.C., particularly the Peace River area, were most competitive, but Alberta was equally competitive. Chapter 2 18 Table 2.2: Regional Cost Differences in B.C. Backgrounding Table 2.2a: Grain Backgrounding with Equal Feeding Period & Weight — profit Difference with Alberta ($/head) \ Region 1 j Region 2 Fraser j Thmpsn-Valley Okngn Region 3 Kootenay Region 4 Cariboo-Chlctin Region 5 Bulkley-Nchko Region 6 Peace River Pacific North West Alberta Difference | ( 6 0 0 5 ) | ( 4 2 3 7 ) (36.92) (12.21) (7.66) 5.62 (26.64) ! 0 Table. 2.2b: Grass Backgrounding with Equal Feeding Period & Weight -- profit Difference with Alberta ($/head) i Region 1 i Region 2 Fraser 1 Thmpsn-Valley Okngn Region 3 Kootenay Region 4 Cariboo-1 Chlctin Region 5 Bulkley-Nchko Region 6 i Peace Risei Pacific North West Alberta DiSLel <3 5-6 1> I ( 3 5 6 ) (7.62) (4.06) 0 16.25 (10.25) | 0 Table. 2.2c:"Drylot/Grasser" Combination Comparison ($/head) 1 Region 1 1 Region 2 Fraser j Thmpsn-Valley Okngn Region 3 Kootenay Region 4 Cariboo-j Chlctin Region 5 Bulkley-Nchko Region 6 £ Peace ! River Pacific North West I Alberta Difference | ( 7 7 ^ | « * * 2 > (79.59) (48.86) (9.64) 8.28 (5.16) | 0 Source: Table 2: KenAgra, April 1992, p: 153, 158, 160 Annotation: Losses in brackets. Table 2.2 summarizes the regional cost difference analysis for B.C. backgrounding as conducted in the study by KenAgra in terms of profit differentials. To make objective comparisons of costs between regions, the first difference for each cost item in each region was measured against a base region. Alberta was chosen as the base region. Because the relative differences between regions are the crucial measures, items of identical cost between regions were set to zero. The prices used in this analysis were for November 1991. Calf purchase prices were assumed to be the same throughout British Columbia. All production factors, such as feeding period, placement weights and selling weights of calves, were also kept equal throughout all regions. Table 2.2a depicts the profit Chapter 2 19 differentials of the drylot backgrounding comparison. All B.C. regions, with the exception of the Peace River area, are at a disadvantage to Alberta drylot backgrounders. In a similar fashion, the regional profit differentials for grassers (Table 2.2b.) and for a combination of drylot and grazing backgrounding (Table 2.2c.) were derived. The results of the total cost analysis show that in general backgrounding is least competitive in the Fraser Valley and most competitive in the Peace River area. However, the authors cautioned that circumstances might exist, which would support backgrounding in each region. The KenAgra study emphasized the regional profit differentials for cattle backgrounding in British Columbia only. Applying prices for November 1991, this study does not highlight the potential return risk associated with cattle backgrounding. The current cattle market situation (March 1996) might give the reader some idea of the risky prospects in the backgrounding industry, however, to further embed this aspect into one's mind, a simple example is presented in table 2.3. From the point of view of a short-term decision making process on a backgrounding operation, the management faces the situation where it knows all costs associated with backgrounding a feeder from 450 lbs. to 950 lbs., assuming that all feedstuffs required are on the backgrounding operation and are paid for at the beginning of the production period, but must rely on previous years' selling prices to estimate the possible revenue at the end of the 10 month production period. Focusing on the percentage return changes from the average return, it is fair to assume: Backgrounding cattle is a risky business. This issue must be addressed in a short-term decision planning frame work by the backgrounding management. Chapter 2 20 Table 2.3: Backgrounding Cattle is a Risky Business Backgrounding Cattle is a Risky Business E.g. September feeder steer. Placed in Sept. with 4.5 cwt., sold at 9.12 cwt. (4% shrink included), 8 months in feedlot, two months on pasture. Assumption: Only the Selling price is unknown at placing $/head Initial Cost: Puchase Price -597.915 -608.915 Selling Price: Total Feeding Costs: Ration Cost -121.43 Pasture -16.8 Hay -7.32 Total -145.55 Other: Bedding -6.21 Medicine & Vet. etc. -14.2 Death loss (2%) -12.42 Total -32.83 Expenses (no interest) -787.295 Avg. $/cwt. July 92 84.558 July 93 99.825 July 94 97.597 avg. July 93.993 per head July 92 July 93 July 94 avg. July Revenue ($): 771.169 910.404 890.085 857.219 Return ($): 123.109 102,790 69.924 Change (%): (-123 ) 76 ( 47 ) (o Annotation: cwt.: hundredweight (100 lbs.) Market data is provided by CANFAX, covering feeder market prices for the Edmonton/Northern Alberta region (from weekly data, not deflated) Production data is provided from Clover Farms Ltd. (as practiced) 2.4 The Cattle Cycle As with most livestock, beef production follows its own cycle—the cattle cycle. The increase and decrease of the cattle population occurs in repetitive patterns, what makes the cattle cycle predictable to some extent. The stage and the progress of the beef cycle provides important information for the beef producer and facilitates her/his long-term decision making process. Or as Harold Dodds (1981)4 put it: "A beefman who does not understand the cattle cycle is like a North Atlantic sea captain who does not know 4 from Gracey Charles (1981, p: 1) Chapter 2 21 about icebergs. He learns the hard way." This section will describe the cattle cycle and will discuss the general implications for the beef producer.5 2.4.1 What is the Cattle Cycle ? The cattle cycle, based on the number of breeding females in the national breeding herd each year, is driven by biological and economical forces. Being exposed to untamed nature, a cow herd would increase in size by its rate of reproductivity complying with the scarcity of resources and the presence of predators or naturally born diseases. Reaching the limit of its environment, the size of a cow herd would tumble from its peak to a more sustainable level, just to regain again in numbers from this point on. The up and down in the herd size constitutes the beef cycle in nature. However, being domesticated and hardly exposed to nature, the number of cattle in a herd is now mostiy determined by the economic decisions of herd owners. There are different ways to describe the cattle cycle. The number of beef cows is an accurate and meaningful description of what is happening. On the other side, changes in beef cow numbers will reflect in the number of inspected slaughters. The beef supply side represents the results of changes in cow numbers. In general, the beef supply cycle lags one to two years behind the beef cow cycle. Starting from the bottom number of breeding cows we can differentiate four distinct stages in the cattle cycle: The first stage is characterized by its consolidation in numbers of breeding cows. This stage takes usually one year in duration. The second This section relies strongly on: The Cattle Cycle, Gracey Charles, 1981 Chapter 2 22 stage is called the expansion phase which last years two through six, i.e., five years. The expansion phase is triggered by a declining beef supply (the beef supply lags one to two years behind the size of the breeding herd) and strengthening prices. Beef producers reduce the cow culling rate and retain more heifers. In the third stage the peak of beef supply is reached and, subsequently, prices start to tumble. The decline of prices is further fueled by an increase in the cow culling rate and a lower heifer retention rate—heifers are sold. The third stage lasts about one year. In the fourth stage, the reduction phase, the reduction of the cow herd continues due to a persistent beef over-supply. The reduction phase is two to three years in duration. The total cattle cycle is normally about ten years long. The cattle cycle can be monitored by following indicators in the slaughter market: The Female-Male Ratio is the most important guide to the cattle cycle. This ratio is based on the fact that the sex ratio at birth is very close to one. Hence, if this ratio is bellow one, fewer females than males are killed, and the herd is growing. An other important ratio is the Cow Culling Rate. Despite making no differentiation between milk cows and beef cows, this ratio illustrates plainly what is happening with the breeding cow herd. The cow culling rate is clearly associated with herd reduction. Thus, a lower rate indicates herd growth. The Heifer-Steer Ratio is also quite helpful in explaining what is happening in the cattle cycle. The rate of heifer kill and the rate of steer kill clearly suggests how many heifers are being retained for breeding. During a herd expansion period this rate is very low, indicating that more heifers are retained. Chapter 2 23 The growth of a beef cow herd is limited to three principles: the cow disposal rate (10 to 20%), combining cow culling and cow death loss, the heifer retention rate (0 to 85%), depending on the beef producer's decision making, and the reproductive performance of the breeding herd (34 to 43% for heifer calves), mainly influenced by proper health care and production management. 2.4.2 The Cattle Cycle and its Impact on Cattle Management The understanding of the cattle cycle helps the cattle producer to decide how to manage her/his cow herd. Most cattle producers follow the cattle cycle in their decision making. They expand their herds as long as prices are favourable and cut back as soon as prices weaken. Others try to keep a more or less steady cow herd, and a few beef producers manage their cattle herd on a counter cyclical basis. The key element to be in the position to respond and to benefit financially from the repetitive cattle cycle is to retain more heifers than required for herd maintenance. Retaining heifers has three advantages: First, they can be sold in the spring as open heifers for feeding or breeding. Second, they can enter the breeding herd and be bred and subsequently sold as bred heifers. Finally, they can remain in the herd for herd expansion. Therefore, the prudent cow-calf producer should attempt to maximize the size of the cow herd to the farm limits at the expense of steers. Steers should be sold as calves rather than yearlings to make room for more cows and bred heifers. Having extra heifers on hand will give the rancher a jump start if economic conditions signal an expansion in cow numbers. However, poorer quality heifers should be sold as feeder calves. Further, if an increase in Chapter 2 24 the number of inquiries for bred cows and heifers is monitored, an inevitable sign that the cycle approaches the peak, the rancher should sell breeding stock. The cattle cycle has also an impact on cattle feeding. Cattle feeding returns depend mainly on the price level for fat cattle, but also on the price of feeder cattle, price of feed and cost of all other production inputs. The feeder cattle price, however, is as well influenced by the cattle cycle (large supply of feeder cattle pressures the feeder price) as by the cattle feeding profits. If current cattle feeding returns fall short of their expectation than the beef producers try to soften or balance losses by lowering the price they pay for feeder cattle. The price of feed, say barley or corn, is usually best tracked by following the ratio between feed costs and the value of cattle produced. This feed ration tends to move in generally the opposite direction to the feeder cattle price ratio. Other costs, such as energy, transportation and on-farm costs tend to pressure the feeder cattle price relative to fed cattle prices. 2.4.3 Cattle Backgrounding and the Cattle Cycle Backgrounding, as the second stage of cattle production, wherein calves mature into cattle, is afflicted by the stage of the cattle cycle. However, a differentiation must be made between cow-calf producers, who conduct backgrounding mainly to mature heifers retained for cow replacements, and specialized backgrounding operations which background beef calves for feedlots. The changes in a cow-calf operator's management strategy, depending on where in the cattle cycle the beef industry is, were illustrated in previous section. Changes in a specialized backgrounding operation's management strategy are closely related to cattle feeding returns. Low fed cattle prices, high feedstuff Chapter 2 25 costs, a peak in the numbers of breeding cows, an increased beef cow culling rate and lower heifer retention rate, causing a beef over-supply, force the demand for feeders down. Subsequently, specialized backgrounding operations would have a hard time to stay in business. On the other side, e.g., before the expansion phase of the cattle cycle, a backgrounding operation could place more heifer calves in the hope to sell them as open or bred heifers. In terms of risk management, being in the up-swing of the cattle cycle, a backgrounding management might feels at ease to engage in more risky activities, such as placing owned animals with no hedging position in place versus custom feeders. Long-term effects of the cattle cycle on one's backgrounding strategy are apparent. However, in the envisioned short-term decision problem, the backgrounding management's decision set reflects all possible backgrounding activities under the current cattle cycle stage. Hence, a short-term backgrounding decision making model can be applied along all stages of the cattle cycle as long as feasible backgrounding activities are provided. It is for this reason, why the course of the cattle cycle and its different stages, despite being highly valuable, is not further pursued in this research. 2.5 Production Characteristics for the Case Study Backgrounding Operation in the Peace River Area The main characteristics of cattle backgrounding in British Columbia have been discussed. This section will turn the attention closer to the case study backgrounding operation in the Peace River area. On an operation level we will illustrate the general production settings without too much emphasis on the specifics, which will be elaborated on in later chapters concerning the empirical model and the data development. Chapter 2 26 2.5.1 Peace River Backgrounding The general characteristics of cattle backgrounding as previously highlighted hold also true for a backgrounding operation in the Peace River area. However, a slight adjustment of these backgrounding services is apparent, in order to conform to the Peace River production environment. First of all, the Peace River district is none too gentle in its climatic conditions. Summers are short and warm, whereas winters are persistent and cold. Sparse 90 to 95 frost-free days are available for farming. Averaging an annual precipitation maximum of about 500 mm, these weather conditions combined with overall marginal soil qualities cause weak and unstable grain crop yields on average. In contrast, from experience, forage production is quite stable and high in quality. This is especially true when pastures are well established, because then they are in the best position to utilize the remaining winter moisture which, in combination with the long daylight days, is the reason why forage production in the Peace River area, from the point of view of production risk, is more favorable than grain production. Spring grains, in contrast, might suffer from water stress. Thus, as a side note, farm operations that rely heavily on grain production might jeopardize their economic survival. In terms of backgrounding this means: Bringing cattle through the severe winter time by keeping them on a non-fattening feed ration and trying to get them as early as possible on well established vast pastures to take advantage of the lower production costs during the short summer period. It is the main objective to produce framed and grown out Chapter 2 27 animals, that will provide the potential to gain on a high energy feed ration during their remaining finishing time in commercial feedlots. Higher transportation costs, resulting from the Peace River's isolated northern location, dictate that these objectives have to be achieved mainly through local resources. On-farm barley grain and straw, grass silage, hay, and pastures are therefore important assets for a viable backgrounding operation in the Peace River area. Only supplements (minerals and vitamins) and medication might be acquired off-farm. It is this combination of production factors that elevates cattle backgrounding to one of the more reliable options to use the agricultural land base in the Peace River area. 2.5.2 The Backgrounding Operation The backgrounding operation underlying the subsequent assumptions in this research complies with the average production character in the Peace River area. However, the size of this case study backgrounding operation, which is part of an overall farm operation, exceeds most common standards in the Peace River area. The reference operation is Clover Farms Ltd. (north east of Fort St. John) and is owned by the author's family. Figure 2.2 illustrates the typical flows of cattle and cash positions in the backgrounding operation. Clover Farms conducts a farm, a cow-calf and backgrounding operation on a land base of 32,000 acres of deeded land. The ranch operation interacts with the farm operation. Forage production is part of the 23,000 cultivated acres. All pastures are improved and are integrated in a crop rotation program, that is, after 4 to 6 years they are plowed under and reseeded for grain production for a couple of years. 10,000 tons of Chapter 2 28 silage (mainly alfalfa-clover), 3,500 hay round bales and 5,000 acres of grain for feed are put up annually to accommodate the feeding requirements for the cow-calf and backgrounding operation during the winter feeding time. Figure 2.2: The Backgrounding Operation Flow Chart The Backgrounding Operation Flow Chart Auction PuichaaeJ Cattle ^'Transport Feedstuff Ha\, Silage, Supplements, Barley, Minerals, Straw Clicnl Custom Feeders Bank Credit Line <-----" A 3H Medicine, Processing material, etc. Bunk Off-farm Investment ±}/ ; t i l Backgrounding operation Production management Feeding management Heath manasicmcnl etc. Broker •>i Hedging Strategy Summer Pasture Death Loss \ 1 • - Shrinkage \ Auction Client Feeder Sale Custom Feeder Finishing Line -> Physical Flows •> Monetary Flows Currently, the backgrounding operation is capable of handling up to 3,000 head of feeders during the winter feeding time. The backgrounding branch comprises feeding, handling, feedstuff storage and waste management facilities. The feedlot like winter Chapter 2 29 confinement consists of a simply designed pen layout. Pens are of wooden construction and have a rectangular shape. All pens, each holding roughly 200 head, are grouped as a modular system, that is, they are located alongside of main alleys that serve as drive ways and/or as feedbunk areas. Heated water bowls are shared by two pens at a time. Because falling snow is of dry consistency, no totally protective sheds are supplied, but wind break fences are located alongside the north and east perimeters of each pen. Shavings and/or straw for bedding during the winter period ensure dry and orderly conditions for the feeders. A cattle handling facility adjoins the pen area. A hydraulic chute facilitates cattle processing, and a network of cattle-wide alleys eases the movement of feeders from holding pens to sorting pens. Weight control and gaining performance is checked with an on-site installed scale. The whole site is drained into several containment areas, and clean water is stored in a close-by 3 million gallon dugout. In late spring or early summer, manure is removed from all pens provided that field conditions allow for manure spreading. Except for the feeding wagons and the hay busters, all other feeding and manure handling equipment is shared with the other branches on Clover Farms. Typically, feeders come to the ranch in fall (September to November) at an average weight of 400-450 pounds. After the feeder calves are wintered, they are put on grass until around August, when they go to feedlots, some of them as far away as Colorado. The feeders average 1.70-1.90 lbs. weight gain per day. The feed ration consists of hay, barley, and grass-alfalfa silage, which are all produced on-farm. To avoid bloating of feeders during the two months on range Rumensin is offered, and a salt/mineral Chapter 2 30 supplement is made available to ensure proper weight gains. The last two items are purchased off-farm. The feeders weigh 900-950 lbs. when they leave and generate a revenue through their sale transaction or through monthly paid custom feeding rates, which are based on the weight effectively gained by each feeder. 2.5.3 Production Decisions in a Risky Environment The management of a backgrounding operation, as we have seen, must confront future risks and uncertainties within its short-term production decision-making process. Despite facing a whole array of "unknowns" that might alter the backgrounder's expected financial objective, the backgrounding operator must establish an as reliable as possible decision-making process. With respect to a backgrounding operation, the following questions must be addressed and evaluated in terms of their likelihood of occurrence and their economical impact: I. What will prices for matured feeders be in 10 months? II. How many feeders will be lost due to death? III. What will the reduction of weight gains and feed efficiency be due to sickness and adverse weather conditions? IV. How will feed cost change? Etc. Identifying possible sources of risk is an important aspect of this decision-making process and will help the management to assess the return and risk trade off for possible activities in its decision set. In general, we can identify following sources of risk (Castle, 1987): Chapter 2 31 Production risk: It is due to the variability in production caused by such unpredictable factors as weather conditions, diseases, pests, genetics. Examples include: Crop yields, rate of gain in animal production, pasture-carrying capacity, death loss, etc. Market risk: It involves the variability of prices that farmers receive for their products and/or must pay for the ongoing production. Financial risk: Use of borrowed capital and unpredictable cash flows create the risk of not having enough liquidity to meet all financial obligations. Obsolescence risk: Describes the risk encountered when assessing the question, when to undertake investments in new technologies. Legal risk: Laws and governmental programs that reflect society's changing attitudes are a growing challenge for farmers. For example: Environmental protection, use of feed additives, insecticides, etc. Human risk: The possibility of losing a key employee during a critical production period is one example relating to this sort of risk. Of these risk sources the production, market and financial risk are of the most prominent nature for the intended short-term decision making process of the Peace River Chapter 2 32 backgrounding operation. All of them do severely impact the backgrounder's short-term decision making process. The market risk is, however, of primary concern. Whereas the occurrence of production risk can be fully acknowledged by establishing minimum/maximum benchmarks such as death loss and pounds of beef gained daily and is mainly confined by employing risk reducing inputs such as vaccination for disease prevention, antibiotics, etc., for treatment, veterinarian consultation and feed control, to mention a few, the market risk does pose some difficult assessment for a backgrounder. Because at the time the production decision, ergo placement decision, must be derived, the backgrounding operator is not aware of the future selling prices of the matured feeders. From the literature, we know that agricultural producers tend to be risk averse in their decision making. And complying to their personal degree of risk-aversity, they try to assess the risk and return trade-off of possible farm activities. In this risk and return trade-off evaluation, e.g. where owning cattle gives the prospects of higher returns, which however, does also come with a selling price induced return risk, it is thought that the Peace River backgrounding operator can utilize the following assigned market risk management tools: Forward pricing through appropriate futures contracts and/or a differentiation in the ownership of the animals to be placed. This is in addition to the differentiation in feeder placements, where just by the mean of placement timing a more stable revenue might be yielded. As a snap shot, the idea of hedging can be summarized as follows: By hedging the expected matured feeder's spot price with futures contracts the backgrounder can trade Chapter 2 33 market induced output risk for basis6 risk. In theory, since the variance of the basis is expected to be smaller than the variance of the underlying spot market prices, the feeder owner is able to stabilize the financial outcome of her/his initial investment. Hence, forward pricing through futures contracts reduces the feeder owner's downside risk in revenues. A detailed discussion follows in section 3.4. The other alternative to cushion market uncertainty is a differentiation in the ownership of the animals. Custom feeding, a one pen or one production unit (per head) at a time agreement for feeding services, is the most common form in the beef cattle industry. It relieves the backgrounding operator from the ownership of the fed feeders. As a result, costs and revenues associated with the ownership of a feeder, like initial costs, interest, marketing costs and selling prices, do not constrain the backgrounder's production decision making framework. As such, a custom feeding agreement transfers the market risk totally to the owner of the feeders and leaves just part of the production risk with the backgrounder. The backgrounder is basically paid for services provided to the feeder to ensure its performance as outlined in a related custom feeding agreement. Equipped with such risk management tools a Peace River backgrounder has several options to cushion the market risk at the time the production decision must be derived. Depending on her/his risk attitude, from totally risk averse to risk taking, the livestock producer can alter her/his individual risk exposure from no risk, by deciding not to produce, to negligible risk, by custom feeding, to moderate risk, by owning and Basis=Cash Price - Futures Price Chapter 2 34 hedging, or to full risk, by owning the animals. Hence, the backgrounder has to assess the individual risk-return trade-off for all activities. And depending if the backgrounder is open towards risk, s/he will decide on activities that provide the highest possible return, e.g., placing owned animals, and in reverse, if s/he does not want to bear risk, sticking with custom feeders might be the best choice. There are many ways to assess the expected price risk for a possible production decision. One way to estimate the potential price risk is to derive the standard deviation and/or variance of the selling prices of interest. The standard deviation is a measure of dispersion of a possible price at a point in time, which is generated from historic data sets or from experience. Having defined her/his personal attitude towards risk and having derived the revenue variances of each possible production activity the backgrounding operator will at least try to match these two sides. This is an important concept! As for other costs for backgrounding feeders and their associated risks, such as changing feed costs, initial costs of feeders, interest, their size of price variance is not a constraint in the intended short-term decision making process. At the time the decision to place feeders is undertaken, the relevant costs are known in case of the outlined Peace River backgrounding operation. For example, feedstuff is acquired at the beginning of a production year (15. September) regardless of when it is actually used within the production year. The emphasis on the variability of feeder returns only, results from the principal difference of a short-term and long-term operation's point of view. In a short-term decision making framework, a backgrounder is interested in the variability of returns or Chapter 2 35 gross margins, since these place financial constraints on the short-term financial outcome of the overall operation. In contrast, in order to determine the feasibility or profitability of an operation's activity, which requires a long-term point of view, the farmer relies on long-run average gross margins only, as it is applied in the well circulated "Planning for Profit"7 sheets. The last of the triad of considerable risk sources in the short-term decision making process is financial risk. Financial risk emerges from the backgrounder's cash flow requirements to meet all financial obligations and return expectations. This means that, as the returns of diverse production activities, e.g. animal placements, are subject to their individual selling price variances, so are the associated cash in-flows of these decisions. Hence, a production decision with a high variance in its return might jeopardize a well balanced monthly cash flow budget. A cash flow budget is the most important management tool for a backgrounding operation because it visualizes the timing of all cash flow requirements. Not only does it note cash flow movements of potential production activities, but it also shows those of the existing backgrounding operation facility. These fixed costs and quasi fixed costs, the latter ones depict for example the costs of the present work force, should not be subject to change especially in the context of short-term decision planning. Furthermore, by visualizing the timing of all cost and revenue positions, the utmost importance of a Province of British Columbia, Ministery of Agriculture and Fisheries. Chapter 2 36 backgrounding operation's liquidity is omni present. Hence, the type of placement and its subsequent cost/return position timings have to be carefully weighed. Having referred so far to a specialized cattle backgrounding operation, one important risk management strategy for the manager of a mixed operation, e.g., cow-calf, backgrounding and feed grain production, has not been discussed yet. An operation that conducts several farm enterprises can cushion its production, market and financial risk by diversification. As cattle and grain prices fluctuate the farm could for example adjust the intensity of cattle placements in favour for an extended feed grain production. In order to make diversification work, it is important to select a combination of enterprises with opposing price cycles, so that when the price for one commodity is down, a normal or higher price for the other offsets the loss. Two such enterprises might be a cattle backgrounding and feed grain production. This study, however, not disputing the general efficiency of enterprise diversification, excludes such effects due to the assumptions of a specialized backgrounding operation and the used software that hmits the size of the model. The reader is reminded that the backgrounding model kept in mind is of short run in nature, i.e., all input prices are known at the beginning of the production period, despite the fact that feed costs and interest rates tend to vary within the production cycle. Thus, the envisioned model is still an abstraction from the reality. 2.6 Backgrounding Operation Characteristics in the Peace River Area -- Summary This chapter described the nature in which the backgrounding operation's management has to find its production decision. In addition to general resource Chapter 2 37 constraints like placement capacity, feedstuff limits, capital constraints etc., the backgrounding management has to consider its willingness to bear risk. This degree of bearing risk is an additional constraint that the backgrounding management likes at least to match with the variability of production activity returns. Whereas the timing of production activities is mainly affected by monthly cash flow requirements of the combined backgrounding operation, the variability of returns or gross margins of these activities is mainly caused by output price risk. The backgrounding management attempts to reduce this output price risk exposure to the extent of its specified degree of risk-aversity. Equipped with previously described risk management tools, the management of a backgrounding operation is then in a position to alter its individual risk exposure on a group of animals from no risk, by deciding not to produce, to negligible risk, by custom feeding, to moderate risk, by owning and hedging, or to full risk by owning and not hedging. In addition, the expected return risk might be altered by different feeder placement dates, since for example returns of a feeder placed in September might occur in less volatile market conditions (July of the following year) than the returns expected from a November placement (September of the following year). The range and optimality of risk exposure broadens for the operation's owner as soon as the backgrounding facility provides multi-production capacity. Parameters that trigger the management's production decision are: the general degree of risk-aversity, ergo its risk preference, and the need to achieve a certain financial objective. Chapter 2 38 Hence, the backgrounding operation management is left with the task of accommodating all these requirements in its short-term production decision-making process, which is to decide how many animals to have under each production alternative and when to make placements, what risk management tools to deploy in order to limit the main source of risk, output price risk, by not violating a sustainable cash flow budget. 39 CHAPTER 3 3. Incorporating Risk Concerns into the Decision Making Process of a Backgrounding Operation This chapter reviews concepts, schools of thought and relevant literature to incorporate risk concerns into the decision making process of agricultural management. It begins with an attempt to clarify the term 'risk' from a real world point of view and leads over to the theoretical approach of how to express and consider risk concerns into a model decision-making framework. In the following section, three methods of risk analysis for farm management will be presented, compared and ranked according to their relevance and efficiency to this research. In the final section, the concept of hedging with cattle futures contracts will be explained and commented on in its relation to the derived theoretical risk approach. 3.1 Uncertainty Versus Risk Before engaging in deeper discussion of how to incorporate risk concerns into the decision making process of a backgrounding operation it is necessary to clarify the terms "risk" and "uncertainty", because they appear to be interchangeable in today's understanding. As widely accepted, Barry (1984), risk and uncertainty influence the efficiency of resource use in agriculture and the decision-making processes of farmers. Risk management is therefore important whenever decisions' outcomes are uncertain. And as Dillon (1971, p. 4) remarked, "A risky choice prevails when a decision maker has to choose between alternatives, some or all of which have consequences that are not certain." Risk influences the decision-making process on manifold levels. Variations in Chapter 3 40 prices and yields and, subsequently, cash flows might overshadow the farm management's financial expectations. Hence, considering possible events and outcomes of different alternatives within a decision-making process is an integral part of risk management. Knight (1921) was one of the first economists who attempted to derive a differentiation in the risk involved within a decision-making process through the state of knowledge. Based on the amount of information available to the decision maker, he distinguished three levels of decision-making knowledge: perfect knowledge, risk and uncertainty. Obviously, perfect knowledge referred to a situation where the outcomes of a decision were considered to be certain. In the case of risk and uncertainty the differentiation was established by the degree of information available. If information was available for the decision maker to estimate probability functions about possible outcomes, the events were considered risky; however, if probability distributions could not be estimated, then these events were uncertain. Hinged upon this concept was somehow the implication that risk and uncertainty could be separated by their degree of objectivity. Having derived probabilities from time series, e.g. the average calving rate from annual data series, which was considered to be objective, the probabilities for characterizing, for example the likelihood of losing human work force on a farm, were considered to be illogical, therefore subjective and thus, uncertain. Anderson et al. (1977) challenged this naive concept and argued that all probabilities were subjective to some degree since the decision maker had to subjectively assess whether any "objective" data was appropriate for an intended decision situation. Chapter 3 41 From today's point of view such attempts at differentiation can only be perceived as hair-splitting, because both terms impact the outcome of possible returns, which is in the focus of interest. In an agricultural context, risk is commonly associated with variations in yields, product prices and/or revenues. Hazell (1984), for example, expressed that the variance of yields and associated revenues would explain best the variation in the grain production pattern in the U.S. and India during the Sixties. Goswami (1993), in developing risk-efficient farm plans for the erosion afflicted West Garo Hills district, used the variability of net returns as a measurement of risk, assuming that these returns were due to price factors and yields, of which the latter one would capture the impact of erosion. Other authors consider the variance of revenues of decision alternatives and their covariances as the most important measures of risk in agriculture. A study by Biswanger (1980) shows that farmers tend to behave in a risk-averse way. Hazell (1986) concludes from the farmer's risk-aversity that they prefer farm plans that provide a satisfactory level of security even if this means sacrificing income on average. He followed that ignoring risk-averse behavior in farm planing would lead to farm plans that were unacceptable to farmers. He argued that farmers would only consider farm plans if they suited their personal risk preference. Possible risk responses by farmers are manifold. In a first step, a farmer might select an enterprise s/he likes to pursue. By pursuing an activity s/he knows best, s/he reduces the likelihood of failure. By combining different enterprises s/he is able to further lower the variability of total returns compared to alternative actions. However, there are Chapter 3 42 limits to this concept of diversification. If the considered risk reducing actions are perfectly correlated, e.g. prices of two agricultural products follow exactly the same directions, then the expected overall risk reduction will fall short of expectation. And although a larger number of enterprises will lower the overall variability of returns, the achieved marginal risk reduction will become progressively smaller. In any event, diversification is limited to resources, climatic and market conditions. Other risk responses might be by selecting enterprises with a low expected selling price variability, timing the production to spread sales or returns, which is basically a diversification of revenues over time, engaging in a forward pricing strategy and/or deploying hedging instruments like hedging with futures contracts. As a final option the farmer might counter an overall risk situation with a financial response, that is to ensure that additional liquidity is on disposition. Of course, a combination of all these risk responses might be the most appropriate action. There are two general approaches to modeling a fanner's choice under risk: expected utility and other. In this thesis the expected utility approach is used, primarily because it has the most solid theoretical foundation. Before describing this approach, two other methods that have been commonly used in the agricultural economics literature are presented. 3.2 Modeling Techniques for Risk Analysis 3.2.1 Dynamic Programming "Dynamic programming is a technique for the solution of decision problems which involve a sequence of interrelated decisions. A sequence of decisions does not necessarily Chapter 3 43 characterize a dynamic decision situation although dynamic prograrnrning is usually applied to problems where a number of decisions have to be made in subsequent period of time. The general decision rule which is followed in the dynamic programming approach is to select the sequence of decisions which contributes maximally or minimally to the value of an objective variable", Hanf (1983, p. 48). Applying Bellmann's principle of optimality8, an optimal policy has the property that whatever the initial state and initial decisions are, the remaining decisions must constitute an optimal policy with regard to the state resulting from the first decision, a simple, dynamic programming model is given in (3.1) (Perry, 1986): n Maximize ^F(u,,w,,t)(l +r)-< subject to w,+\ = h(u,,w,,t) 0<xt<d, (3.1) where n is the number of stages being analyzed, F(...) is the return function, u, is the decision or control variable in stage t, w is the state variable in stage t, r is the discount rate, h(...) is the equation of motion, and dt is the resource constraint in stage t. In respect to a continuous backgrounding operation, the production period could be divided into one month stages; the states of nature could be defined by calf prices and feeder prices and/or Bellmann, Richard E. and Dreyfus, Stuart E., 1962, p. 15 Chapter 3 44 live weight levels; and the decision variables might be animal placement decisions, that is, animals to sell, buy or continue feeding (Freeze, 1989). Although dynamic programming has been widely used in modeling livestock production systems (Glen, Yager, Meyer and more recently Rodriguez, 1988, and Lawrence, 1989) and has proven itself to be an effective technique for finding the optimal times and live weights at which to sell and buy livestock, dynamic programming falls short of some of the objectives in this study. The dynamic programming approach places emphasis on a multitude of states of nature over a time horizon which would subsequently require a short term change in the decision variables. However, for the envisioned short term production decision framework of the depicted backgrounding operation, the dynamic programming approach, despite being accurate, would be too elaborate, given the available information and limited flexibility of the depicted short term backgrounding management problem. Referring to the portrayed comparative production cost advantage in cattle backgrounding for the Peace River area, the beef production type of backgrounding cattle follows naturally the abundant, cheap, and local forage supplies, especially through the summer months where marginal profits are higher than during the harsh winter feeding period. The 300 days feeding period that it takes to grow a 450 lbs animal to 950 lbs does not allow for a high turn-around per production unit. Consequently, future states, which would indicate a softening in feeder prices and would require a change in already initiated placement or feeding decisions, could not possibly be considered in the short term decision making Chapter 3 45 framework. A steer placed in September is likely to stay in this restricted production environment for its anticipated production period of 300 days! The situation is different in the case where Lawrence (1989) applied the dynamic programming approach to the production decision making problem of a hog raising facility in U.S. Midwest with an one-time capacity of about 1,000 head. An average days-on-feed of 125 days and a flexible feeding program allowed for short-run returns in response to forecasted states in feed and hog market conditions. Another point of consideration is the "curse of dimensionality" that clings to dynamic programming. Probabilistic dynamic programming models considering risk tend to be very complex. In addition, dynamic programming requires a development of a solution algorithm specific to the problem under consideration. This is a difficult and time consuming process from the researcher's point of view. For these reasons, dynamic programming was not considered the most optimal approach, given the objectives and limitations of this study. 3.2.2 Linear Risk Programming - MOTAD MOTAD, Minimization Of Total Absolute Deviation, is commonly used in problems involving risk and was developed originally as an approximation to expected value-variance (E-V) analysis (Hazell, 1971; Barry, 1984; Hazell and Norton, 1986). In a MOTAD model, risk is measured as linear deviations from the expected value. Implicitly, due to the assumption of risk aversion, risk is undesirable and, hence, is minimized. The trade-off occurs between expected value returns (E) and absolute deviations (A). The E-A frontier is developed by parametrically solving the model with respect to expected value Chapter 3 46 returns (A,). The E-A frontier is derived to closely approximate the corresponding E-V efficient set (Freeze, 1989). The MOT AD model can be formulated as (Hazell, 1971): s such that n (for all h, h = l,...,s) n ^fjXj =X (A, = 0, to unbound) 7=1 n ^ayXj < bj (for all i, i= 1,..., m) 7=1 Xj,yK>0 (for all h,j) (3.2) where Negative income deviation below the mean xj: Activity j au: Resource / requirement for activity j W- Resource / limit Chj '• Income of the activity j in observation period h ir- Sample mean income of activity j fr- Expected income of activity j At the time when Hazell (1971) developed the MOT AD approach, the availability of quadratic programming codes with the necessary parametric options that would have been able to handle quadratic programming formulations (E-V criterion) were not given. The E-A criterion's main advantage over the E-V criterion was considered to be that it led Chapter 3 47 to a linear programming model when deriving efficient E -A farm plans which were, in terms of computer performance, easier to solve. Times have changed, and Onal and McCarl (1989) questioned Hazell's produced arguments. Having conducted a comparative study between a M O T A D and a non-linear farm model formulation, they concluded that the day of M O T A D programming-based objective function approximation may well be over in cases involving both risk and sector models. Their results showed that the direct solution of a nonlinear problem was faster and naturally more accurate, with this advantage growing as model size increased. This study did not conclude that the M O T A D formulation should never be used, but rather that it should be used in fewer situations such as considering M O T A D as a superior risk criterion or as a fall-back position when nonlinear software was unavailable. Acknowledging the developments in computer and software technology, this research will apply the E-V criterion by using a quadratic programming formulation in assessing the optimal E -V efficient sets for short run backgrounding operation plans. 3.3 Expected Utility Approach Decision making under risk has interested economists for centuries. Conceptualizing, modeling, and measuring risk attitudes of decision makers has been of primary interest. Bernoulli in the 1700's postulated that people did not choose the event with the highest expected return, but rather they assigned "moral expectation values" to each outcome. In a later stage these assigned values were called utilities. Von Neumann and Morgenstern (1947) completed this approach by developing the expected utility model based on a set of axioms. They proved that, if an individual's behavior conforms to these Chapter 3 48 axioms, an ordinal utility function can be derived to arbitrarily assign values to contingent values (Lawrence, 1989). The expected utility model and the Von Neumann and Morgenstern axioms have been the foundation for risk management studies in agriculture. 3.3.1 Theory of Expected Utility (EU) The expected utility theory is based on four axioms: ordering of choices (assures the hierarchy of the solution), transitivity among choices, substitution among choices, and, finally, the certainty equivalent among choices (which reasons a revenue variability of zero for a revenue that a farmer is certain to obtain). If a decision maker regards these axioms, a utility function can be established that reflects the decision maker's preference (Hey, 1979). Thus, facing different risk alternatives, a rational economical decision maker will choose those actions that will maximize her/his expected utility subject to her/his personal attitude towards risk and that are determined by the utility function's second order conditions. Depending upon whether the marginal utility is decreasing, zero or increasing we call such a decision maker either risk-averse, risk-neutral or risk-inverse (figure 3.1). Figure 3.1: Utility Function Representations Utility Utility Utility • Averse: \ > 0 ($) ^ > Neutral: k = 0 ($) — > Inverse: X < 0 ($) Chapter 3 49 The major inconvenience with this expected utility decision criterion approach is that a specific utility function, that is with respect to the decision maker's risk attitude, must be established and estimated. Thus, because of the complexity and quantification problem of a decision maker's risk attitude, more user friendly decision critera like the expected value variance analysis are commonly applied. The expected value variance analysis is discussed in the following paragraph. 3.3.2 Expected Value-Variance Analysis: (E-V) Criterion Expected value variance (E-V) analysis approximates a specific method of expected utility maximization. Essentially, the expected income-variance (E-V) criterion assumes that a farmer holds preferences among alternative risky farm plans solely on the basis of their expected income E and associated income variance V. This is true if the farmer derives decisions according to an E-V utility function. Markowitz H.M. (1952) originally developed the portfolio selection, E-V model. In this model an investment is allocated such that the maximum profit less a risk measure is obtained subject to constraints on investible funds. The mathematical representation of this problem is (McCarl, Bruce A. and Hayri Onal, 1989): max/? - t y - \ (R -R)2 j ^njXj-Ri=0 for alii j JjRi/n-R = 0 Xj >0, Ri, R.ZO, for alii and j (3.3) Chapter 3 50 where Xj is the amount invested in alternative j;f is the total investible funds; ()) is the risk aversion coefficient; iy is the return to investment in Xj under state of nature i; R is the total return to all investments under state of nature i; R is the average return across all states of nature; and n is the number of states of nature. The lower case symbols represent parameters, while Xj is the decision variable and R and R are depending on it. The first term in the objective function is the average return, while the second term (neglecting the <|)) is the variance of returns. The E-V decision criterion can be derived from an exponential utility function which is based on a normally distributed income. U(Y) = \-e-W (Exponential utility function) (3.4) E(U(Y)) = 1 -g-PE(ww/2)v(r), (Expected utility function) (3.5) Maximizing equation (3.5) is equivalent to maximizing E(Um) = E(Y)-(k/2)V(Y) (3.6) Hence, mean-variance analysis applies when maximizing the exponential utility function, and normality is assumed. The magnitude of A represents the degree of risk aversion under exponential utility. The larger A, the more penalty is placed on large variances and the more risk averse is the decision maker. Maximizing the last equation for a given A is the mean-variance decision rule. Chapter 3 51 3.3.3 Quadratic Programming Quadratic programming is how the E-V approach is typically implemented. It assumes that a farmer has a utility function which is dependent on the expected return and the associated return variance as discussed in previous section. As suggested in the portfolio selection theory by Markowitz (1952), the main objective of a farm model, incorporating uncertainty, is to minimize the overall portfolio variance for alternative levels of expected returns, e.g., gross margins or farm incomes. The most risk-efficient E-V set of farm plans can be derived by minimizing the variance of the gross margins or farm incomes for all possible activities subject to an expected total gross margin (farm income) and other resource constraints. Of course, minimizing variance subject to achieving a specific expected total gross margin is, at a general level, equivalent to maximizing a weighted sum of expected return and variance of return. Thus, model equations (3.3) can be rearranged accordingly. In this adjusted quadratic programming model set-up, the variance of the overall return is an aggregate of the variability of its individual enterprise returns, and of the covariance relationships between them. Note that the covariances of the individual enterprise returns are important in the decision-making process as they determine the degree of diversification among all selected activities. As we recall the consequences of portfolio diversification, activity combinations with negatively correlated returns will show a smaller combined return variability, however, at the cost of lower expected and combined returns. The covariances between individual returns allow the associated Chapter 3 52 activities, in context of a diversification among farm activities, to act as hedging means against risk (Hazell, 1986). The expected returns for each activity define Lambda. Lambda (X), which is a scalar of the aggregated expected returns of all activities or of the farm plan, is the key element in the quadratic risk model. Assuming that the actual returns of different activities are stochastic and can be characterized by their individual distributions and means, then by varying lambda, the decision maker is in the position to indirectly qualify her/his degree of risk aversion. Hence, if the decision maker chooses a relatively lower lambda, ergo a lower overall expected operation's return, s/he reveals a higher risk-aversity and, subsequently, favours less risky activities. And by varying lambda from zero to the maximum value that can be achieved within all given farm operation constraints, the decision maker can derive the feasible E-V farm plans set along the efficient E-V boundary. Continuing this parametric process of increasing Lambda will lead to a situation where the quadratic programming approach will equal the linear programming case of maximizing farm return subject to numerous constraints. This point is reached as soon as the maximum value for Lambda is chosen or exceeded. When the most efficient E-V farm plans set has been produced, the decision maker can choose the most desirable farm plan from the efficient E-V boundary. Citing Hazell (1986, p. 80): "Given an E-V expected utility function, then for a risk averse farmer the iso-utility curves will be convex when plotted in E-V space (Figure 3.2). That is, along every iso-utility curve the farmer would prefer a plan with a higher V only if E were also greater (i.e., dE/dV > 0), and [...]. The farmer should then rationally restrict Chapter 3 53 her/his choice to those farm plans for which the associated income variance are minimum for given expected income levels." Figure 3.2: The Optimal E-V Farm Plan Set ThQ optimal E-V farim plan It is the objective to derive the set of feasible farm plans complying to the property that the variance V is minimum for associated expected income levels E. The focus is on the efficient E-V pairs which are located on the efficient boundary over the set of all feasible farm plans (Segment OQ in Fig. 3.2). If the components of the decision maker's expected utility function were known, an optimal farm plan could be rigorously identified. Such a farm plan would provide the farmer with the highest utility and could be represented by farm plan P in Fig. 3.2. However, lacking the parameters of the farmer's utility function, it is the best approach to develop a whole set of feasible farm plans, and to let the decision maker choose which of Chapter 3 54 these farm plans s/he considers the most suitable, a choice that will express the interdisciplinary of the farmer's management objectives. In the case of the depicted backgrounding operation, such a farm plan might comprise placement decisions for September and November feeders either owned, and/or owned and hedged, and/or custom fed. The selected farm plan is thought to be the backgrounding management's best response to balance its individual degree of risk-aversity. Studies that have employed quadratic programming in beef or livestock management are sparse because of the problems in linking the activities for feed and animal production in a manner that would preserve the risk attributes of variable feed production. Nevertheless, some of the studies undertaken characterize quite well the possibilities and limitations of quadratic programming in livestock management. "Recognizing the substantial variation in equity and income of cattle producers and feeders in the 1970's due to wide variations in prices of cattle and purchased feed, Whitson et al. (1976) developed a multiperiod quadratic programming model to examine the potential for vertical integration (retention of calf ownership through to finishing) to reduce income variability. Whitson concluded that using vertical production alternatives in ranch planning was an effective response to risk, but that such alternatives should not be evaluated independently of other risk responses. Falatoonzadeh, Conner and Pope (1985) conducted a portfolio analysis of risk management options available to farmers to determine which strategy or strategies were most effective in reducing variability in net farm income. Specifically, they simultaneously examined five risk management strategies: crop diversification, futures market hedging, Chapter 3 55 forward pricing, cotton seller's call option and the federal crop insurance program (FCIP) for a representative dryland farm in Knox County, Texas. Participation in FCIP at high production-guarantee and price-election levels was found to motivate futures market participation and production uncertainty appeared to have a greater effect on income than price uncertainty (Freeze, 1989, p: 110)." The Portfolio Problem in Context of the Backgrounding Operation: The E-V analysis extends to the problem of portfolio selection. Instead of considering choices of an all of this or all of that nature, portfolio selection is concerned with situations where combinations of risky prospects are feasible and persistent. In the context of our backgrounding decision making problem this implies, for example, that rather than having a decision problem of hedge or not to hedge, various combinations of hedging and not hedging would be considered. Another example would be that it may be risk reducing (through the capture of time) to simultaneously produce different types of cattle. It is the objective to select the portfolio that maximizes the backgounding management's expected utility. The shift from the all to nothing choice problem to the portfolio problem is straightforward. However, in the portfolio problem the shape of the EV efficient set boundary is the result of imperfect correlations between risky prospects in the portfolios and the assumption that the decision maker is risk averse (see figure: 3.2). The resulting E-V efficient sets are influenced by the diversification effects, which depend on the degree of correlation among potential activities, the number of activities in the portfolio, and economies of size. Chapter 3 56 The latter one, which reduces average cost as production increases, favors specialization and, subsequently, might offset the loss in risk reduction which would have resulted with diversification (Freeze, 1989). However, it is widely recognized that substantial economies of size exist for an entire cattle operation. Cost reductions occur because of the spreading of fixed costs (feed mill, forage and silage storage facilities, hospital pens, feeder and water delivery systems), marketing power and specialized management (better price forecasting, preventative care, nutritional information). Under these aspects, it can be expected that the general notion of economies of size does not jeopardize the potential in risk reduction through portfolio selection. 3.4 Hedging with Futures Markets Hedging with cattle futures contracts is one of the key decision variables for risk management in this backgrounding model. In order to understand why hedging with cattle futures contracts can cushion return risk, this section will first highlight the principles of hedging with futures markets. Second the theory of the optimal hedge will be presented, and, third, an overview of literature relating to using hedging strategies in a feedlot environment will be reviewed. 3.4.1 The Principles of Hedging The concept of hedging is based on the principle that prices in the cash and the futures market tend to move together. Although this relationship may not be perfect, it is usually sufficiently close such that a farmer can reduce her/his price risk in the cash market by taking an opposite position in the futures market. By pursuing such a strategy, losses Chapter 3 57 in one market are countered by gains in the other market (Gaspar, 1994). The following example9 will shed some light on this mechanism. Suppose a backgrounding operator plans to place 50 head of steers (each 450 lbs.), which s/he expects to be finished for the cash market in August. It is now October and the operator is uncertain about the outlook for cattle prices in next year's firushing month. The manager expects the animals to finish with about 950 lbs. Satisfied with the current price of August Feeder Cattle Contract prices trading on the Chicago Mercantile Exchange (CME) (i.e., after subtracting the expected basis10, the price that remains will be sufficient to cover the per lb. cost of production) s/he decides to hedge the entire group of animals against price risk by selling (going short) one 50,000 lbs. contract of August feeder cattle which s/he will offset shortly prior to the actual selling date in August. The following discussion provides a detailed description of the hedging procedure. It should be noted that the US$/Cdn.$ exchange rate is kept constant, and that the prices stated are for explanatory purposes only. Step 1: The backgrounding operator must open an account with a Futures Commodity Merchant. This involves the filling in and signing of: a new client commodity application form, a margin form, a risk disclosure form, and in the case of a hedger, a hedging agreement. The hedging agreement confirms that all the trades made by the Much of the following paragraphs on how hedging works relies on material discussed in the Self Study Guide to Hedging with Livestock Futures published by the Chicago Mercantile Exchange and on the MSc. thesis by Victor Gaspar, 1994 Basis = Cash Price - Futures Price Chapter 3 58 backgrounder will be for the sole purpose of hedging. Speculative trades must be done through a different account where they will be margined at a full speculative margin. Step 2: In October, the backgrounder places a short-hedge order for one 50,000 lbs feeder cattle futures contract with August delivery which are trading at $94.27 per cwt. The operator expects the cash price at the time of delivery to the local cattle market to be $91.60 per cwt. The backgrounder has based this expectation upon the expected value of the basis which s/he believes will equal the current basis. Once the short-hedge order is placed, the backgrounder must provide an initial margin. The initial margin required by the CME in this case would be $866.67 (US$650 per contract times US$/Cdn.$ 0.75) or $1.73 per cwt. Step 3: In August, the operator offsets her/his position by purchasing one 50,000 lbs. August feeder cattle contract at $87.33 per cwt., and s/he sells her/his cattle to the local cattle auction market for $84.67 per cwt. Table 3.1 below summarizes the farmer's transaction and derives her/his selling price for a single contract when the basis is assumed to be constant. Notice, that by entering the futures market the farmer has locked in a net selling price equivalent to the cash price s/he suspected would exist in August at the time of the delivery to the local cattle market. This is known as a "perfect hedge". Had the farmer not entered the futures market s/he would have received $84.67 per cwt., which is an inferior strategy. Of course, to assume that the basis remains constant may be overly simplistic, especially when time and/or local supply and demand factors can greatly affect the volatility of futures prices. Table 3.2 shows how the background operator will do when Chapter 3 59 the basis is not constant. A weaker than expected (widening) basis can reduce the effectiveness of a short hedge. Table 3.1: Short Hedge Scenario Under Constant Basis and Exchange Rate Cash Market Cdn.$ Futures Cdn.$ Basis Cdn.$ October August Expected Sell 91.60 84.67 Sell Aug. Buy back 94.27 87.33 Expected Actual -2.67 -2.67 6.93 Cash Price Gain Fut. Net Price received 84.67 6.93 91.60/cwt. as expected Table 3.2: Short Hedge Scenario Under Widening Basis and Constant Exchange Rate Cash Market Cdn.$ Futures Cdn.$ Basis Cdn.$ October August Expected Sell Cash Price 84.67 91.60 84.67 Sell Aug. Buy back 94.27 88.67 Expected Actual -2.67 -4.00 6.93 Gain Fut. Net Price received 5.60 = 90.27/cwt. lower than expected As demonstrated in above examples, the basis, the relationship of the local cash market price for cattle and the underlying futures contract price, is important for the desired hedge performance. By knowing the likely basis mean one can translate an available futures price for deferred delivery into an expected cash price that will result from an anticipated hedge. Hence, since the basis reflects factors like: 1. Availability and cost of transportation Chapter 3 60 2. Supply and demand conditions in the cash market relative to delivery points for the futures markets 3. Quality differences between the cash commodity and the product specified in the futures contract 4. Availability of storage at the cash market relative to the futures market etc. (Blank, 1990), which are more of structural character and will therefore lead to a more limited basis variability, it is the hedger's objective to trade the wider cash price variability with the more confined basis variability! Knowing the expected basis and the expected cost of production, the backgrounding operator can establish a local cash price for her/his feeders and can decide whether or not to place a short-hedge position. The example above assumes one other simplification, that is, that the futures price movement would be favourable. The futures selling price at placing time is higher than the average futures purchase price at lifting time, thus reflecting an upward BIAS. However, if the futures selling price at placing time is lower than the average futures purchase price at lifting time (downward BIAS), then not only might the farmer be required to put up additional margin money, but s/he would be better off not entering the futures market. For the latter case, the farmer would expect to make a loss on the hedge transaction. As with the basis the BIAS is also important for the hedging performance: e.g., a downward BIAS on average reduces the overall return prospects, hence, higher hedging costs will deter cattle-hedging interested persons. Chapter 3 61 Helmuth (1981), referred to such a situation, when he argued that a systematic downward BIAS for the live cattle futures contract would deter beef-cattle-hedging interested persons from utilizing these contracts for reducing spot market induced return variability. Yager (1981), however, rejected Helmuth's argument vehemently. When facing higher hedging costs, the backgrounding management must confront the question of whether or not an overall expected farm return reduction, caused by increased hedging costs, is justifiable for an achieved reduction in the overall farm return variation. Ergo, if BIASes increase, the question of the risk-return trade-off becomes even more imperative for the short-term decision maker, and should lead to a situation, where hedging activities become non-attractive elements in a cattle management's decision set. In this study we will impose a downward BIAS in order to demonstrate the backgrounding management's responses to the persistent question of the risk and return trade-off caused by downward biased hedges. Nevertheless, in context of the discussed expected value-variance analysis, the relation between the cash and the futures market provides a risk management tool for the risk averse cattle backgrounder. As we recall, the expected income-variance (E-V) criterion assumes that a farmer holds preferences among alternative risky farm plans solely on the basis of their expected incomes and associated income variances. Subsequently, the more nervous a farmer is, the more likely s/he will pursue a price risk minimizing hedging strategy. Chapter 3 62 3.4.2 Theory of the Optimal Hedge As illustrated in previous section, feeder cattle producers have a valuable tool which can allow them to shift price risk to speculators. E.g., feeder cattle futures contracts, traded on the Chicago Mercantile Exchange, can be used to hedge for example the sale of feeder cattle. Hence, a cattle backgrounder can sell feeder cattle futures to "lock in" the price of feeder cattle that will be coming from pasture. This section will shed some light on how the optimal hedge can be found, and how an assumed downward BIAS will affect the optimal hedge. In order to investigate the optimal hedge position and the impact of a downward BIAS on hedging, a simplified hedging model is constructed employing the E-V theory developed by Markowitz. By neglecting production and hedging costs one can establish equation (3.7). Equation (3.7) derives the net revenue (71 ) received when a feeder (X) is sold at the spot market for a price of Ps, and its underlying short-hedge position, number of feeder cattle futures contracts (h) sold for a futures contract price of f0 at the hedge placing time, is lifted at the end of the hedge holding period at a futures contract price of /]. Equation (3.7) corresponds with the net price received rows in tables 3.1 and 3.2. If there are only two risky assets, the cash commodity (number of feeders) and the corresponding futures contracts, then the expected net revenue (E(n)) on this portfolio can be expressed as equation (3.8). it = PsX + (f0-fl)*h (3.7) E(n) = X = PsX + (f0-fl)*h (3.8) Chapter 3 63 Similarly, the variance of net revenues is Var(n) = X* *Var(Ps) + h* *Var(f) -2Xh* Cov(Ps,/,), (3.9) where Var(fx) is the variance of the revenues from holding a futures position, Var(Ps) is the variance of revenues from holding a cash position, and Cov(Ps,/,) is the covariance between the revenues from holding a futures position and the revenues from holding a cash position. Now, as suggested by Markowitz (1952), the main objective of this simplified hedge model is to minimize the net revenue variance subject to a level of expected net revenues. Hence, setting up a Lagrangian expression as in equation (3.10) gives where P is a Lagrangian multiplier. If the level of the cash commodity is given (i.e., if X is given), one can determine the optimal futures market position by differentiating the Lagrangian function with respect to h. This yields the F.O.C. in equation (3.11). L=X* *Var(Ps) + h* *Var(f)-2Xh * Cov(Ps ,/,) + P *[k - PSX - (f0 -/,) *h] (3.10) dL dh = 2r.*var(/1)-2X*cov(/'s,/1)-P*(/o-/1) = 0 (3.11) In order to reveal the optimal hedge ratio, which represents the most desirable combination of cash and futures positions, equation (3.11) is divided by 2X. var(/ 1 )-cov(P s , / 1 )- P *(/o-/i) = 0 (3.12) 2X Chapter 3 64 h Solving equation (3.12) for the optimal hedge ratio (—) yields equation (3.13). X Bias component / * V h ^ T * ( / o - / , ) + COV(P s , / I ) — = -2^  = (3.13) X var(/,) The first interesting finding is that the optimal hedge ratio will not depend on the degree of risk aversion. This means that regardless of their levels of risk aversion, backgrounding managers, who have the same expectations regarding returns and variances of cash and futures positions, should employ the same hedging ratio. The second finding is with regard to the BIAS of the hedge position's underlying futures prices (BIAS = / , - fQ). If we assume a BIAS of zero, then the BIAS component term in equation (3.13) does not materialize, and the optimal hedge position is specified by the ratio of the covariance between the spot market and futures market prices and the variance of the futures market prices. If we further assume a perfect correlation between these two market prices, that is c o v ( P 5 ) = var(/,), a hedge ratio of one will result. We call the latter case a perfect "textbook" hedge, where the price risk is totally eliminated. However, as soon as a downward BIAS is present, implying that the expected futures price at lifting time exceeds the futures price at placing time, the nominator of the hedge ratio equation (3.13) declines, causing the hedge ratio to be smaller than one. This relation illustrates why a downward BIAS deters from using hedging with cattle futures contracts as means to reduce revenue risk in cattle backgrounding. A similar situation Chapter 3 65 arises when the relation between the cash market and futures market prices is less than perfectly correlated. Importance of Basis Changes: The basis was defined as the difference between a cash price and a futures price. It is the idea of a hedge to trade the price risk of a cash position with the basis risk of a futures position, the variance of the basis is thought to be smaller than the variance of the price of the cash position. Hence, as soon as an operational hedge is placed, the hedger becomes concerned primarily with basis changes rather than changes in the absolute price level. An operational hedge speculates on the basis. The reason why the basis is of utmost importance is that the profitability of the hedge is largely determined by the basis behavior. If the hedge is lifted at the same basis which prevailed when the hedge was initiated (a "textbook" hedge), the hedger receives exactly the expected price prevailing on the date the hedge was initiated. As the basis often changes, this rarely occurs. The financial impact of a basis change on a hedger's hedge revenue is as follow: a short hedger (the example of a cattle backgrounder) gains financially from a narrowing" basis and loses from a widening12 basis. The impact of a basis change on a long hedger is exactly the reverse. Being able to predict basis changes facilitates the timing when to place a hedge position. If, for example, the basis is large and expected to decline, then e.g., a grain Cash price gains on the futures price. Cash price falls relative to the futures price. Chapter 3 66 merchant will take a long spot position and a short futures position (going short). If a cattle producer had a similar expectation for corresponding cattle futures, s/he would also go short in the futures markets. In general, it is easier to predict the basis for storable products than for non-storable products. Usually, the basis for storable commodities is at its widest levels in the immediate postharvest period, with a gradual narrowing over the course of the year. There is an upper theoretical limit to the size of the basis which is equal to full carrying costs, and the spot and futures prices will converge during the futures delivery month as the costs of storage approach zero. For non-storable commodities, such as feeder cattle, basis patterns are not as recurrent and predictable as in the case of storable commodities. That is why ranchers engage in anticipatory hedges, the type of hedge a rancher would enter into in the fall of the year if s/he were hedging her/his feeders to be sold in the late summer of the next year. "Therefore, hedging to profit from basis changes is not really relevant in these markets. For example, a feedlot manager would not buy feeder cattle and sell live cattle futures which mature after the feeding period (approximately six months) simply because of a wide basis. The feeder cattle cannot be placed in a warehouse and forgotten about! They must be fed daily and then sold for slaughter. During the feeding period the hedge cannot be easily lifted until the cattle are finished. For the fundamental reason that the storage activity cannot provide a linkage between the current supply of feeder cattle (or any other perishable product) and the demand 12 months, hence, carrying-charge markets and declining bases over time are not necessarily observed in nonstorable markets (Blank, 1991, P: 227)". Despite the apparent difficulty to establish recurrent basis patterns, the Chapter 3 67 observation of a widening basis in the fall might help to find the best point in time to place a short hedge. This study, however, applies an anticipatory hedge when the feeders are placed in the fall, which is later lifted one month before the animals are sold at the spot market. The placement and lifting time of the hedge positions do not follow a favourable basis opportunity. 3.4.3 Review of Hedging Literature Relating to Feedlot Management Although the economic effectiveness of hedging cattle has been widely discussed in literature, its worthiness is still disputed. Whereas most U.S. studies done in this field conclude positively with respect to the risk minimizing possibilities of certain cattle hedging strategies, the sparse Canadian counterpart is undecided. Obviously, a Canadian wishing to hedge a commodity such as feeder cattle or live cattle must use contracts traded at the Chicago Mercantile Exchange. This involves unusual difficulty for a Canadian producer due to different currencies, grades and, most of all, the fact that s/he is dealing with two different countries. Caldwell, Copeland and Hawkins (1982) has been one of the few papers that examined the feasibility of a Canadian feedlot producer using U.S. futures markets to hedge specific products. Two inputs (barley and feeder cattle) and one output (fat cattle) had been hedged by the underlying futures contract. They concluded that during the time of September, 1975, to January, 1978, an Alberta feedlot operator could have increased her/his income level by hedging, but in doing so, s/he would have incurred a greater degree of instability. They attributed this instability to the fluctuating exchange rate and the highly unpredictable Chicago live cattle contract. The latter finding coincides with Chapter 3 68 Helmuth (1981) who found the U.S. live cattle futures market operates with a consistent downward price bias. Carter and Loyns (1985) also analyzed the usefulness of the U.S. futures markets to reduce the price risk exposure for a western Canadian feedlot operator. Being supplied with data on 100,000 head of custom feeders in Western Canada, capturing a decade, their case study tested following four hedging strategies: (1) routine insurance hedge or "classic" hedge, (2) "naive selective" hedge or forward pricing that was placing a hedge if profit conditions were favorable, (3) an alternative form of selective hedge that was placed within the first weeks after the feeding period had commenced as long as critical profit levels were satisfied, and (4) a "threshold" strategy that only placed cattle on feed and hedged them if threshold levels of price and profits were met. Input factors like feeder cattle, barley and interest rates were not subject to any hedging strategy. The "threshold" strategy yielded higher profits with lower price risks, however, the numbers under this strategy were too small to guarantee the continuity of a feedlot business in function. The routine hedges resulted in reduced or in some cases even negative returns and increased surprisingly price risk levels in the period in question. By removing the exchange rate risk the authors were able to improve the hedging strategy results — concluding that the exchange risk did certainly contribute a considerable amount of price risk to the return function. Carter and Lyons attributed the poor hedging results to the erratic behavior of the finished cattle basis. Not totally rejecting the hedging-induced price risk minimizing effects, their research concluded that more appropriate hedging strategies might be designed if the under lying parameters of the basis were more understood. Chapter 3 69 Freeze (1989) investigated risk-minimizing strategies for feedlot finishing of beef cattle in Southern Alberta. The strategies included hedging of cattle on feed, participation in the National Tripartite Stabilization Plan and diversification of production plans. Of primary concern was to evaluate the efficacy and interaction effects of these strategies in reducing net income variability in cattle feeding. The Expected Value-Variance (E-V-Criterion) and safety-first risk analyses were chosen as suitable mathematical frameworks to address the feedlot management problems. Linear risk programming models (MOTAD) were than established to test the alternatives for reducing income risk. The results suggested that, at moderate levels of risk aversion, feedlot managers should maintain high levels of hedging of both live cattle and the Canadian dollar with moderate participation in the stabilization plan. The study showed significant portfolio effects. Hedging was found to increase output levels by increasing the finishing weight. Participation in Stabilization was found to reduce hedging by 10%. Hedging of the Canadian dollar improved the performance of live cattle hedging. However, this study did not take a position on what risk minimizing strategy is more efficient. In conclusion of this hedging review, it can be expected that output levels of price riskier activities will increase if hedging possibilities are provided. Further, a complete hedge might be undertaken when the expected futures market price is equal to the current futures market price, as long as necessary cash requirements are satisfied, otherwise a partial hedging strategy might be the most optimal price risk minimizing solution. Chapter 3 70 3.5 Summary This chapter explained how return risk concerns can be incorporated into the decision making process of a backgrounding operation. First, the theory of choice under risk was addressed which led to the Expected-Value Variance Criterion. After reviewing the more prominent risk programming frameworks, the quadratic programming model has been chosen to anticipate output price induced return risk, since a linear framework would not adequately simulate the variability of revenues for possible activities by parametrically changing output prices. In addition, the quadratic programming framework, because of its intuitive set-up, is appealing with respect to the objective of minimizing the backgrounding return variance and can easily accommodate and illustrate the question of risk and return trade-offs for the activities in the management's decision set. The chapter concluded with the hedging principles for cattle futures positions, highlighting not only the relation between spot market and futures market prices but also the one between the futures purchase and futures selling price (BIAS). 71 CHAPTER 4 4. Empirical Model This chapter outlines the activity alternatives that form the basis of the decision set inherent in the depicted short-term backgrounding operation management problem. A description of the quadratic risk programming model is given followed by its empirical notations. An outline of essential cash flow constraint coefficient will conclude this chapter. 4.1 Activi ty Alternatives The backgrounding model anticipates three categories of activity alternatives in the management's decision set: animal placements, hedging with futures contracts, and activities that do not directly affect the variability of overall farm returns. 4.1.1 Animal Placements The animal placement alternatives and their specifications in the backgrounding operation model are based on experiences gained from actual placements in previous years on Clover Farms Ltd. 1 3 and on industry practices (Albin, Robert C. and G. B. Thompson, 1990). Feeders can be placed in September, October and November, later referred to as fall feeders, and are managed under a blend of "Grassers" and "Drylot Backgrounding" for larger framed exotic crossbred cattle (e.g. Hereford-Simmental crossbred steers). Fall feeders arrive at 450 lbs., are fed on a threefold feeding regime ("Starter" ration, 3000 custom feeders have been fed annually for the last couple of years (1993, 1994). Chapter 4 72 "Growing" ration14 and two months summer pasture) that makes them gain 500 lbs. after a 10-month period (950 lbs. at the end of the feeding period). The fall feeders are taken off the backgrounding operation in July, August and September15 depending on their placement months. Fall feeders can be placed as custom feeders and/or backgrounding operation owned feeders. To increase the usage of the 3,000 head winter feeding confinement and to spread the cash in-flows, a May animal placement alternative is provided. This type of animal consists also of a larger framed exotic crossbred cattle (e.g. Hereford-Simmental crossbred steer) but is placed at 700 lbs., is fed on a twofold feeding regime ("Welcome" ration (20 days) and a "Finishing" ration16 (for the remaining 100 days)) that enables it to gain 375 lbs. in a 120-day period (1,075 lbs. finishing weight). This type of placement is considered to be a light slaughter cattle production. The May placements are taken off the backgrounding operation in September. May feeders can also be placed as custom feeders and/or backgrounding operation owned feeders. The cattle placement alternatives are limited to eight choices (i.e. 15SSO, 150SO, 15NSO, 15MSO, 15SSC, 150SC, 15NSC and 15MSC). As for the notation the following system applies: the number and the first letter refer to the placement date, the second letter relates to the sex17 of the ariimal and Starter and Growing ration are feed rations developed in the feeding regime (appendix 5) The production year of the modeled backgrounding operation starts from September 15. and ends on September 14. of the following year! Welcome and Finishing ration are feed rations developed in the feeding regime (appendix 5) In the cattle placement notations, e.g., 15SSO, the sex of animals is specified. However, due to software limitations, heifer placements were not considered. The specification of the animal's sex results from a previous notation and is somehow redundant. Chapter 4 73 the last letter specifies the kind of ownership (e.g. number of owned steers placed on September 15. — 15SSO). However, to facilitate the linkage with hedging activities, the model calculations are conducted in hundredweights (cwt.) placed in corresponding months. For consistency reasons, this applies also to the custom feeder alternatives even if they are not subject to overall return risk-minimizing hedging strategies; note, their revenues generate from fixed custom feeding rates! The cattle placement alternative of owned animals is represented by the variable x (cwt. placed of owned animals) whereas custom feeding is depicted by the variable z (cwt. placed of custom fed animals) in the empirical model notation (see section 4.2). However, solutions will be reported in the first format — that is on a head basis! Because each animal placement alternative is comprised of a specific production and marketing strategy, average gross margins18 for each of the alternatives have been calculated; optimal feeding regimes or target finishing weights are not in the model's focus. Instead the gross margin variations of the feeder placement alternatives and the monthly cash flow requirements for each placement alternative, and also for other backgrounding operation related commitments, within the production year are of particular interest. Gross margins are thought to vary with the variation of their associated selling prices19 only, because it is assumed that when the cattle are placed their futures The cost side of the average gross margins accounts for initial costs, ration costs, bedding costs, medicine, processing and death loss. Interest charges on initial costs and on ration cost were not included since the model, to emphasize the opportunity cost concept, provides off-farm investment alternatives. Purchase prices and selling prices for the Edmonton-Alberta region were provided by C A N F A X . Chapter 4 74 selling prices remain the only virtual unknowns in the depicted backgrounding management problem. In other words, it is assumed that at the feeder placement time all other placement related costs are known. Having weekly time series of spot selling prices on hand, the backgrounding management can calculate possible gross margin outcomes, and by substituting the selling price of each feeder alternative with the average spot selling price from these time series, the management can produce the average gross margins for each of the feeder alternatives. For a visual presentation of these gross margin variations, please refer to the simplified example in table 2.3. Gross margin variations apply only to the category of animals owned by the backgrounding operation. The average gross margins of cattle placement alternatives are part of the expected return constraint, Lambda. The quadratic risk programming model minimizes the variance of cattle gross margins (objective function) subject to cash flow, placement and other constraints by selecting an optimal farm plan that obeys the expected overall farm return constraint, Lambda. As discussed, by changing Lambda the backgrounding operation management can express its degree of risk-aversity. 4.1.2 Hedging with Futures Contracts In order to reduce the selling price induced gross margin variation, the model offers activities to hedge with cattle futures markets contracts. Originating from the idea of a "classical" or anticipatory hedge the backgrounding management can utilize Feeder Cattle Futures to reduce the gross margin variation for fall feeders and can apply in a similar fashion Live Cattle Futures for the May feeder category. Both contracts are traded Chapter 4 75 at the Chicago Mercantile Exchange. Subsequently, the backgrounding operation management can reduce the selling price induced variation of the gross margins by placing an appropriate short hedge (selling a Futures contract with a delivery date close to the finishing date of the corresponding cattle placements) at the time the animals are placed in the amount of hundredweights of beef to be delivered at the end of the backgrounding period. In a second step, the management then lifts this short hedge (buying back a futures contract) prior to the actual spot market delivery. This procedure complies with industry standards.20 Table 4.1 summarizes the cattle futures contracts as used in the model. Table 4.1: Cattle Futures Contracts in the Backgrounding Operation Model Futures Contract For Delivery (month) Place Short Hedge (month) Lift Short Hedge (month) Hedge Duration (months) 15SSH Feeder Cattle August September June 9 150SH Feeder Cattle August October July 9 15NSH Feeder Cattle Sept. November August 9 15MSH Live Cattle October May August 3 Annotation: Trading unit of Feeder Cattle Futures: 500 cwt. of feeder steers; Trading unit of Live Cattle Futures: 400 cwt. of choice grade steers. The hedging alternatives are limited to four choices (i.e. 15SSH, 150SH, 15NSH, 15MSH). As for the notation, a similar system as for the cattle placement alternatives applies: the number and the first letter refer to the placement date, the second letter relates to the sex of the animal, and the last letter specifies a hedging activity (e.g. number Phone conversation with Taylor, Douglas. J., Richardson Greenshields, July, 1995 Chapter 4 76 of futures contracts bought on September 15. to hedge steers — 15SSH). The model calculations are conducted in hundredweights (cwt.) of placed steers hedged in corresponding months. This is done in order to link the hedge alternatives with the cattle placement activities. In the empirical model notation, the hedge alternatives are expressed by the variable y (cwt. of placed steers hedged). Again, solutions will be reported in the first format, that is on a contract basis! As for the hedging costs, the following components are considered: futures contract price at the hedge placing time, futures contract price at the hedge lifting time, brokerage fees and margin calls. However, the latter ones are, depending on the sensitivity analysis, not considered at times. In addition, as indicated in the section concerning the principles of hedging with futures (section 3.4.1), to accommodate some analyses on the change of optimal farm plans if the BIAS between the average futures lifting and futures placing price changes, a BIAS parameter is introduced that will drive a wedge between the futures placing price from the average futures lifting price. In the same fashion as with the feeder gross margins, hedging costs vary with the variation of their underlying futures purchase prices at the hedge's lifting time. This follows the same logic as before, as at the time the backgrounding operation management engages in a futures contract hedge, it does not know the underlying futures purchase price at the end of the hedging period. The average costs of the hedging alternatives are part of the expected overall farm return constraint, Lambda, whereas their associated futures purchase price fluctuations are tied into the objective function. Chapter 4 77 4.1.3 Off-Farm Investment, Outside Financing and Structural Costs The returns or costs of off-farm investments, outside financing, and structural (i.e., fixed) costs are also part of the expected farm return constraint, Lambda. However, they do not contribute to the overall variance of the optimal farm plan's return, and are therefore not directly addressed in the objective function. They are introduced into the model to assure a more real world simulation of a backgrounding operation management's decision set. Their construction follows common practice in the banking industry and on Clover Farms Ltd. Off-Farm Investment Alternatives: The backgrounding operation management can invest funds temporarily available within the production year in term deposits. The money invested is locked in for 90 days and yields a discounted interest return. Four consecutive investment opportunities are provided: Inva (Sept. - Dec), Invb (Dec. - March), Invc (March - June) and Invd (June -Sept.); also, by making these off-farm investments available, the concept of opportunity costs will play into the selection of optimal farm plans. In the empirical model notation these off-farm investment alternatives are depicted by the variable /. Outside Financing: To ensure a smooth operation of the backgrounding operation, a line of credit is established. This line of credit is in accordance with the rules of the B.C. Credit Union in Fort St. John.21 The fixed annual-interest-rate line of credit can be accessed on a monthly Phone conversation with Creg Sutherland, 1995 Chapter 4 78 basis. The management pays interest only on funds actually used and must deposit a percentage of previous overdrafts each month. This feature guarantees that the actual interest rate paid, at the end of the year, is much less than the high fixed annual interest rate. Twelve borrowing activities are considered in the backgrounding operation's decision set. Structural Costs: Most structural costs like maintenance and replacement of equipment, insurance, fuel, phone, etc. are already considered in the feed ration costs which are part of the gross margins of the cattle placement alternatives. However, labour costs allocated to the backgrounding operation are forced into the model by their own activity. This is different to charging a yardage fee per head. The reasoning for this method is that in the considered short-term decision making problem labour costs are of quasi-fixed cost character. They should not change depending on the number of animals placed! The unit of this activity is one. 4.2 The Backgrounding Operation Quadratic Risk Programming Model At this point, before detailing the quadratic objective function and its associated constraints, we will state the backgrounding model in general terms. This statement will not consider the hundredweight conversions as indicated above and will only regard those activities in the backgrounding management's decision set that provide positive returns. The general statement of the problem intends to summarize the assumptions and Chapter 4 79 specifications made so far and to make the reader familiar with the empirical notations to come. 4.2.1 General Statement of the Problem Let P( denote the gross margins ft denote the Futures price when the hedge is lifted f0 denote the Futures price when the hedge is placed c denote the custom feeding fee z denote the off-farm investment return Xt denote the number of placed owned animals Hi denote the number of hedged animals Xf denote the number of custom fed animals /„ denote number of off-farm investments / = particular placement month (Sept., Oct., Nov., May) m = particular month (Sept., Dec, March, June) then Overall farm return: li = £ P, X, + £ if0 -f)* Hi + £ PfXf + 5>m/B (4.1) m Lambda constraint: A, = E(JC) = 23X* + -fi)*H, (4.2) Variance of overall farm returns: Var(n) = ^ X? *Var(Pi) + Y,H? *Var(f) • 2 £ J^Xi*Hj*Cov(Pi,fj) (4.3) Chapter 4 80 The main problem facing the backgrounding management is now to choose Xt, Hit Xf and Im in order to minimize the variance of overall farm returns (Var(n)) subject to the Lambda constraint (k) and to a set of feeder placement and monthly cash flow constraints. The latter two types of constraints are not depicted in the above general statement; they would be of linear character. Lambda is parametrically varied in order to trace out the E-V frontier of the optimal farm plan set (see figure 3.2). The derivation of the objective function (Min Var(ji )) requires some consideration, especially with regard to the variance and covariance terms. The variance and covariance terms are estimated by applying the Forecast Error method. The specific calculations of these objective function parameters are discussed in the next section. 4.2.2 Using the Forecast Error Method to Obtain Parameter Estimates This section explains the derivation method for the parameters of the backgrounding objective function, given in equation 4.3; note, that P is now prices per hundredweight. In the backgrounding operation model, hedge-placement activities are available as instruments of portfolio adjustments to the management which is concerned with return volatility. At the time when the decision of a possible cattle placement is made, the backgrounding management knows the feeder's spot purchase price and the futures price of the appropriate hedge position. However, the spot selling price at the feeder's finishing time and the close-by futures lifting price are unknown. Recalling the theoretical convergence of the future spot price and the futures lifting price, the futures price at the Chapter 4 81 time of the feeder placement can be used to determine the correlation between the spot and futures price, and, henceforth, to estimate the parameters of the quadratic programming objective function. It is assumed that the backgrounding management, in accordance with a "classical" hedge, can enter the futures market (e.g. in September) with a feeder futures contract which matures in August of the following year. To lift the hedge position, the management offsets its position in the cattle futures market one month before it sells its finished steers (July) to the local spot market in Edmonton. Time frames and data requirements for all hedging alternatives are displayed in table (4.2). Table 4.2: Data Requirements for Rolfo Forecast Errors For Delivery N Place Short Hedge Weeks ] (f) Years I.in Short Hedge Weeks 1 (f) Years Spot Selling Price Weeks 1 (PS) Years 15SSH Feeder, August 12 Sept. (36, ! 37, 38, 39) ] 91,92, 93 June (23, i 24, 25, 26) ] 92, 93, 94 July (27. J 28, 29, 30) | 92 94 150SH Feeder, August 12 Oct. (41, ! 42, 43, 44) ' 91,92, 93 July (27, ! 28, 29, 30) | 92, 93, 94 Aug. (32, ! 33, 34, 35) j 92, 93, 94 15NSH Feeder, Sept. 12 Nov. (45, J 46, 47, 48) i 91,92, 93 Aug. (32, j 33, 34, 35) i 92, 93, 94 Sept. (36, ] 37, 38, 39) i 92, 93, 94 15MSH Slaughter October 16 May (18, \ 19,20,21) ] 91,92, 93,94 Aug. (32, | 33, 34, 35) ] 91,92, 93,94 Sept. (36, ] 37, 38, 39) j 91,92, 93,94 Source: f a n d / : Stats. Database, Chicago Mercantile Exchange, Raw data on daily trading, Jan 1990 - May 1995 and US/Cdn-Exchange rate, C A N S I M , daily basis. P5: Database: Cash market prices of all weight classes for the Edmonton-Northern Alberta Region, C A N F A X , weekly basis, Jan. 1991-week 29. 1995. Following the Rolfo method (1980), one can express the forecast errors for the September hedging activity (15SSH) as, Chapter 4 82 Ps ~ fs fs - f? e f tv = — — , E f i = — — — (4.4) J s J s The variable e Ps is the forecast error of the spot price and e f\ is the forcast error of the futures lifting price. Rolfo defines a forecast error as being the difference between realized and forecast prices divided by the forecast price. He suggests that by doing so this allows for differential rates of historical inflation. The forecast error terms of the remaining hedging activities are obtained in the same manner. A list of all forcast error terms is contained in Appendix 5. For obtaining the variances of the spot and futures prices, equation (4.4) is first rearranged in such a way that each price is a function of its forecast error, Ps =f°*(eps+l), / ^ / ""Ce , .+ 1 ) (4.5) In a second step, treating P5,/, epS and ef, as random variables, one can derive the variances of the expressions in (4.6) as, Var(Ps) = (f°)2 *Var(epS), Var(/>) = ( / ° ) 2 *Var(zfl) (4.6) Next, the covariance parameters of the quadratic risk programming objective function must be derived. These parameters are important in the risk minimizing attempt, because they link the fluctuation of one activity's return with the fluctuations of all other returns in the backgrounding model. Hence, they bring diversification and hedging effects into play. However, estimating the covariances between the spot and futures markets requires a more elabourate approach. This approach is presented in following equations. The September and November hedging alternatives are used as references. Chapter 4 83 As with the lifting futures price variances, their covariances should also be expressed by the covariances of their associated forecast errors. Expressions (4.7) summarize this thought. The left column shows the covariance development from the forecast error side, and the right one starts this process from the lifting futures prices side. f i _ f 0 f 1 _ f o Cov(fs „ / 5 , J N J N ) fs° J N <=> covin, fA) (4.7) /.9 JN Applying the general rule of obtaining the covariance between two variables22, the two expressions in line (4.7) can be expanded to equations (4.8) (Note, that the partition of the two sides continues!), = E f o v fo _y JS p JN p = E[(fsl-fsl)*(fN-fN)] (4.8) Expanding the two equations in (4.8) yields the terms of (4.9), = E fs * fh fs /N J fO fO fO fO J S J N J S J N =*[nfA]-2*fsifA+fsin (4.9) By further simplifying, one obtains the two equations (4.10), = E fs * IN J S J N fs ftl fO f 0 J S J N + 1 — E[/s fhl ] fs fh (4.10) Cov(x,y) = E[(x-x)*(y-y)] Chapter 4 84 The right hand side equation in (4.10) is rearranged and divided by the denominator of left hand side's expected value term. In a second step, the left hand side is expanded in order to converge to the right column expression (4.11), = E fs * / N fs fiv f f 0 f 0 _J S J N _ fsfS v fs _j_ fH/ fs fit .fs ffi fsffi 1 f\ ^ ) CovUlfh) fs'fS (•) cov{fsi,n) = *[fsin] nn f o f o f o f o f o f o J S J N J S J N J S J N (4.11) By substituting the right hand side expression into the left hand side expression the simplified equation (4.12) is obtained, r ( c P , covin,U) ... J S J N (4.12) And solving equation (4.12) for the covariance of both lifting futures prices yields, Cov(tt,tt) = fs°ft *[Coviefi,en)-i»)] (4.13) Expression (4.13) recovers the specific covariance between the lifting futures prices of the September and November hedging alternatives. The generic formulas (4: 14, 15, 16) are used to recover all other covariance terms of the objective function. C0Vifn\ tt) = fn°tt* CoviPns,Pj) = PnsPj* Cov(efi,efi) + ^ r7 + J n J w J n J w fO fO fOfO J n J w J n J w •1 ps ps CoviePs,£Ps) + - £ 7 + - ^ ps ps ps ps (4.14) (4.15) CoviPns,tt) = Pnstt* ps fi ps fl Cov(e p S ,e f i ) H 1 1 ^ n Jw ' pS r\ ps f\ 1 n J w 1 n J w (4.16) n,w = (S, O, N, M) Chapter 4 85 As for the parameters actually used in the model, following annotations have to be made. Originally, it was thought to generate the variance-covariance matrix from the individual data sets of each owned cattle placement and hedging activity (see table 4.2.). However, when these parameters were produced, it was felt that due to the small sample sizes, N ranges from 12 to 16 observations, the yielded parameters were not consistent and reliable. The sample size impact was unexpected! In order to make the available data set useable, the forecast errors for the fall feeder were stacked. This data adjustment assumes that the price variations of the fall feeder placement activities, either spot or futures prices, should fall within the same range. By applying the variance and covariance recovering formulas (4: 6, 14, 15, 16) on this combined data set, the resulting variance-covariance matrix turns out to be rather simplified. The variance of the selling spot price of the October owned feeder placement activity, for example, equals the one of the November owned feeder placement activity. Subsequently, similar simplifications must be anticipated for the covariance parameters. The loss of return variance minimizing effects through different owned cattle and hedge placing in the fall period must be acknowledged. Nonetheless, because the data set for the May activities produced reasonable variance and covariance parameters, this timing effect is at least still in place between the fall and May activities. The stacked forecast errors and the model relevant variance-covariance parameters are listed in the appendix 5. The backgrounding quadratic risk programming objective function minimizes the variance of overall returns. Because the actual dollar value of the overall farm return Chapter 4 86 variation is of interest, the standard deviation of the overall farm returns will be reported as a result. 4.2.3 The Objective Function and Subsequent Constraints A detailed mathematical statement of the objective function and Lambda constraint can now be specified. The objective function will be presented in matrix form, whereas the Lambda constraint will be established in non-matrix form to facilitate the model understanding. In particular, the problem facing the farm manager is to choose his decision variables. MIN Var (IT) = [ x s , y s , X o , y o , x N , y N , x M , y M ] * 1x8 Var(P s s) -coCPs'.fs1) co(P s',P6) -co(P s ' , f 0 ) co(Ps',Pfi) -co(Ps*,fA) co(Ps', Pfl) -co(Pss,fI) -coCfsJ.Ps') Var(fs') -co(f^,P6) co(f^,f 0) -co&' .Pf i ) co(U,^) -co(f>,P^) co(f>,f^) co(P6, Pi) -co(P 0 , U) Var(P 0) -co(P6 , f 0 ) co(P 0 , P£) -co(P£, f A) co(P 0 , Pj5,) -co(P 0 , f^) -co(f 0 ,P s s ) coCfo.fs1) -co(fo,P6) Var(f 0) -co(f 0 ,PA) cotfo.fA) -co( f 0 ,P^) co(fd,fi) co(P£, Ps") -co(P£, fs') co(P£, P G ) -co(PA, fo) Var(PA) -co(P£, f ) co(P£, ) -co(P^, ft) -co(fA.Ps') coCfA.fs1) -co(fA,P6) co(fA,fo) -co(fA.PA) Var(f>) -co(fA,P^) crXfA . f t ) coCPj!,, PJ) - c o ^ , f J) co(P£,, P^) -co(Pj5,, f I ) co(P^, P£) -co(Pj5,, f A) V a r ^ ) -co(P^, f &) - c o ( f , P|) co (U , f •) -co(f&, P£) co(f&, f Q ) -co(fi , , P£) co(f^, fA) -coCf^, P&) Var(f ) * [ x s , y s , x o , y o , x N , y N , X M , y M j ( 4 - 1 7 ) 8x1 where: Var(vT) = variance of combined farm plan returns23 x n = placement weight (cwt.) of owned cattle placed in n t h month y n = placement weight (cwt.) hedged in n t h month The objective function considers only those activities that contribute to the variance of the combined farm plan returns. Except for the cattle placements and the hedging activities, the return variances of all other activities are zero. Chapter 4 87 Var() = variance term co() = covariance term P„ = selling price ($/cwt.) of the nth month owned cattle placement activity /„' = lifting futures price ($/cwt.) of the nth month hedging activity n= {S,0, N, M24} Subject to: Expected Return Constraint - Lambda: M M M X=^XnHPnS-PnP-CxJ + Jjyn*(fn°-fnl-Cyn) + JJZnHPnC-CZn) n=S n=S n=S +JJim*hm-YJbt*Ibi-ST m=\ 1=1 (4.18) where: X = expected returns ($) of owned cattle placement, hedging, custom feeder placement, off - farm investment, borrowing and structural cost activities Pns = average selling price ($/cwt.) of the nth month owned cattle placement activity Pnp = purchase price ($/cwt.) of the nih month owned cattle placement activity CXn = combined cost ($/cwt.) of the nth month owned cattle placement activity — transport, feeding, medicine, processing, death loss, shrinkage /„° = placing futures price ($/cwt.) of the nth month hedging activity /„' = average lifting futures price ($/cwt.) of the nth month hedging activity Cyn = combined cost ($/cwt.) of the nth month hedging activity — brokerage fees, margin calls (if not retrieved) M - May Chapter 4 88 z„ = placement weight (cwt.) of custom fed cattle placed in nth month P„c = custom feeding fee ($/cwt.) of the nth month custom fed cattle placement activity CZn = combined cost ($/cwt.) of the nth month custom fed cattle placement activity — feeding, medicine, processing, shrinkage im = off - farm investment (1 unit = $5,000) in the mth period m={l,2,3,4} Iim = interest return ($/unit) of off - farm investment in the mth period b, = amount borrowed ($) from credit line in t"1 production year month t={l,..., 12} Ibi = actual borrowing interest charges ($) in tth production year month ST = structural costs (1 unit = $74,604) — mostly labour cost and subject to additional constraints described next. Placement Constraints: There are four cattle placement constraints embedded into the backgrounding model. They control the cattle placement within a production year on the backgrounding operation. The cattle placement capacity is dependent on the time feeders are placed and on their type. The main constraining element is the winter feeding confinement, which handles 3,000 feeders at once (Fall Feeder Capacity, 4.19). Due to a larger frame of May feeders the facility's Fall Feeder Capacity reduces to 2,000 of these feeders (May Feeder Capacity, 4.20). In May September cattle placements should be finished and should be removed from the winter confinement. Hence, May and the remaining fall feeder activities compete with the available capacity for May Feeders (4.21). Subsequently, if only September and May feeder activities are deployed then the maximum placement capacity of the backgrounding operation, 5,000, is available (4.22). Chapter 4 89 N xn + zn) * WFn < Fall Feeder Capacity (4.19) (xM +zM)*WM < May Feeder Capacity (4.20) N (X xn + ^) * WF„ +(xM + zM) * WM < May Feeder Capacity (4.21) n=0 (xs + zs) * WFs + (xM + zM) * WM < Max. Placement Capacity (4.22) where = fall cwt. placement to animal (head) conversion rate = May cwt. placement to animal (head) conversion rate Hedging Constraint: This constraint binds hedging activities with feeder placement activities. The constraint originates from the idea of a "classical" hedge where, by taking equal but opposite positions in the spot and futures markets at the same time, the hedger "plays-off' price fluctuations in the two markets against each other. This constraint is relaxed at times in this research to allow hedging across time and futures contracts. Relaxing the hedging constraint opens the door for cross-hedging. Cross-hedging refers to a situation in which the underlying deliverable item for the futures contract is different than the cash market item. E.g., feeder cattle being hedged with live cattle futures contracts. Maximum Available Funds to be Borrowed: This constraint is introduced into the backgrounding model to ensure some flexibility with the level of maximum available funds to be borrowed. The initial line of xn - yn > 0 (4.23) Chapter 4 90 credit can be increased by 50% of the purchase price of owned cattle placements. This assumption is in accordance with local banking practices. M 12 (-1) * ]T xn * BXn + £ b, < Initial Line of Credit (4.24) n=S (=1 where: BXn = amount of capital ($/cwt. placed) contributed to the initial line of credit by owned cattle placement activities Cash Flow Constraints: The cash flow constraints consist of 13 monthly cash flow constraints. The 13th cash flow constraint is an inventory balance. To facilitate the presentation of how this constraint set is linked with the overall model a matrix format has been chosen. To accommodate an easier understanding of the cash flow constraints structure, the cash flow constraints matrix formulation is split up into segments. It is cautioned that the presented cash flow coefficients (CA) are compounded and are elements of a cash flow coefficient matrix. Hence, they do not show the actual signs as applied in each fully expanded model's cash flow constraint. However, the underlying idea of the cash flow constraints is the concept of a monthly cash flow budget, showing cash in- and out-flows within the 12 month production year. A general description of the nature and deriving process of these cash flow coefficients is assigned to section 4.3 The cash flow coefficient matrix is included in the Appendix 4. Chapter 4 91 For Owned Placements and Hedging Activities where: CA xy where: CA? CAXy CAfy ^^xy <r-?l^f\xy 13*8 XS ys Xo yo XN y» X M (4.25) 8*1 monthly cash flow coefficient for owned cattle placing ($/cwt. placed) and hedging activities ($/cwt. placed hedged) For Custom Feeding Activities CA? ^ CA\A X X 13*4 Zs Zo ZN ZM + (4.26) J 4 * l monthly cash flow coefficient ($/cwt. placed) for custom fed cattle placing activities For Off-Farm Investments where: CA C A 1 ' 1 C A / ' 4 X X CAP" ^ C A , 1 3 ' 4 13*4 + (4.27) J 4 * l = monthly cash flow coefficient ($) for off-farm investment activities Chapter 4 92 For Monthly Borrowing Activities CA^ 1 <-» C 4 U 2 ' X t CAj 3- 1 <-> C A f 1 2 13x12 V r &12 + (4.28) 12x1 where: CAb = monthly cash flow ratios for amount borrowed from credit line in the tth production year month For Structural Cost CAS'T CAST' + 13x1 (4.29) where: CAST = monthly cash flow coefficients ($) for structural costs Cash Transfers. Inventory and Right Hand Side C\ cAy T t t * i CA^ 13x12 < RHS\ t i RHSu (4.30) 13x1 12x1 where: CAC = monthly cash flow ratios for monthly cash and inventory transfer activities c12 = inventory transfer activity RHS] = initial available capital ($), all others equating monthly cash flow constraints (value = 0) Others: xM = 0 ST = 1 Xn> yn> Z n , im> bt, Ct ^ 0 (4.31) Chapter 4 93 4.3 Deriving the Cash Flow Constraints Set The cash flow constraint set documents all cash in-flows and cash out-flows of activities and transfer activities considered in the backgrounding model. The underlying notion for this set is the concept of a monthly cash flow budget. Modeled for the time frame of one production year, the cash flow constraint set comprises twelve monthly cash flow constraints and an inventory balance for the end of the accounting period. For example, having the Excel spread sheet model set-up on hand (see appendix 4), "Cash 1" represents all cash in-flows and cash out-flows across all activities for the first month of the production year, namely, September (Sept. 15. - Oct. 14.). It was decided to introduce monthly cash flow constraints into the backgrounding model, since a cash flow budget is an integral part for a backgrounding management. It facilitates the financial planning and enables the management to stay calm in periods of high expenditure and low or even no income at all. In establishing a cash flow budget the backgrounding management tries to foresee the incomes and expenditures for each activity over the whole production year. These positions depend on events like placement date, finishing date, are subject to production management, or are imposed by structural circumstances, etc. The next section will shed some light on the monthly distribution of the cost and income positions for considered activities. 4.3.1 Income and Cost Structure for Cattle Placements Each cattle placement activity consists of a specific placement, production and marketing strategy. Most of the activity's gross margin cost and income positions occur Chapter 4 94 at the placement and finishing time. This is especially true for the owned cattle placements, and shows the typical cost-revenue gap in the backgrounding business. Table 4.3 indicates the monthly income and cost distributions used in setting up the monthly cash flow budget. Table 4.3: Monthly Income and Expenditure Distribution for Cattle Placements Cattle Costs Type IProduction Period (Months)! 1. 2. 3. 4. 5. 6. 7. H. 9. 10. 11. Initial X F X M \\ Feeding X F Z F X M Z M 'I Up-front payment Z F Z M \ Processing x F zF xM Z M Medication x F Z F X M Z M -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 -1/2 Miscellaneous X F Z F X M Z M -1/3 -1/3 -1/3 -1/3 -1/3 -1/3 -2/3 -1/3 -2/3 -1/3 Pasture x F Z F -1/2 -1/2 -1/2 -1/2 Death Loss X F xM -1 -1 Shrinkage x F Z F X M Z M -1 -1 -1 -1 Selling Price X F X M 1 1 Custom Fee z F Z M 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/4 1/4 1/4 1/4 Annotation: Industry Standards and as practiced on Clover Farms Ltd. Index F represents fall activities. Chapter 4 95 The entries are ratios of the income and cost positions over the activity's whole production period. The signs are meant to reveal the nature of these positions, thus cost positions are preceded by a negative sign, and income positions are positive. The production period of a cattle placement does not coincide with the production year of the backgrounding operation! Initial costs, purchase price per head plus transportation, occur at the moment a feeder is placed on the backgrounding operation. Cattle undergo a so called "processing" upon arrival. Custom feeders are accompanied by an up-front payment for processing and medication purposes on their placement date. Incomes for owned cattle placements compromised by death loss (2%) and shrinkage (4%) are received in the month following their finishing month, because there is a technical time lag between the selling event and the actual receiving of the cash funds. As for custom feeders, a custom feeding fee is booked as income on a monthly basis beginning one month after placement. An adjustment for shrinkage takes place after the finishing month. However, no death loss related costs will arise, since the assumed custom feeding agreement discounts for this event. The occurrence of medication and miscellaneous costs, relatively minor cost positions anyway, cannot be exactly pin-pointed. However, from experience it is known that they are more likely to happen in the beginning production months after the cattle placement. The distribution of these cost positions proceeds accordingly. Fall cattle placements spend their last two production months on summer pasture. In the depicted backgrounding management problem, the backgrounding operation does Chapter 4 96 not hold the required land base, hence, does pay a fee for finishing its cattle on summer pasture. With regard to the feeding costs, the two main assumptions are that the backgrounding operation does not engage in any forage production and as a result acquires the needed feedstuffs for the whole production year from its mother operation. This purchase is done in the first production year month, regardless of when the actual cattle placement takes place. Because of the nature of the feedstuffs available, grass silage, hay, straw and barley, and to reflect the production cycle in the Peace River area, it was felt appropriate to do so. The feeding costs for each type of cattle placement are calculated by multiplying the feedstuff costs per unit with the various feed rations25 to yield the feed ration costs per lb. In a second step, the amount of daily feed ration, and the numbers of days on a certain feed ration are specified. Applying this for the whole production period generates the total feeding costs for a cattle placement26. Table 4.3. explains the cost and income distribution for each cattle placement. However, besides the feeding costs, which will always occur in the first month of the production year, the remaining distribution ratios move along the cash flow constraint set depending on the month of their associated cattle placement. Fall feeder: Starter, Growing Ration May feeder: Welcome, Finishing Ration Feeding and Bedding Schedules, and Feed Rations are enclosed in appendix 5. In combination with the gross margin calculations (see appendix 5), the total feeding cost can be recovered. Chapter 4 97 4.3.2 Hedge Activities Cash Flow Requirements Two types of cattle futures contracts are deployed in the backgrounding model: feeder cattle contract and live cattle contract. Their monthly cash in and cash out-flows are according to recommendations from Richardson and Greenshields in Vancouver. On the day of going short an initial margin is due, which is expected to be balanced in the month following the lifting of the hedge position. During the holding period of the hedge activity the backgrounding management can expect to have to comply with margin calls. Because the amount and the actual date of possible margin calls are unknown, margin calls are due when the futures markets do not develop in favour of the management's hedge position, an even spread of total expected margin calls over the hedge holding period is assumed. As for the brokerage fee and the balance of the futures contract selling and purchasing price, they also come to play in the month after the lifting of the hedge position. Table 4.4: Cash Flow Requirements for the Hedging Activities Hedge Hedging Costs Type rr: ' ^  'gs-g™'"'"1-. " 7 — T ^ j r | ] Hedge Holding Months | 2. 3. 4. 5. 6. 7. H. 9. 10. 11. Initial Margin V F y M -1 1 -1 1 Margin Calls V F y M -1/8 -1/8 -1/8 -1/8 -1/8 -1/8 -1/8 -1/8 1 -1/2 -1/2 1 f'-f' V F y M 1 1 Brokerage fee V F y M -1 -1 Table (4.4) summarizes this arrangement of cash in-flows and out-flows for the hedging activities; as with the cattle placements, the distribution ratios move along the Chapter 4 98 cash flow constraint set depending on the placing month of their associated hedging activity. 4.3.3 Off-Farm Investments, Monthly Borrowing Activities, Structural Costs, Transfers Off-Farm Investments: The cash flow coefficients for the off-farm investments are only twofold. A cash out-flow is registered at the time of investing, and a subsequent cash in-flow, discounted interest and invested funds, occurs in the month after the three month investment period. Structural Cost: Monthly structural costs, i.e., prominently labour costs, are evenly spread over the whole production year. Cash Transfers: Cash transfer activities link the monthly cash flow constraints in a consecutive manner. They allow for moving excess cash funds from a previous month to the following month. Ergo, a cash transfer activity causes a cash out-flow in the preceding month, but will provide cash funds in the next period. Monthly Borrowing Activities: The cash flow coefficients of the monthly borrowing activities are a function of the credit line agreement. The coefficients are ratios of the total amount borrowed in the particular production year month. A cash in-flow is noted in the month where outside financing is needed; hence, in the following cash flow constraints the ratios consist of the Chapter 4 99 compounded principal and interest payments. At the end of the production year, the monthly borrowed funds are paid back. 4.4 Summary This chapter outlined the quadratic risk programming model used in this study. The different activities were detailed, and their embedding into the model was explained. It also made the reader familiar with the particular structure of the cash flow constraint set. The next chapter elaborates on the data requirements and the data development. 100 CHAPTER 5 5. Data and Data Development The values of the model parameters are estimated such that the model is a close representation of the real world. Each of the backgrounder's optimization problems must reflect situations that would be encountered in a typical backgrounding management decision making scenario. Hence, the parameter's values will be derived accordingly. 5.1 Main Data Sources The model uses price and production data from two types of sources. Price data were obtained from accessible databases, whereas most of the production data were constructed from the experience of Gordon Waldorf, current manager of Clover Farms Ltd., in order to achieve an as close as possible simulation of a backgrounding operation's decision set in the Peace River area. Tables like feed rations, feeding regimes and bedding schedules for fall feeders, feeding regimes for May feeders etc. are included in appendix 5. All other production data and their associated costs, like medicine and processing costs etc. are listed in the gross margin calculation table also in appendix 5. Prices concerning the hedging activities were retrieved from the STATS DATABASE maintained by the Chicago Mercantile Exchange's Records Retention MIS Administrative Services. This database is a raw dump of the main history file of all daily trading activities at the Chicago Mercantile Exchange since January 1982. The data made available from this database for this study covers the trading activities of the Feeder Cattle and Live Cattle Futures Contracts from January 1990 to May 1995. Prices are in US$. Chapter 5 101 Cattle spot market prices were from the CANFAX database and were generously provided by Dr. Brian Freeze from the Agricultural Research Branch, Lethbridge, Alberta. This database contains the weekly, averaged cattle market prices of all weight classes for the Edmonton/Northern Alberta Region. Data made available for this research covers the trading of 4-5 cwt. steer calves and more than 9 cwt. yearling steers (fall feeders) and in a same fashion for the May feeders (7-8 cwt. yearling steers and slaughter steers) for the period from Jan. 1991 to week 29, 1995. Prices are in Cdn.$. The daily spot U.S. dollar exchange rate (average at noon) was retrieved from CANSIM, Matrix B 100,000, for the period from January, 1991, to Aug. 25, 1995. Because of the cattle spot market data's weekly nature, the daily trading data from the Chicago Mercantile Exchange was first converted into Cdn.$ and then aggregated to average weekly data, in the course of which, one resulting average weekly observation stands for aggregated trading days in a calendar week. 5.2 Selection of Sample Size (Time Frame) The cattle placement date and the cattle production management (fall feeders are sold ten months after placement and May feeders after four months respectively) specify the spot market price series considered in this model. As for the hedge activities, their underlying futures market price series were selected under a time frame of a classical hedge, where a short hedge is placed coinciding with the cattle placement and is lifted prior to the actual spot market delivery. Hedge positions for fall feeders are held nine months and three months for May feeders. Having allocated the cattle placement month, the cattle selling month, the short hedge placement month and its lifting month, the four Chapters 102 weekly observations representing each of these key months were introduced into the model's data base. The introduction of four weekly observation per month was deemed necessary to compensate for the loss of price-variation information due to the aggregation of the futures market's daily data and to the availability of weekly data for the spot markets only. Next, the time frame of the main data determined the number of years considered for the model's data base. Table 4.2 summarizes these data requirements (Appendix 5 holds a list of the model's data base). From the model data base, following equation (4.4), the Rolfo error forecasts are calculated, which are also appended to this thesis (Appendix 5). The variances and covariances of these forecast errors, abiding by the annotations illustrated in section 4.2.2, are then produced, which later on form an important element in recovering the variance and covariance matrix of their associated futures and spot market prices (applying equations: 4: 6, 14, 15, 16). A matrix of this recovered variance-covariance matrix, for a BIAS of 0, is provided in appendix 5. 5.3 Gross Margin Calculations In order to capture an as close as possible real world backgrounding operation's decision set situation, the model's parameters regarding mainly the cattle production management are based mostly on the experiences and common practice on Clover Farms Ltd. This information is obviously not accessible by the public. By describing the general deriving process of the activity gross margins, it is thought to make the parameters of the assumed production management more understandable. Note that, even if the type and the levels of these parameters were considered to be practicable and good, their main Chapter 5 103 purpose is to put life into the depicted backgrounding quadratic risk programming model! First, the cattle placement gross margins will be discussed, then the costs involved with hedging and, finally, the origin of the remaining Lambda constraint parameters will be addressed. 5.3.1 Cattle Placement Activities Equation (5.1) illustrates the generic procedure of calculating the average gross margins of the nth cattle placement alternative (gross margin ($) per cwt. placed in nth period). Custom feeder alternatives differ from this equation in that their gross margins do not account for initial costs and death loss, however, consider an up-front payment from the cattle owner covering part of the medication and processing costs. Otherwise, the same principles apply for the custom feeder option. r avg. gross margin,, = (-(Pnp * Placement weight,, + Transport,, + P?" * /" + Bedding,, + i=0 Medicine & Processing,, + Death loss„) + Pns * (Finish weight,, - Shrinkage,,)) / cwt. placed,, (5.1) i=(Starter-, Growing-, summer-, Welcome- and Finishing ration) where: Pjin = price ($/lb.) of i t h feed ration for cattle placement alternative in nth month If = total amount of i t h feed ration for cattle placement alternative in nth month The gross margin calculation starts with the initial costs of the cattle placement (purchase plus transportation costs). P/ is the average purchase price ($/cwt.) for the nth Chapter 5 104 cattle placement (Placement weight: 4.50 cwt. for fall feeders and 7 cwt. for May feeders) drawn from the model data base. This price is considered to be known at the time the cattle placement is decided. Thus, constructing this price as an average from the model's data base is solely done to have a reasonable value for this parameter. Placement weights conform to the weight expectations of steers in the Peace River area at their placement time. Transportation costs ($/head) are based on common freight fees for hauling cattle from the Edmonton spot market to the backgrounding location near Fort. St. John, e.g. one truck load can haul up to 100 head of fall feeder steers. A detailed table (Purchase Costs, Transportation and Selling Price) is provided in appendix 5. Feeding costs are calculated on a dollar per head basis. The calculation complies with the assumption that all forage and grain feed components must be acquired locally. Hence, since Clover Farms Ltd. is the mother operation of the backgrounding branch, its production costs for these items (accounting books, 1994) plus a 3.50% profit margin estimate a market price of these feed components ($/unit). In the next step, the specific feed rations (combinations of feed components) are put together for the fall and May cattle placement alternatives. Fall feeder rations (Starter, Growing and pasture during summer months) are put together from on-farm experience whereas a feed ration formula (Albin & Thompson, 1990) is applied to establish the appropriate feed rations (Welcome and Finishing) for the May feeder alternatives. From the unit costs of the feed stuff components, the cost per lb. of the four feed rations are derived (see table: FEED Rations in appendix 5). In the final step, by following the feeding and bedding schedule, the total Chapter 5 105 amount of each feed ration for each cattle placement activity is calculated and, subsequently, the total feeding cost of each cattle placement activity can be established. As for bedding, medicine, processing costs and death loss (2%) per head the model assumes parameters as they were typically experienced on Clover Farms Ltd. in recent years. The death loss cost per head is calculated by multiplying the number of expected dead cattle by their initial costs and dividing this term by the remaining number of cattle. The expected cattle placement revenues are compounds of the cattle firushing weight subject to an industry standard shrinkage rate of 4% times the average selling price, Pns, generated from the model data base. The resulting average gross margin per placed animal is then divided by the appropriate placement weight (cwt.y to yield the gross margins per cwt. placed. These gross margin calculations were only conducted for steers, since an inclusion of corresponding heifer placements would have inflated the quadratic risk programming model to an extent that computing time would have been too extensive. A comprehensive table of the steer gross margin calculations is included in appendix 5. 5.3.2 Hedging Activities The gross margins for hedging activities represent more hedging costs per hundredweight placed in the nth period ($/cwt. placed) than gross margins in a narrower sense. Equation (5.2) demonstrates the nature of the hedging costs deriving process. The brokerage fee is in accordance with the service fees schedule of Richardson Greenshields in Vancouver as of July, 1995. The brokerage fee is Cdn.$90 per contract, Chapter 5 106 regardless of the contract type, and is due when the total hedge transaction (place and lift hedge) has been completed. The brokerage fee is converted in $/contract cwt. Hedging costs„ = (-Brokerage fee„ + (fn° - / „ ' ) / 1 0 0 0 (5.2) where: j = {l,...,h} h, number of months margin calls are expected, (h = 8 for fall feeders and h = 2 for May feeders) In estimating the size of possible margin calls this study relies on the advice by Douglas J. Taylor with Richardson Greenshields. As a rule of thumb, the amount of possible margin calls can be expected to be in the range of the initial margin, that is, US$650 for a feeder cattle futures contract and US$600 for the live cattle futures contract27. Because margin calls pose a possible cash flow threat on the backgrounding's cash flow budget, their magnitude as a percentage of the initial margin will vary in this study (0%, 100%, 150%). Margin calls, when they apply, and initial margins are assumed to be balanced on the hedge account at the end of the hedge's holding period. Hence, they do not contribute to hedging costs. As for the futures prices, the following applies: The model calculates the average futures lifting price (/„') from the stacked model data base. The futures placing price (/„°), however, is a biased parameter of the average futures lifting price. The BIAS of the placing price will be changed in this study to acknowledge the discussion of a systematic downward BIAS in the cattle futures markets, which was started by Helmuth (1981) and Initial Margins as of July 14, 1995 Chapter 5 107 vehemently rejected by Palmer and Graham (1981). The range of this BIAS is from 0 to 0.075 with 0.025 step-values and is based on the Rolfo forecast error means generated from the model data before the stacking procedure. The futures prices are divided by thousand to yield $/contract cwt. Finally, as the corresponding cattle placement activities are expressed in hundredweights placed, the resulting hedging costs per contract cwt. are made proportional to the cattle placement activities by dividing them by the appropriate placement weight (cwt.) and multiplying them next with the selling weight (cwt.) accordingly. Both initial margin and margin calls are converted into Cdn$ funds. A table of the cash flow requirements for the hedging activities is provided in appendix 5. 5.3.3 Remaining Lambda Constraint Parameters The remaining parameters of the Lambda constraint are based on following sources: The three month off-farm investments and the line of credit were suggested by Creg Sutherland28, North Peace Savings and Credit Union in Fort St. John. The model can invest off-farm at a 5% per annum return and can utilize a credit line, as outlined before, at a 15% fixed interest rate annually. Structural costs are based on running the backgrounding operation under full capacity. The level of structural costs is taken from Clover Farms Ltd.'s 1994 accounting books (Structural costs: $74,604 per annum). July 20, 1995 Chapter 5 108 5.4 Software Application The model is set up and estimated using the Microsoft Excel software package. The Excel software package is used because of its self-explanatory layout and its built in Solver tool that allows, in an extended version (Premium Solver), to easily accommodate for a quadratic programming framework. The provided "QUADPRODUCT"29 function allows the user to set up the model in a linear programming fashion on an Excel spreadsheet without losing the ability to perform sensitivity analysis or impose additional constraints with little difficulty. The QUADPRODUCT-function (=QUADPRODUCT(variables, linear coefficients, quadratic coefficients)) performs following calculation: Having two variables (a and b) with their associated variances (Var.) and covariance (Cov.), which are the quadratic terms, this function will produce following equation: a*0+b*0+a*b*Cov(a,b)+b*a*Cov(b,a)+aA2*Var(a)+bA2*Var(b) 109 CHAPTER 6 6. Results and Sensitivity Analyses This chapter presents the results of the base case and the subsequent sensitivity analyses. The base case will be discussed first, in order to establish the principles of the risk minimizing attempt for the modeled backgrounding operation. As for the sensitivity analyses, they will be presented mainly in a comparative fashion to the base case, and their farm plans will be paid more attention only if their discrepancy from the associated base case optimal farm plan is apparent. Because of the vast amount of results, only a selection of optimal farm plans or E-V combinations will be presented. This applies as well for the base case as for the scenario results. The actual review will start with the base case (section 6.2). The base case result presentation will validate the relation between the backgrounding management's risk-aversity and the return standard deviation of short-term farm plans by complying with operations' physical and monetary constraints. Along with a selection of E-V combinations, general trends and their general intuition will be discussed. Section 6.3 reviews the results of the scenario groups (sensitivity analysis). The detailed, associated solution sheets are appended in Appendix 6. However, the applied and maintained solving procedure for the modeled backgrounding operation is clarified first. Chapter 6 110 6.1 Solving Procedure When exploring the Premium Solver software it was discovered that its solving engine, a nonlinear GRG Solver, is sensitive to the precision setting and the scaling of the model's parameters. The precision setting determines how closely the calculated values on the constraint left hand sides must match the right-hand sides in order for the constraint to be satisfied. A precision setting of 0.0000001 was used for all model runs. With regard to the scaling problem, for example large variance and covariance terms outweigh small cost/(cwt. placed) parameters, the automatic scaling option in the Solver software was selected for all model runs to let Solver attempt to scale values of the objective and constraint functions internally, in order to minimize the effects of finite precision computer arithmetic. The automatic scaling option requires that the starting values of the decision variables (e.g., cwt. placed in a certain period) must be reasonable, i.e., should be in the range of the optimal solution. In attempting to trace the entire expected return and standard deviation frontier, the starting values for finding the optimal farm plan for the Lambda equals zero case, were selected under the expectation that such a case should not involve any risky ventures. Thus, a starting value of zero was given for all owned cattle placement activities, for all hedging activities, for all borrowing activities, and cash transfer activities. Each custom feeder option was assigned a starting value of 1,000 cwt., which translates to 222 steers placed for each fall feeder activity and 142 animals for the May feeder activity. Off-farm investment opportunities, despite bearing no risk, were given a Chapter 6 111 zero starting value too, since their monthly return (0.41%) falls short of the monthly return for fall feeders (approx. 1.70%). In deriving the discussed expected return and return's standard deviation frontier, Lambda is raised from zero until a value is reached, which represents the maximum return that can be achieved under a given setting of model parameters. The maximum value case equals the linear maximization of the overall backgrounding return. With regard to the determination of the Lambda step value (right hand side parameter), it must be said that the deployment of previous farm plan solutions as starting values for the finding of the next optimal farm plan is important. A Lambda change of $5,000 is considered to guarantee that the solutions of the previous farm plan are close to the optimal solutions for the following farm plan. This $5,000 step value is maintained until the range of farm plans is reached, where expected returns are desired that require more risky solutions in their subsequent farm plans. Acknowledging, from theory, the exponential increase of the portfolio variance in the higher range of expected returns, the step value of Lambda is reduced to $2,500 from Lambda equaling $80,000 and higher. By doing so, the changes in farm plan solutions should be more visible. This solving procedure is applied to the base case and to all subsequent sensitivity analyses. 6.2 Base Case It is the intent of the base case to demonstrate and validate the relationship between the risk-aversity of the backgrounding management and the return standard Chapter 6 112 deviation of short-term farm plans subject to all operations' physical and monetary constraints. The management, by expressing its degree of risk-aversity, through setting a desired overall farm plan return (Lambda), seeks a farm plan that complies with this specification and provides a minimal variation in the associated overall farm return. By entering the full range of possible Lambda values, a set of all risk-efficient farm plans will be produced. A frontier of the expected value (Lambda) and the standard variation of overall farm returns can then be traced. Managements, eager to know what the optimal farm plan under a specific Lambda should look like, follow this frontier until they reach the desired expected return level, from where they can look up the associated farm plan. Each individual farm plan should, depending on the desired overall farm plan return, disclose the intended ranking and combination of the main activities in terms of their variability of returns, that is, from custom feeding and off-farm investments, with no market risk, to owned cattle placements and hedging, with a moderate market risk, and to owned cattle placements only, with the highest variability in returns. The base case solutions will also clarify the cash flow budget aspects of the backgrounding operation. Monthly revenues of custom feeders, monthly borrowing activities, the total borrowed amount, and transfer activities should be good indicators in demonstrating the importance and necessity of a backgrounding operation's monthly liquidity. The risk-efficient frontier for the base case is generated under the intention to yield the least "risky" optimal farm plans set. This requires that all constraints should be as Chapter 6 113 relaxed as possible. Thus, despite having the concept of a classical hedge in mind, the hedging activity constraint where the number of feeder hundredweights placed must be larger or equal than the number of hundredweights hedged, is disabled. This relaxing should result in more efficient hedges. The BIAS of possible hedge positions is set to zero, that is, the futures placing price (going short) does accurately reflect the average futures lifting price (going long). Initial margins will be balanced at the end of the hedging period, and margin calls are not considered. This setting of the hedging parameters will ensure that the backgrounding operation's cash flow budget will not be compromised by hedging-induced cash flow constraints and will leave the management with brokerage fees as hedging costs only. 6.2.1 Optimal Farm Plans Coinciding with the parametrical increase of Lambda levels, the standard deviation of overall farm plan returns is increasing. Figure 6.1 provides a graphical presentation of the risk-efficient base case frontier. To simplify the graphical illustration, standard deviation returns for Lambdas below $55,000 are not traced. The accurate values and optimal farm plans for the base case can be found in Appendix 6. Following the course of the base case frontier, we encounter the first return standard deviation ($705 ) at the Lambda level of $70,000. Optimal farm plans with a lower Lambda value than $70,000 do not produce a standard deviation of their returns, Chapter 6 114 whereas farm plans with a higher Lambda level show an exponential increase of their standard deviations of return, following the parametrical increase of Lambda30. Figure 6.1: Expected Return and Return Standard Deviation Frontiers: Base Case and Changes in Hedging Strategy 45000 55000 60000 65000 70000 75000 80000 85000 90000 95000 96800 Expected Return Parameter (Lambda), $ Base case Hedging constraint — - - No hedging The maximum standard deviation of $42,909 is reached at the $96,800 overall expected return parameter. This maximum solution also could have been generated by maximizing all farm returns in a linear programming set-up. Table 6.1 shows a selection of optimal E-V case combinations (an extensive solution table is provided in Appendix 6). Owned cattle placements, custom feeder 3 0 The base case frontier in figure (6.1) confirms this exponential increase of the return standard deviation, which is, however, less obvious in the upper segment of the frontier, due to smaller Lambda step values towards the maximum optimal farm plan. Chapter 6 115 placements, the number of cattle futures contracts, the number of off-farm investments, and monthly draws from the credit line are reported for the 55,000, 70,000, 85,000, 90,000, 92,500 and 96,800 Lambda level farm plans. With the parametrical increase of Lambda, we can identify the following general trends. The number of custom feeders increases until the 55,000-Lambda farm plan is reached. As soon as the maximum backgrounding capacity is exhausted (3,000 feeders in September and 2,000 feeders in May), the October and November custom placements are slowly phased out. At the $55,000 lambda level they are not part of the management's decision set anymore. Being committed to achieve an expected overall return value of $55,000, the management invests the remaining initial capital in the September off-farm investment alternative (20.2 units). A total of 36 off-farm investment units is deployed in the 55,000-farm plan. Off-farm investments are made possible through accumulating custom feeding fees and excess cash flows within the production months. With the continuation of the Lambda iteration process, optimal farm plans are produced, where off-farm investments do further increase, but custom feeders are kept at the maximum backgrounding capacity. The backgrounding management attempts to satisfy its overall farm return expectations by progressively increasing the number of units invested off-farm. However, this comes to an end at the 70,000-Lambda level. At this point, having depleted all excess cash funds (RHS variables equal zero), the management is required to place owned feeders in order to achieve its return expectations. Hedging activities also appear for the first time, implying that the range of running the Chapter 6 116 backgrounding operation without return risk has been explored; from this point on managing a backgrounding operation becomes a "risky" business! Table 6.1: Selection of Base Case E-V Combinations Farm Plans: Lambda 55,000 70,000 85,000 90,000 92,500 96,800 St. Deviation ($) 0 7(15 7,129 13.426 16,875 42,9(19 Total Owned 0 41 461 867 1.D45 1163 Hedge Ratio 0 0.82 0.97 0.97 0.85 0 Sept. Owned 0 41 200 247 269 303 Sept. Hedged 0 0.3 6.55 12.33 13.97 0 Oct. Owned 0 0 49 39 35 32 Oct. Hedged 0 0 0 0 0 0 Nov. Owned 0 0 212 581 741 828 Nov. Hedged 0 0.31 0 0 0 0 May Owned 0 0 0 0 0 0 May Hedged 0 0 2.02 3.82 2.89 0 Total Custom 5,000 4,959 4278 3,511 3,179 2,977 Sept. Custom 3,000 2,959 2,539 2,132 1,955 1,837 Oct. Custom 0 0 0 0 0 0 Nov. Custom 0 0 0 0 0 0 May Custom 2,000 2,000 1,739 1,379 1,224 1,140 Off-Farm Inv. 36 219 82 33 12 4 Sept. Off-Farm 20.2 15.2 0 0 0 0 Dec. Off-Farm 15.7 38.3 6 1.6 0 0 Mar. Off-Farm 0 65.6 25.2 8.7 1.8 0 June Off-Farm 0 99.8 51 22.6 10.6 3.9 Tot. Borrowed 0 0 94,633 315,191 411,717 479,893 Nov. Borrowed 0 0 94,633 315,191 410,416 462,936 Dec. Borrowed 0 0 0 0 1,302 6,893 Jan. Borrowed 0 0 0 0 0 5,785 Feb. Borrowed 0 0 0 0 0 2,269 Structural Cost 1 1 1 1 1 1 In the 70,000-farm plan, 41 September owned cattle share the maximum backgrounding capacity with their September custom feeder counterparts. Off-farm Chapter 6 117 investments decline from their peak unit number to 219 units. Return risk associated with owned cattle is cushioned by selling 0.30 feeder cattle contracts for August delivery in September and 0.31 feeder cattle futures contracts for September delivery in November. That is, 82% of the September owned cattle placements are hedged (fall hedge ratio: 0.82). The 70,000-farm plan is based on self-financing. The initial capital is utilized to its full extent in the first production month. All first month excess funds are invested off-farm (15.20 units in September). In general, all other monthly excess money, roughly revenues from September custom feeders minus monthly structural costs, is transferred to the closest off-farm investment alternatives (in December, March or June). This explains the distinct segmentation of the transfer activity columns for the "risk-Lambda" optimal farm plans (see IB in Appendix 6). When Lambda is further increased, more owned feeders are progressively placed, at the expense of their custom feeding counterparts. Feeders are preferably placed in September, but, for higher expected return values ($80,000 and $82,500), feeders are also placed in October and November, however, limited by the scarcity of September custom feeder cash in-flows. Hedging activities keep up with the increase in owned feeders, and reach their peak in the 85,000-Lambda farm plan (combined hedge ratio: value of 1.0831, Providing a BIAS of zero and imposing cost on hedging activities, the model should not exceed a hedge ratio of 1. This holds true for the Fall hedge ratio, but does not seem to apply for the combined hedge ratio. One explanation might be, that the non-conformity of the live cattle futures contract costs (established for May owned feeder, 7 cwt. - 10.32 cwt.) to the owned placed feeders (4.5 cwt. to 9.12 cwt.) raises difficulties in recovering the true combined hedge ratio of one. The hedge ratio of 1.08 is considered to be a good approxy of the true value. Chapter 6 118 indicating that a further increase of Lambda will result in progressively smaller numbers of owned animals hedged). Obviously, off-farm investments decline. In the 85,000-farm plan September owned steers have increased to 200 head and November owned steers jump up to 212 head, requiring May custom feeders to decline accordingly (1,739 head). Owned cattle are being hedged by 6.55 September feeder cattle contracts and 2.02 May live cattle contracts, resulting in a smaller combined hedge ratio of 97%. Off-farm investments also experience a reduction to 82 units, which is mainly fueled by the lack of excess funds, due to the sharp decline of custom feeders to 4,278 heads, and the increasing number of owned animals, which widens the cost/revenue gap. Outside financing becomes necessary in the 85,000-Lambda farm plan to accommodate the backgrounding activities. In November, the backgrounding management draws $94,633 from the available annual credit line. This is interesting, because in the previous farm plan the November feeder placement was realized through self-financing; ergo, September custom feeder fees provided the financial means. Thus, the increase of November placements can be made responsible for the November credit line use. This pattern applies to all higher Lambda farm plans. Because of the selective use of the credit line, no funds are transferred from November; we can therefore draw insights on the importance of September custom feeders with regard to balancing the monthly cash flow requirements. Their custom fees finance medication costs for the September and October owned feeders, pay for structural costs, and allow for hedging activities. Chapter 6 119 Increasing Lambda further reveals the same activity patterns as illustrated. The number of September owned feeders increases modestly, 247 head for the 90,000-farm plan, October owned feeders decline slightly, and November owned feeder placements increase drastically, again coinciding with the credit Une drawing in November. Hedging activities maintain a constant hedging level (combined hedge ratio 0.97). Custom feeder activities as well as off-farm investments are further reduced. Approaching the optimal farm plan solution for the maximum lambda parameter, owned feeder placements, November placements especially, continue to rise, and the hedging ratio declines. The management draws cash funds from the credit line in November, to mainly finance the initial costs of November owned cattle placements. However, in contrast to previous farm plans, where due to more September custom feeders more cash in-flows were available, these additional funds are also deployed to cover cost positions not related to the November owned feeder placement. As anticipated, the decline of September custom feeder revenues (smaller number of placements) and the increase in principal and interest payments lead to a tightened cash flow situation in subsequent months, hence, further outside financing in the months following the November borrowing activity is required. Interest and principal payments for funds borrowed in November accrue to the biggest cost position in the monthly cash flow budgets following the November borrowing activity! This cost position increases with the increase of Lambda, demanding progressively higher borrowing in the months following the initial November drawing from the credit line. Chapter 6 120 Finally, the maximum Lambda farm plan is produced. At $96,800 the backgrounding management places 303 September owned, 32 October owned and 828 November owned feeders. No hedging positions are established. 1,837 September and 1,140 May custom feeders are placed. The return percentage generated by "risky" activities rises to 83.14%, which is the highest value for all optimal farm plans in the base case. Combined with the new expansion of November owned feeders, the maximum farm plan requires overall outside financing of $479,893. Outside financing is required in the subsequent months to cover increasing principal and interest payments resulting from the November borrowing activity. With a standard deviation of $42,909, the maximum Lambda farm plan is the most risky farm plan. 6.2.2 Principles in the Base Case Risk Minimizing Strategy Having described the optimal farm plans along the course of the risk-efficient frontier, we can draw the following risk minimizing principles: The larger the Lambda parameter, ergo, the lower the backgrounding management's degree of risk-aversity, the more "risky" activities are favoured. Risky activities, despite having a higher return variability, provide the prospect of higher returns. The parametrical increase of Lambda causes a gradual shift from non-risky to risky activities. Thus, the backgrounding management holds on to non-risk activities as long as they can materialize a set expected return value. Custom feeders are given the first choice followed by off-farm investments. Custom feeders are placed to the extent of the backgrounding operation's maximum placement capacity. Off-farm investments are then deployed to match higher overall return expectations without engaging in risky activities. Chapter 6 121 In the upper range of Lambda, hedging activities and owned cattle placements come into play. Hedging activities are not bound to the month of the actual cattle placement. Cross-hedging occurs, e.g., the management sells live cattle contracts in May to cushion the overall variability of all farm returns, although fall feeders are the only cattle category placed. The combined hedge ratio reaches its peak value in the 82,500-farm plan and declines from there to nil in the maximum Lambda farm plan. For the maximum Lambda farm plan, the percentage of returns generated from risky activities is at maximum. The number of custom feeders decreases progressively in the upper range of Lambda. Off-farm investments decrease from the point where risk associated activities are necessary to meet a set expected return value. The decline of off-farm investments also coincides with diminishing revenues from custom feeders and increasing borrowing costs. Outside financing is required from the 85,000-optimal farm plan on and occurs in November, which is when owned feeders are placed. Principal and interest payments for this borrowing activity cause a precarious cash flow situation for the subsequent months, which is alleviated by further, however minor, monthly drawings from the credit line. September custom feeding fees, especially, contribute significant revenues to satisfy monthly cash flow requirements. They are an important cash source to finance current expenditures such as medication, processing and structural costs and hedging activities. Chapter 6 122 6.2.3 General Intuition of the Base Case Results The course of the base case optimal farm plans along an increasing Lambda provokes questions, such as why custom feeding decreases, why hedging activities decrease, why the placement of owned animals increases, etc.? These questions can be generally answered with the return-risk ranking of the backgrounding operation's activities set, that is, from custom feeding and off-farm investments, with no risk, to owned cattle placements combined with hedging, at a moderate risk, and to owned cattle placements only, with the highest variability in returns. This risk return ranking assumes that more risky activities come with the potential of higher returns. Hence, when the backgrounding management specifies its degree of risk-aversion, by setting the expected overall return value Lambda, it influences the choice of backgrounding activities. Thus, the larger Lambda the more "risky" activities are favoured, which explains the gradual shift from non-risky to risky activities over the succession of an increasing Lambda. 6.2.4 Some Subtle Aspects of the Base Case Results The Maximum Return Risk Free Farm Plan: Due to the size of the Lambda step value, the maximum return-risk-free farm plan was not explicitly produced in the base case solutions. To identify this "peak" farm plan is rather simple. We can produce this farm plan, if we keep the number of custom feeders at the maximum backgrounding capacity, if we transfer all excess funds towards off-farm investment alternatives, and if we follow the associated monthly cash flow requirements. In this case, the backgrounding management must place 3,000 September and 2,000 May Chapter 6 123 custom feeders, and must invest in 242.10 off-farm investment units in order to achieve an expected return level of $67,678. Cash Flow Burden of November Borrowing on Subsequent Monthly Cash Flows, e.g. 95,000-FarmPlan: In the 95,000-farm plan the cash flow burden of the November borrowing activity ($458,553) becomes especially apparent. Large principal and interest payments require additional draws from the credit line, in order to balance the associated monthly cash flow budgets. As table 6.2 illustrates, the principal and interest payments for the November borrowing activity weigh heavy, however, they decrease over the production year, which is due to the 5% principal payments. September custom feeder fees for backgrounding (1,856 head) keep constant, except for March where no September custom feeder related expenditures are budgeted. Having listed the main cash in- and out-flows, the production months, where outside financing is required, are exposed: December, January and February. Table 6.2: Comparison of Largest Monthly Cash Flow Positions Following the November Cash Flow Budget in the 95,000-Farm Plan November +458,553 (all values in $) Month Principal & Interest Structural Cost Total Sept. Cust. Fees December -28,581 -6,217 •34,798 31,655 January -27,151 -6,217 -33.368 31,655 February -25,794 -6,217 -32,011 31,655 March -24,504 -6,217 -30,721 32,583 Chapter 6 124 6.3 Sensitivity Analysis: Results of the Scenario Groups The first scenario group (section 6.3.1) will highlight the range of all possible risk-efficient farm plans. That is, first the option of hedging with cattle futures contracts is removed from the backgrounding management's decision set, and second, hedging activities are bound to the month of cattle placement in order to establish an anticipatory hedge. The second scenario group (section 6.3.2) addresses the impact on the backgrounding management's risk management strategy, when the BIAS between the two considered futures prices of the hedge positions increases. Thus, an increase in BIAS should make hedging activities progressively less attractive. The final scenario group (6.3.3) addresses the backgrounding management's concern regarding a possible cash flow threat from hedging-related margin calls. Thus, monthly margin calls as a percentage of the initial margin are imposed. This set-up will cause a temporary absence of cash funds. Compared to the base case, risk management strategies should not change a lot. To give a general overview of the scenario groups' results, table 6.3 presents a selection of optimal farm plans or E-V combinations for the base case, the no-hedge scenario, the 0.025 BIAS scenario and the 100% margin call scenario. Combinations for the 55,000-, 70,000-, 85,000-, 90,000-, 92,500- and the 96,800-farm plan are compared. Note that the results for the 55,000-farm plan and the maximum farm plan are identical for the base case and the scenarios (Heading: Equal). See next page! 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O I ° x O I a «; « J > > > >J co o o o o ra ra 0) O O Z Z 5 E o E § E •5 o S o § ts « s . o ° o a ~ > CO C J o i n O Z E E E | ffi i i CO IB 3 = 3= o o Q S T J T J II s ° CO OQ > ci o cu Z Q TJ T l co co I o o OQ m C J O Chapter 6 126 6.3.1 1. Scenario Group: Base Case, No hedging, Anticipatory Hedging This scenario group places emphasis on changes in the backgrounding operation's strategy of risk management, when the option of hedging with cattle futures contracts is not available in the management's decision set or when only an anticipatory hedging strategy is pursued. No Hedging: When hedging alternatives are removed from the backgrounding management's decision set, the general characteristics of selecting the optimal farm plans set, as described in the base case, do not change. Farm plans up to the 65,000-Lambda level are a mirror of the corresponding base case farm plans. However, from the 70,000-Lambda value on, the management' risk management strategy changes. First, one observes the dramatic increase of the overall farm return standard deviation, e.g., the standard deviation for the 90,000-farm plan is 84% higher than for the base case. However, following the rule of diminishing risk "bettering" rates, this discrepancy eases in the upper range of Lambda. Indeed, the risk-efficient frontier of the no-hedging scenario converges with the base case frontier (see figure 6.1). The number of owned cattle placements is considerably lower. November owned cattle placements suffer the hardest drawback, causing the borrowing activities to decline sharply until the maximum farm plan is established. An increased placement of September custom feeders supports a slightly increased placement of October owned feeders. More custom feeders and their subsequent revenues favour more off-farm investments, too. Chapter 6 111 Altogether, this compounds to the highest percentage rate of returns generated from non-risk activities compared to the base case. Anticipatory Hedge: Hedging Activities are Binding to Cattle Placements: Overviewing table 6.3, we see that the overall farm return risk-minimizing principles, as derived in the base case, also apply for this scenario. The standard deviation of overall farm returns is exponentially increasing with the parametrical increase of Lambda, custom feeder options are given the preference as long as they can materialize Lambda, off-farm investments expand the range of non-risk activities by capturing excess funds from custom feeding fees, and borrowing activities coincide closely with the November owned cattle placements. As an anticipated result of the introduced hedging constraint, the monthly hedge ratios do not exceed a value of one. The risk-efficient frontier follows slightly off-set along the left hand side of the base case frontier (see figure 6.1). Farm plans 70,000 and 75,000, despite being already in the Lambda range where the deployment of risk associated activities is necessary to meet the set expected return parameter, show no disparity in the number of fall futures contracts sold compared to the corresponding base case farm plans. The reasoning for this is, that the solutions in the base case already did not select for May hedging activities, and that the number of fall contracts sold kept the fall hedge ratio below one. Subsequently, when hedging and the cattle placement were linked, this could not have a strong impact on the newly derived farm plans. Now, hedging activities take place in the month of the actual cattle placement (September). Chapter 6 128 The farm plans for the anticipatory hedging scenario adapt, as soon as we enter the range of farm plans, for which a May hedging activity in the base case was selected. Starting from the 80,000-farm plan we can identify following changes: The standard deviation of overall farm returns is slightly higher than in the base case, except for the maximum expected return parameter case. Figure (6.1) illustrates the slight increase in return standard deviation; The combined hedge ratio is lower, indicating that cross-hedging in the base case was a better mean in reducing the overall portfolio standard deviation; The new optimal farm plans set places more custom and less owned feeders, and engages more in off-farm investments, causing the percentage of returns generated from non-risk activities to be higher than in the base case. The percentage value for owned to custom feeders is lower; Fewer November owned cattle and larger cash in-flows from the increased number of custom feeders reduce borrowing activities over all farm plans; and. Finally, more excess cash funds, provided through increased numbers of September custom feeders, allow for a larger number of off-farm investments in March than in the base case. Summary of Changes in Hedging Scenario Group Results: This scenario group established the full risk range of all possible optimal farm plans for the backgrounding operation (figure 6.1). With the parametrical increase of Lambda, the finding of the optimal farm plans set follows the discussed base case principles, Chapter 6 129 regardless of what the underlying model parameters are. The same risk-return trade-off ranking prevails! In light of progressively constraining hedging activities, from no constraint in the base case, to physically constraining them to the logical cattle placement month, to the extreme scenario where hedging was disabled, the adjustments of the farm plans along the risk-efficient frontier can be characterized as follows: Custom feeder placements are deployed in the same magnitude for all scenarios until the Lambda value is reached, where owned cattle must be considered in the optimal farm plan to meet the expected return parameter. From then on, keeping the order of base case, constraint hedging scenario and no-hedging scenario, the number of custom feeders is less and less reduced and owned cattle are being progressively less increased. The increase in custom feeders is followed by enlarged off-farm investments; and As hedging activities become more and more constrained, the optimal farm plan sets reduce the number of November owned cattle placements especially, leading to a lower credit line borrowing activity. Hedging activities are reduced from the base case to nil in the no-hedging scenario, resulting in higher return standard deviations. This is an indication that the general notion of an anticipatory hedge, which was the basis for the calculations of the hedging cost parameters, is not the best strategy. By allowing for cross-hedging in the base case, fall feeder placements were hedged by May live cattle futures contracts for October delivery, a slightly lower return standard deviation was achieved. In light of the no-hedging scenario, where the standard deviation of farm returns almost doubled compared to the base case, the worthiness of a classical hedge Chapter 6 130 cannot be disputed, however, its optimality might be revised to make room for more sophisticated hedging strategies. 6.3.2 2. Scenario Group: Changing the BIAS The BIAS, the relation between the two considered futures prices of a hedge position, is important for the hedging activity's hedging performance. The BIAS affects the backgrounding operation's expected return constraint through higher hedging costs, thus, the backgrounding management must confront the question of whether or not an overall farm return reduction, caused by an increased BIAS, is justifiable for a possible reduction in the overall farm return variation. By increasing the BIAS, the question of the risk-return trade-off becomes more and more imperative for the backgrounding management and should lead to a situation where hedging activities become non-attractive elements in the backgounding management's decision set. As we recall, Helmuth (1981), referred to such a situation, when he argued that a systematic downward BIAS for the live cattle futures contract would deter persons interested in beef cattle hedging. Yager (1981) rejected Helmuth's argument vehemently. However, this discussion regarding a possible downward BIAS in the live cattle futures markets is still unresolved. The following scenario group, which produces optimal farm plans sets for a changing BIAS from 0 to 0.075, in step values of 0.025, will not resolve this discussion, but will rather investigate the impact of an artificial downward BIAS on the utilization of hedging alternatives as a means to reduce the standard deviation of overall operations' Chapter 6 131 returns. The BIAS will be the only parameter to be changed in the model's specifications, except for Lambda. All other model parameters comply to the base case specifications. BIAS Optimal Farm Plans: Figure 6.2 shows that the risk-efficient frontiers move to the left hand side of the graph along with the increase of the futures price BIAS. Although this movement was expected, the indicated standard deviation values for the 65,000-farm plans, especially, and the 70,000-farm plans, are inconsistent with previously produced results. 65,000-farm plans in this scenario group come with a standard deviation of above zero. They should be zero32! Hence, the 65,000-farm plan solutions will not be considered. Another breakaway33 can be identified for the 70,000-farm plan in the BIAS equals 0.05 scenario. This solution will not be further investigated either. By increasing the BIAS, the hedging costs for fall-hedging activities (May hedging activities are not in the solution set) increase from $0.49 to $5.78 to $11.00 and, finally, to $16.36 per hundredweight of fall cattle placed. Increasing hedging costs lead to a situation where the risk-return trade-off for hedging activities becomes more and more unfavourable. A possible overall return risk reduction has to be paid for with higher and When recalling the course of the no-hedging scenario risk-efficient frontiers, we must discount these farm plan solutions as not being the optimal farm plan solutions with regard to minimizing the variance of overall farm returns. The insensitive solving engine of the Premium Solver software package is to blame for this inconsistency. If we extend each of the risk-efficient frontiers, starting from the 70,000-Lambda solution, to the point of the 65,000-Lambda solution, with a standard deviation of zero, we can isolate the 70,000-farm plan of the 0.05 BIAS scenario as not being the best optimal farm plan solution, because its location on the risk-efficient farm plan frontier is well above the expected area. Chapter 6 132 higher costs. Subsequently, hedging activities decrease as a means of combating the backgrounding operation's overall return risk. Figure 6.2: Expected Return and Return Standard Deviation Frontiers: Changing BIAS 45000 T 1 55000 60000 65000 70000 75000 80000 85000 90000 95000 96800 Expected Return Parameter (Lambda), $ Base c a s e 0.025 BIAS 0.05 BIAS 0.075 BIAS The changes in the management's hedging strategy can be documented by the combined hedging ratio development, which specifies the fraction of placed animals hedged. Table 6.4 lists the combined hedging ratios for the changing BIAS scenario group. First of all, as we have concluded from the base case, the combined hedge ratio declines along the increasing Lambda parameter. This pattern holds true for all BIAS scenarios, except for the 0.075 BIAS scenario, where the backgrounding management does not engage in hedging activities at all. Second, the combined hedging ratio declines Chapter 6 133 with an increase in BIAS, to the point where hedging becomes non-attractive (BIAS 0.075). This course of the combined hedging ratios was expected. Table 6.4: Combined Hedging Ratios for the BIAS Scenario Group Expected Return ($) BIAS = 0 BIAS = 0.025 BIAS = 0.05 BIAS = 0.075 55,000 0 0 0 0 60,000 0 0 0 0 65.000 0 70,000 OS 16 0 675 0.305 0 75,000 0.798 0.680 0.285 0 80,000 1.077 0.487 0.078 0 82,500 1.079 0.180 0.079 0 85,000 0.971 0 0 0 87,500 0.972 0 0 0 90,000 0.973 0 0 0 92,500 0.854 0 0 0 95,000 0.380 0 0 0 96,800 0 0 0 0 Annotation: As argued, shaded area is not considered to be part of the optimal farm plans solution set. As indicated by table 6.4, farm plans for Lambda values of below 65,000 are identical with the base case solutions, where the available backgrounding decision set was only used to the extent of custom feeder and off-farm investment alternatives. On the other side, farm plans from the 85,000-Lambda parameter on are identical to the no-hedging optimal farm plans set (see also table 6.3). The highest BIAS scenario (0.075) merges to the no-hedging solutions from the 80,000- Lambda benchmark on. Figure 6.2 illustrates the convergence of the risk-efficient frontiers in the upper range of the Lambda parameters. Assuming that hedging encourages a larger number of owned cattle placements, because it reduces the return-risk associated to owned cattle, a declining hedging ratio suggests a progressively smaller number of owned feeder placements. However, as table Chapter 6 134 6.5 shows, when the BIAS increases to 0.025, the percentage of owned animals to custom feeders increases for the 70,000- to 82,500-Lambda range. A similar increase, although smaller and for a more confined Lambda range, must be noted for the BIAS equals 0.05 farm plan solution set. The explanation for this seeming contradiction is again related to the risk and return trade-off for each activity. Despite an increase in their underlying BIAS, hedging activities still provide a means to reducing return-risk, however, at higher and higher hedging costs. Thus, as long as the backgrounding operation generates sufficient cash in-flows, and the hedging caused overall return reduction can be compensated by returns from other activities, the backgrounding management will engage in hedging activities and will place more owned cattle to compensate for the overall farm return reduction. Table 6.5: Percentage of Owned Animals to Custom Fed for the BIAS Scenario Group Expected Return ($) BIAS = 0 BIAS = 0.025 BIAS = 0.05 BIAS = 0.075 55,000 0.0 0.0 0.0 0.0 fio.onn 0.0 0.0 0.0 0.0 65.000 ().() 1.2 0.9 70,000 0.8 1.3 2.0 1.1 75,000 2.7 4.0 3.7 2.9 80,000 4.9 6.2 4.9 4.6 82,500 6.1 6.3 6.2 5.7 85,000 10.8 8.0 8.0 8.0 87,500 17.0 12.3 12.3 12.3 90,000 24.7 17.3 17.3 17.3 92,500 32.9 23.1 23.1 23.1 95,000 38.1 29.9 29.9 29.9 96,800 39.1 39.1 39.1 39.1 Annotation: As argued, shaded area is not considered to be part of the optimal farm plans solution set. Chapter 6 135 Hence, from the 85,000-farm plan on, when outside financing is required for placing owned feeders in November, the optimal farm plan solutions for all BIAS scenarios collapse to the optimal farm plan solutions provided by the no-hedging scenario. From then on, the number of owned cattle is higher in the base case, the number of custom feeders is lower in the base case, so are off-farm investments, and engaging in hedging activities prevails until the maximum Lambda farm plan is reached. Principles in the Changing BIAS Scenario Group: By increasing the BIAS, the question of the risk-return trade-off associated with hedging activities becomes more and more imperative for the backgrounding management. The question of whether or not an overall farm return reduction, caused by an increased BIAS, is justifiable for a possible reduction in the overall farm return standard deviation, is approached as follows: Despite an increase in the BIAS, hedging activities still provide a means of reducing overall return risks, however, at higher and higher hedging costs. This means that, as long as the backgrounding operation generates sufficient cash in-flows, and the hedging-caused overall return reduction can be compensated for by returns from other activities, financed through self-financing, the backgrounding management will still decide to engage in hedging activities and will place more owned cattle to compensate for the overall farm return reduction in its short-term decision making problem. Nevertheless, with the increase of the BIAS, the hedging ratio declines and diminishes even to zero for the BIAS equals 0.075 scenario. Chapter 6 136 As soon as outside financing is required (85,000-farm plan), the additional costs of hedging do not support hedging activities in the backgrounding management's decision set, and the assumption that hedging activities encourage a larger number of owned cattle placements resumes in favour of the base case. Some Subtle Aspects of the BIAS Scenario Group: The suspected backgrounding management's behaviour of placing more owned animals in order to compensate for a suffered overall return reduction can be identified for the 70,000- to 82,500-Lambda range of the BIAS scenarios. In order to comply, for example, to the set 70,000-Lambda value in the 0.025 BIAS scenario, the management must place owned animals. In the BIAS scenario (see table 6.3), five head of owned feeders are placed in September and 60 head are placed in October respectively. This is in contrast to the base case solution, where 41 head of owned feeders were placed in September. Both cases engage in hedging activities resulting in 67% (BIAS scenario) and 82% (base case) combined hedging ratios. The number of May custom feeders is reduced, corresponding to the October placements. September custom feeders are also reduced by 24 head (now 2,935 head) causing the off-farm investments for the first period (September to December) to rise from 15.20 units to 20.80 units. However, because of generally lower custom feeder numbers, the management invests fewer units off-farm in the consecutive off-farm investment alternatives. A similar pattern applies to November owned feeder placements in the upper segment of the Lambda range. The question of why October placements increase, can be answered as follows: as in the discussed base case solutions, the October owned feeder placements are self Chapter 6 137 financed through the September custom feeder placements. Their cash in-flow occurs in October. October feeders, despite offering the same return variance as September owned feeders (we recall that the individual data sets were stacked), offer a slightly higher return than their September counterparts, which is mainly due to lower purchasing costs for October calves. Hence, October feeders enable the backgrounding management to cushion the overall return reduction, caused by increased hedging costs, more effectively. 6.3.3 3. Scenario Group: Margin Calls Margin calls are due when futures markets, over a certain time period, develop in a direction that is not in favour of a hedge holder's futures contract position. The hedge holder is then required to deposit an appropriate amount through her/his broker in order to signal her/his financial strength to live up to the futures contract's specifications. The timing and the amount of margin calls are difficult to predict. However, the backgrounding management, abiding with a defined cash flow budget, must provide financial means to be in a position to comply with such calls when they should occur. This sensitivity analysis will look into the impact of margin calls on the backgrounding management's risk management strategy. Margin calls will be specified as a percentage of the initial margin, which has to be deposited when the hedging position is placed. One hundred percent of the initial margin marks the first possible level and 150% the second one. It is assumed that the margin calls will be balanced at the hedge lifting time. This assumption accounts for the situation that not only margin calls are issued over a hedging period, but also that for the hedge holder favourable futures market developments occur, Chapter 6 138 which will subsequently accumulate credits on her/his hedging account. Hence, when the hedge position is lifted, paid margin calls are de facto balanced. This assumption will cause a stress on the backgrounding operation's cash flow budget that can be described as a temporary absence of cash funds. The General Impact of Margin Calls: Figure 6.3 depicts the course of the risk-efficient frontiers for the margin call scenarios. The margin call risk-efficient frontiers for the 100%-scenario and 150%-scenario, follow closely the base case frontier. If we consult table 6.3, the course of these two frontiers is confirmed by the associated standard deviation values which tend to increase more rapidly in the upper area of the Lambda parameters (92,500.- and higher). As in prior scenarios, the optimal farm plan solutions for both scenarios are identical with the corresponding base case solutions within the expected return range of 0 to $65,000. As soon as the Lambda range is reached that requires the placement of owned feeders, hedging activities are deployed to reduce the return-risk, despite margin calls. However, in order to satisfy the upcoming margin call cash flow requirements, the base case optimal farm plan activities are rearranged. September cattle placements are reduced, thereby freeing initial capital to accommodate hedge placements in the first production month. The loss of September feeder placement returns is offset by additional feeder placements in November. Hence, by rearranging the optimal farm plan, the backgrounding management is able to produce the necessary cash flow requirements for margin calls and to keep the standard deviation of overall farm returns almost as low as in the base case, Chapter 6 139 e.g., the standard deviation for the 82,500-farm plan changes along with the margin call increase from $4,257 to $4,286 and to $4,295. Figure 6.3: Expected Return and Return Standard Deviation Frontiers: Margin Calls 45000 55000 60000 65000 70000 75000 80000 85000 90000 95000 96800 Expected Return Parameter (Lambda), $ Base case — — Margin call 100% - - - - Margin call 150% Annotation: The standard deviation values provided for the 70,000- and 75,000-farm plans are slightly lower than in the base case, which, in light of a caused cash flow budget stress and a margin call free base case scenario, points to the base case farm plan solutions as having missed the most efficient solutions by a small fraction. Outside financing is required as soon as the 85,000-farm plan is reached. At this point, the backgrounding management must address the question of how much it can afford to borrow in order to maintain an as low as possible standard deviation of overall returns, but also to match the set-expected return parameter. Thus, November owned placements increase sharply to base case levels and hedging activities are moved to November. The additional placement of hedge positions in November causes the Chapter 6 140 November borrowing activities for the 85,000- and 90,000-farm plan to exceed the amount for the corresponding farm plans in the base case. The borrowing of funds increases even further, compared to the base case, when the amount of margin calls is raised to 150%. In order to compensate for the indirect hedging costs, which are borrowing costs, the number of September owned feeder placements is increased. Still, despite borrowing costs, the achieved return standard deviations are close to the base case solutions. From the 92,500-farm plan on, future margin calls significantly stress the backgrounding operation's cash flow budget. The combined hedging ratio declines (92,500-farm plan: 0.85 for the base case; 0.69 for the 100%-scenario), because custom feeding fees that usually picked up the margin calls are too low to maintain a higher hedging level without neglecting other cash flow requirements (see figure 6.4). Figure 6.4: Development of the Combined Hedging Ratio for the Margin Call Scenario Group Expected Return Parameter(Lambda), $ Chapter 6 141 Increased outside financing for possible initial margins and even margin calls themselves would now taint the expected return constraint to an extent that return shortcomings could not possibly be caught by increased owned cattle placements, without violating the backgrounding operation's capacities and financial commitments. Nevertheless, the achieved standard deviations of returns are in the proximity of the base case solutions. Similar patterns apply, however more strongly, to the 150%-scenario. For the highest Lambda parameter level ($96,800) the quadratic risk programming model selects for both scenarios the same farm plans as established in the base case solutions. Finally, it can be stated that risk management prospects for the backgrounding management are hardly affected. The common notion that margin calls would deter ranchers from engaging in hedging with cattle futures contracts cannot be supported. Some Subtle Aspects of the Margin Call Scenario Group: Table 6.6 illustrates the relationship of additional November owned feeder placements to November hedging activities and to the November borrowing activity for the 100%-scenario. Borrowing activities, not only for November but also for consecutive production months, cause a penalty on the expected overall farm return constraint-Lambda. Hence, the question for the backgrounding management arises, how much can it afford to borrow in order to maintain an as low as possible return standard deviation, but also to match the set expected return parameter. For the $85,000 to $90,000 Lambda range, this question is answered with an increase of borrowing activities, which is taken even further in the 150%-scenario. Moving hedging activities from September to November and placing more owned feeders in November, in order to compensate for the Chapter 6 142 expected overall return loss caused by hedging, requires outside financing, and, as presented, even more in the margin scenarios than in the base case. Thus table 6.6 illustrates the relation between feeder placements, hedge placements, and borrowing in November for the 100%-scenario. Table 6.6: Estimate for the November Borrowing Activity of the 100%-Scenario Lambda November Steers Change from 82,500 (Head) Initial Costs ($) -1-November Hedging Change from 82,500 (Contracts) Initial Margin ($) -2-Total Changing Costs ($) (1+2) Borrowed in Nov. in $ 85000 161 93,584 6.63 5,758 99,342 100,609 87500 345 200,536 9.55 8,294 208,830 213,527 90000 530 308,070 12.48 10,839 318,910 326,445 92500 650 377,822 12.30 10,693 388,505 398,771 95000 742 431,299 6.24 5,420 436,718 447,359 96800 777 451,642 0 0 451,642 462,936 Because of indirect higher hedging costs, i.e., increased borrowing costs, it is then in the second step, that additional September owned feeders are placed. The management places more September owned feeders because they can be financed through initial capital, hence, do not increase borrowing costs. 6.4 Summary This chapter reported and discussed the results for the base case and the scenario groups. A conclusion will be given in Chapter 7. 143 Chapter 7 7. Summary and Conclusions 7.1 Thesis Summary 7.1.1 Problem Backgrounding cattle is a risky business. First, large amounts of short-term capital are required to buy feeder cattle and feedstuffs. Second, a lengthy ten-month production period must be sustained, causing a cost-revenue gap, which requires the management to establish a carefully planned monthly cash flow budget to maintain financial liquidity. And third, cattle prices of finished cattle are volatile and, frankly, unknown at the time the the decision is taken to place feeders. Despite these uncertainties, the successful management must address and assess these potential risks in its short-term decision-making process, where structures and financial commitments for the operation do not change. For a given production environment in the Peace River area, this study developed an economic model that reveals the risk and return trade-offs in cattle backgrounding and assists the backgrounder in the formation of specific management strategies for her/his operation. Short-term optimal backgrounding plans are derived, which acknowledge the volatility of feeder finishing prices, the management's risk-aversity and the necessity to maintain financial liquidity. 7.1.2 Study Approach To set a stage for this study, an overview of backgrounding cattle in the Peace River area was presented in Chapter 2. It was identified that the Peace River area Chapter 7 144 provides comparative advantages for cattle backgrounding compared to other regions in British Columbia. The return risks associated with cattle backgrounding were highlighted by emphasizing the return variation of backgrounding in a short-term decision-making context, which assumed that all costs were known at the time feeders were placed, the unknown factor is the underlying finishing price. Chapter 2 then described production characteristics for the case study operation. For this backgrounding operation, feeders could be placed in fall (Sept., Oct. and Nov.) for an overall production period of ten months and in May for a four-month production period. Backgrounding of both feeder groups had to be achieved through local feedstuffs. Section 2.5.3 identified the main sources of return risk: production, market and financial risk. Production risk was determined to be off-set by adequate animal health care management, market risk could be cushioned by forward pricing through appropriate futures contracts and by placing custom feeders, and financial risk could be eased by placing feeders at different months, by providing access to outside financing and by staying with a well planned monthly cash flow budget. Chapter 2 concluded that the management of a backgrounding operation would then be in a position to alter its individual risk exposure on a group of feeders from no risk, by deciding not to produce, to negligible risk, by custom feeding, to moderate risk, by owning and hedging feeders, or to full risk, by owning and not hedging feeders. In addition, the management would be able to alter the overall farm return risk by different feeder placement months. Chapter 7 145 In Chapter 3 the literature of decision making under uncertainty was reviewed, to determine the approach which would best accommodate the backgrounding management's risk concerns in its short-term decision making process. The Expected Utility Theorem and the subsequent maximization of the decision maker's utility function were identified to be the most powerful approach to accommodate these risk concerns into the short-term decision making process. It was shown that the expected utility problem could be transformed into an expected value-variance analysis (E-V Criterion) as long as normality in its variable distribution is assumed. This led to the application of Markowitz's portfolio selection theory (1952), which states that the main objective of a farm model, incorporating uncertainty, is to mirdmize the overall portfolio variance for alternative levels of expected returns, e.g., farm returns. Thus, for our backgrounding operation, the most risk efficient E-V set of farm plans could be derived by minimizing the variance of activity returns subject to an expected total backgrounding operation return (Lambda) and other resource constraints. The nature of the E-V framework allows us to show the changes in the backgrounding risk management strategies, i.e., hedging, placing of custom feeders, off-farm investments or different placement months of feeders. Depending on the management's degree of risk-aversity, specified by the set expected return parameter (Lambda), the E-V framework selects risk-appropriate activities in order to achieve Lambda; hence, if the decision maker chooses a relatively lower Lambda s/he reveals a higher risk-aversity and, subsequently, the E-V framework will favour less risky activities, and vice versa. By varying Lambda from zero to a maximum value, the decision maker can trace the risk efficient E-V frontier, representing all optimal farm plans. After having Chapter 7 146 produced this frontier, the backgrounding management can then select the most desirable farm plan along the risk-efficient E-V frontier. A quadratic programming model was chosen to capture the E-V criterion, since a linear framework would not have adequately simulated the variability of revenues for possible activities by parametrically changing output prices. In addition, the quadratic programming framework is appealing with respect to the objective of minimizing the overall return variance and can easily illustrate the question of risk and return trade-offs for activities in the management's decision set. Chapter 3 concluded with an explanation of cattle hedging principles with cattle futures markets, highlighting not only the relation between spot market and futures market prices but also the one between the average futures purchase and futures selling price (BIAS). The actual model was developed in Chapter 4. The backgrounding activity set consisted of production alternatives defined by various fall feeder placements (Sept., Oct., Nov.), same production type, and May feeder placements (light slaughter cattle production); both of them could be either placed as custom feeders or as backgrounding operation owned feeders. In order to reduce overall return risk, the backgrounding management could employ hedging activities complying with the idea of a routine hedge; hence, Feeder Cattle Futures hedges could be utilized to reduce the return variation for fall feeders and Live Cattle Futures hedges could be placed for May feeder placements. Further options available to the decision-maker included off-farm investment opportunities and access to a line of credit, to ease financial risk. Structural costs were imposed on the management's cash flow budget. Production data and technical coefficients for the model were derived mostly from current backgrounding practices on Clover Farms Ltd. Price Chapter 7 147 data and hedging related data were derived from secondary sources. Despite the model calibration for a specific ranch, the model results were assumed to be generic enough to be relevant for backgrounding operations throughout North-Western Canada. The study then addressed the interaction between ownership options of cattle placements, the cattle placement month, the monthly cash flow requirements, and the management's degree of risk-aversity. Further, by changing hedging options, by widening the BIAS between relevant futures prices for hedging activities, and by increasing the cash flow burden caused by hedging activities, this study revealed the changes in optimal backgrounding plans that the management would consider in its short-term decision making process. The model results were presented in Chapter 6. First, the base case, with the least constraint decision set, was presented to identify the principles of the backgrounding management's risk minimizing strategy. Next, the results of three scenario groups in comparison with the base case were discussed. The first scenario group dealt with changes in the hedging strategies, that is from non-constraint hedging (base case), to constraint hedging (constraint to the logical cattle placement) and to no hedging at all. The second scenario group emphasized changes in the BIAS of the futures prices associated with the hedging activities. Once again, starting with the base case, with no BIAS, the BIAS was increased from 0.025 to 0.075 in step values of 0.025. The final scenario group addressed the impact of margin calls on the backgrounding management's attempt to reduce risk. The results were presented in the form of risk-efficient frontiers, along with their optimal farm plans sets (Appendix 6). Chapter 7 148 7.2 Conclusions The overall objective of this study was to identify the most effective feeder placement, hedging, and off-farm investment strategies for reducing net revenue variability on a cattle backgrounding operation. Thus, the models identified detailed backgrounding activity plans for the time frame of one production year that varied depending on the assumed backgrounding management's risk-aversity and the change in underlying model parameters. The different farm plans sets were portrayed graphically as risk-efficient frontiers (E-V analysis), which enable the backgrounding management to visualize the risk and net return trade-offs for different farm plans. In general, the intended risk-return ranking of the backgrounding operation's activities set, that is from custom feeding and off-farm investments, with no risk and low return, to owned cattle placements combined with hedging, at a moderate risk and moderate return, and to owned cattle placements only, with the highest risk and the highest returns, was confirmed by the farm plan solutions. Thus, the larger the expected return level, ergo, the lower the backgrounding management's degree of risk-aversity, the more "risky" activities were favoured. For the Lambda range from zero to $65,000, the backgrounding management engaged in custom feeding and off-farm investments only, giving custom feeders the first choice and increasing their numbers depending on the set expected return parameter. Off-farm investments captured mainly excess cash funds within the production year. However, in the upper range of Lambda, $70,000 to $95,000, hedging activities and owned cattle placements came into play, echoing the management's lower degree of Chapter 7 149 risk-aversity. As for the base case, cross-hedging occurred, that is, the management sold live cattle contracts in May to cushion the overall variability of farm returns, originating from fall feeders only. Hedge ratios reached their peak value in the 82,500-Lambda farm plan and declined from there to nil in the maximum farm plan ($96,800). With the increase of Lambda beyond the $70,000 level, the number of custom feeders and off-farm investments declined. Outside financing was required from the 85,000-farm plan on. Increasing borrowing amounts in the November feeder placement month, caused a precarious cash flow situation for consecutive months, which was alleviated by further borrowing activities. The necessity of outside financing at the 85,000-Lambda level showed that monthly custom feeder fees, especially from the September placements, were a significant cash source for the backgrounding operation below the 85,000-Lambda level. In the first scenario group, where hedging activities were progressively constraint, from no constraint to fully banned, the adjustments of farm plans along the risk-efficient frontiers could be characterized as follows. Adjustments occured only for farm plans within the 70,000- to 95,000-Lambda range. In the order of base case, constraint hedging scenario and no-hedging scenario, the number of custom feeders was less and less reduced whereas owned cattle placements were being progressively less increased. The increase in custom feeders caused more off-farm investments too. With respect to the hedging activities, they were reduced from the base case to the constraint hedging scenario resulting in a slightly higher standard deviation of the optimal farm plan returns. As a routine hedge was assumed for deriving the hedging costs, the evidence of higher standard deviations of returns compared to the base case indicated that the true classical hedge Chapter 7 150 strategy was not the most optimal risk minimizing strategy for the backgrounding operation; however, compared to the no-hedging scenario, where the return standard deviations almost doubled, the worthiness of a classical hedge could not be disputed. When an increasing downward BIAS for hedging activities was assumed, second scenario group, the risk-return trade-off of hedging alternatives became more and more imperative for the backgrounding management. Despite an increase in BIAS, hedging activities still provided a means towards reducing the overall farm return standard deviation, however at higher and higher costs. As long as self-financed, the management maintained hedging activities, and placed more owned feeders than in the base case to compensate for the hedging cost-induced overall farm return reduction. With the BIAS increase hedging ratios declined and diminished to zero for the BIAS equals 0.075 case. As soon as outside financing was required, the additional hedging costs did not support hedging in the management's decision set, and the assumption that hedging encourages a larger number of owned cattle placements resumed in favour of the base case. The last scenario group imposed changes on the hedging activities' margin calls. It was assumed that margin calls paid over the hedging period would be balanced at the hedging position's lifting time; thus causing a temporary stress on the backgrounding operation's cash flow budget. The backgrounding management responded with rearranging the feeder placements for self-financed farm plans This was done to free the necessary cash in-flows for upcoming margin calls and to keep the standard deviation of returns almost as low as in the base case. As soon as outside financing was required, the backgrounding management had to address the question of how much it could afford to Chapter 7 151 borrow in order to maintain an as low as possible standard deviation of return. Additional cattle placements and hedging activities in November caused the borrowing activities for the 85,000- and 90,000-farm plan to exceed the amounts for corresponding farm plans in the base case. As the risk-efficient frontiers showed, the achieved farm return standard deviations were still close to the base case solutions. From the 92,500-farm plan on, the combined hedge ratios finally declined sharply; still, the course of the risk-efficient frontiers was in the proximity of the base case solutions. The final scenario group showed that the risk management prospects for the backgrounding management were hardly affected by margin calls. 7.3 Limitations and Areas for Further Research 7.3.1 Limitations The results and conclusions of this study must be viewed in light of the assumptions made in setting up the backgrounding operation model. Among these assumptions are hedging strategy, exchange rate, feeder type, price data and feeding schedule. The model employed a routine hedging strategy for feeder cattle and light slaughter cattle as a basis to make comparisons in the risk management strategy of the backgrounding management. Despite having allowed for cross-hedging, other hedging strategies like selective hedging, where a hedge position is taken only when a profit can be made in the futures markets, or hedging strategies based on options, etc., might have been better means to reduce the overall return risk. As in the study by Carter and Loyns (1985), which analyzed the usefulness of U.S. futures markets to reduce the price risk Chapter 7 152 exposure for Western Canadian feedlot operators, this research could have included hedging alternatives different in strategy instead of being different in their deployment time only. The inclusion of hedging against the Canadian and U.S. dollar exchange rate might have also widened the risk management strategies for the backgrounder; because, as any profit or loss on a futures transaction is in U.S. dollars, the net profit or loss in Canadian dollars would be determined by the current exchange rate (Caldwell, et alt., 1982). Caldwell explains this effect as follow: Assume the Canadian was at par at the time the hedge was placed, and that at the time the hedge was lifted, the Canadian dollar was worth $0.85 U.S. This difference would directly affect the Canadian hedger by increasing any profit or loss from the futures contract. [...] The key point is that this change in the profit or loss from the futures contract cannot be anticipated since it is due solely to the exchange rate. This change will not be directly offset by an equal change in the profit or loss from the cash transaction; thus, the result of the hedge is affected by any abrupt change in the exchange rate (Caldwell, et alt., 1982, p. 262). Hence, by isolating the variability of the exchange rate and by taking specific precautions against the exchange rate risk, i.e., hedging against the exchange rate, the backgrounding management, in this study, might have been in the position to develop more efficient risk management strategies. Freeze (1989) detected an improvement in the performance of live cattle hedging when the Canadian dollar was hedged. The management's participation in a government stabilization program for feeder finishing prices could have been investigated too; however, this study, in order to be able to anticipate the backgrounding activity interactions, focused on risk-return trade-offs of routine hedging, placing of owned and custom feeders and off-farm investments only, through maintaining a sustainable cash flow. Chapter 7 153 Another assumption within this study is that feed rations were not optimized. Feed rations and feeding schedules were taken from cattle backgrounding experiences in the Peace River area. Two aspects seemed to make this procedure justifiable. First, the intended production management for the to-be-backgrounded feeders was not flexible. Feeders were either backgrounded from 450 lbs. to 950 lbs. in a ten month period or were fed from 700 lbs. to 1,050 lbs. in four months starting in May. Feeder holding strategies, which would require lower energy feed rations, or intensified feeding strategies, in response to changing finishing feeder prices, were not considered in this short-term decision making problem. Such considerations do more apply in a feedlot management problem, where the production period per unit is shorter and placements can occur over the whole year. Second, the applied feed rations and feeding schedules could already be considered to be optimized to some degree, because they were drawn from on-farm experience over a couple of years; hence, they accounted for the desired weight gain performance and even reflected the severe climatic conditions in the Peace River area. It is for this reason, why further provisions for environment changes in the model were not made (e.g., colder temperatures would impact a followed feeding regime). A unique aspect in this backgrounding model is the simplification regarding the data set of the futures prices for fall hedging activities and the finishing prices for fall feeder placements. Due to the insufficient sample size of the data sets for each activity, hedges and feeder placements, the original idea of deriving individual variances and subsequent covariances had to be abandoned. Instead, to make the available data sets useable, the individual data sets for fall activities were stacked. This stacking procedure Chapter 7 154 generated rather simplified variance and covariance terms for all fall backgrounding activities. Subsequently, the loss of return variance minimizing effects through different owned cattle and hedge placing in the fall period had to be accepted. Thus, it would have benefited the study to have larger data sets available. 7.3.2 Areas for Further Research The graphical presentation of risk and return trade-offs for specified backgrounding operation parameters and risk management alternatives helps the backgrounding management to form specific management strategies. Risk-efficient frontiers add a new dimension to backgrounding management, because they set return prospects of backgrounding activities and their variation in context with the management's personal willingness to bear risk. To this end, it would be useful to develop a more generic backgrounding model that could easily adopt specific backgrounding operation parameters. A more generic short-term decision-making model would require a broader range of risk management strategies. The range of risk management options should be extended by different hedging strategies with cattle futures and/or option markets respectively, government stabilization plans and custom feeders, but also with respect to the type of cattle operation. In contrast to the case study, which represented a specialized backgrounding operation, a more generic model should also account for mixed operations, where, for example, grain production and cattle ranching are both present. Hence, parameters that describe risk associated with grain production should be introduced, to take advantage of the risk minimizing effects of diversification in production. A broader Chapter 7 155 range of marketing alternatives would also enhance the backgrounding management's ability to manage risk. Finally, in order to acknowledge the potential access to a wider range of feedstuffs, a least-cost feed ration program should be build in into a more generic short-term cattle backgrounding decision-making model. Having programmed such a model on a user-friendly software package, this program could then be made available to backgrounding managements and could strongly assist local backgrounding managements in finding risk-efficient backgrounding plans; however, to guarantee the viability of this tool, automatic access to extensive data bases would be a necessity. 7.4 Key Conclusions The tracing of risk-efficient frontiers for backgrounding operations' returns reveals risk and return trade-offs in cattle backgrounding and assists in the formation of specific management strategies for a backgrounding operation. Risk-efficient frontiers set return prospects of backgrounding activities and their return variations in context with the management's degree of risk-aversity. The simple rule, higher risks follow higher returns, is visualized. Following a rule of profit maximization would not consider this aspect in management; hence would lead to farm plans that would be unacceptable for a backgrounding management. The participation in a routine hedging program with Feeder Cattle and Live Cattle Futures contracts provided a compelling return-risk management tool for the backgrounding operation. The introduction of a downward BIAS reduced hedging ratios drastically, whereas margin calls did hardly affect the use of hedging. By linking all Chapter 7 156 backgrounding activities through the operation's monthly cash flow budget, the importance of cash flow management was underlined. Custom feeder options proved themselves essential in closing the typical cost-revenue gap in backgrounding and, despite offering the lowest returns, enabled the backgrounding management to engage in higher return-risk backgrounding activities. 157 Bibliography Albin, Robert C. and G. B. Thompson. 1990. Cattle Feeding: A Guide to Management. Trafton Printing, Inc. Anderson, J. R., J. L. Dillon and B. Ffardaker. 1977. Agricultural Decision Analysis. Iowa State University Press, Iowa. Barry, Peter, J. 1984. Riskmanagement in Agriculture. The Iowa State University Press. Bellman, Richard E. and Stuart E. Dryfuss. 1962. Applied Dynamic Programming. Princton University Press. Princton. Biswanger, H. P. 1980. Attitudes Towards Risk: Experimental Measurement in Rural India. American Journal of Agricultural Economics 62: 395-407 Blank, Steven C , Colin A. Carter and Brian H. Schmiesing. 1991. Futures and Option Markets: Trading in Financials and Commodities. Prentice-Hall, Inc., New Jerssey. Caldwell, J., J. Copeland and M. Hawkins. 1982. Alternative Hedging Strategies for an Alberta Feedlot Operator. Canadian Journal of Agricultural Economics 30 (3/Nov.): 257. CANFAX. 1995. Spot Market Prices of all Cattle Weight Classes for the Edmonton -Northern Alberta - Region (weekly basis). Jan. 1991 - Week 29. 1995. Provided by: Brian Freeze, Agricultural Canada Research Branch, Lethbridge Alberta. CANSIM. 1995. Exchange Rate US/Cdn.. Spot Rate Average Noon. Daily Basis. Jan.l, 1991 - August 15, 1995. Series B 100,000. Carter, C. A. and R. M. A. Loyns. 1985. Hedging Feedlot Cattle: A Canadian Perspective. American Journal of Agricultural Economics 67 (1/ Feb.): 32-39. Castle, Emery N. 1987. Farm Business Management. Macmillan Publishing Company, New York. Chicago Mercantile Exchange. 1994. Commodity Futures and Options: Facts & Resources. Chicago Mercantile Exchange. 1994. Self Study Guide to Hedging with Livestock Futures. Bibliography 158 Chicago Mercantile Exchange. 1995. Raw Data on Daily Trading in Live and Feeder Cattle Futures Contracts. Jan. 1990 - May 1995. Records Retention MIS Administrative Services, Chicago. Dillon, J. L. 1971. An Expository Review of Bernoullion Decision Theory in Agriculture: Is Utility Futility? Revision Marks Agricultural Economics 42 (3): 80 Equuus Consulting. October 1990. Into the Nineties - A Sectoral Profile and Situation Analysis of the Beef Industry of British Columbia. Falatoonzadeh, Hamid, J. Richard Conner and Rulon D. Pope. 1985. Risk Management Strategies to Reduce Net Income Variability for Farmers. Southern Journal of Agricultural Economics 17 (1): 117. Freebaim, J. W. 1973. Some Estimates of Supply and Inventory Respense Functions for the Cattle and Sheep Sector of New South Wales. Review of Marketing and Agricultural Economics 41 (1973): 53-90. Freeze, Brian S. 1989. An Analysis of Risk Management Strategies for Southern Alberta Feedlots. Ph.D Thesis. Oregon State University (June 30.). Freeze, Brian S., A. Gene Nelson, Wesley N. Musser and R. Hironaka. 1990. Feeding and Marketing Portfolio Effects of Cattle Feeding in Alberta. Canadian Journal of Agricultural Economics 38 (2/July): 233. Gaspar, Victor. 1994. Hedging with Options on Commodity Futures Contracts: A Safety-First versus Expected Utility Approach. M.Sc. Thesis. University of British Columbia (July, 1994). Glen, John J. 1980. A mathematical Programming Approach to Beef Feedlot Optimization. Management Science 26 (5/ May): 524. Goswami, S. N. 1993. Farm Planning in Hills under Risk and Uncertainty - A Parametric Linear Programming Approach. Indian Journal of Economics 74/292 (July 10.): 51. University of Allahabad. Gracey, Charles. 1981. The Cattle Cycle. Canadian Cattlemen's Association. Hanf, C. H. and G. Schiefer. 1983. Planing and Decision in Agribusiness: Principles and Experiences. Elsevier Scientific Publishing Company. Bibliography 159 Hazell, Peter B. R. 1971. A Linear Alternative to Quadratic and Semivariance Programming for Farm Planing under Uncertainty. American Journal of Agricultural Economics 53 (1/ February): 53. Hazell, Peter B. R. 1984. Source on Increased Instability in India and U.S. Cereal Production. American Journal of Agricultural Economics 66 (1984): 303-311. Hazell, Peter B. R. and Roger D. Norton. 1986. Mathematical Programming for Economic Analysis in Agriculture. MacMillan Publishing Company. New York. Helmuth, J. W. 1981. A Report on the Systematic Downward Bias in Live Cattle Futures Prices. Journal of Futures Markets 3: 347-58. Helmuth, J. W.,-Staff report of the Committee on Small Business. 1981. A Report to the Honorable Neal Smith, Member of Congress, on the Systematic Downward BIAS in Live Cattle Futures. House of Representatives, 97th Con., 1st Sees., 27. February. Hey, J. D. 1979. Uncertainty in Microeconomics. University Press. New York. Kahl, Kandice H. 1983. Determination of the Recommended Hedging Ratio. American Journal of Agricultural Economics 65 (3/August): 603 Knight, F. H. 1921. Risk, Uncertainty and Profit. Boston: Houghton Mifflin. Lawrence, John and Michael S. Kaylen. 1993. Risk Management for Livestock Producers. Hedging and Contract Production. Journal of the American Society of Farm Managers and Rural Appraisers 57 (1): 59. Lawrence, John D. 1989. A Stochastic Dynamic Programming Model for Livestock Producers. Ph.D. Thesis. University of Missouri-Columbia. (December). Maiga, Attaher. 1994. Analyse Regionale de Differentes Methodes de Stabilisation des Revenus Agricole au Quebec. M.Sc. Thesis, Universite Laval (Juin). Markowitz, Harry M. 1952. Portfolio Selection. Journal of Finance (7/March). Markowtiz, Harry M. 1959. Portfolio Selection. Cowles Foundation Monograph 16, Wiley. New York. Marsh, John M. and Clyde R Greer. 1994. Backgrounding Montana Steer Calves. Montana AgResearch (fall 1994): 19. Bibliography 160 McCarl, Bruce A. and Hayri Onal. 1989. Linear Approximation Using MOT AD and Seperable Programming: Should it be done? American Journal of Agricultural Economics 11 (1/February): 158. Meyer, C. F., R. J. Newett. 1970. Dynamic Programming for Feedlot Optimization. Management Science 16 (6/February): 13-410. Northern Horizon. 1995. Clover Farms Ltd. Northern Horizon (February 1995): B4. Oellermann, Charles M., B. Wade Brorsen and Paul L. Farris. 1989. Price Discovery for Feeder Cattle. The Journal of Futures Markets 9 (2/April): 113. Palme, Lennart A. Jr. and James Graham. 1981. The Systematic Downward Bias in Live Cattle Futures: An Evaluation. The Journal of Futures Markets 1 (3):359-366. Perry, Merrill G. 1986. Toward a Holistic Approach to the Cropping Mix Decision. Unpublished Ph.D. Thesis. Texas. A&M University. Rae, Allan N. 1994. Agricultural Management Economics: Activity Analysis and Decision Making. Massey University. New Zealand. Rodrigues, Abelando and R. G. Traylor. 1988. Stochastic Modeling of Short-Term Cattle Operations. American Journal of Agricultural Economics 70 (1/ Feb.): 121. Rogers, J. A. and E. T. Osborn. 1979. The Beef Backgrounding Sector of the British Columbia Beef Industry, Working Paper (March 1979). Rolfo, Jacques. 1980. Optimal Hedging under Price and Quantity Uncertainty: The Case of the Cocoa Producer. Journal of Political Economy 88 (1/ Feb.): 100. Schroeder Ted C. and Marvin L. Hayenga. 1988. Comparison of Selective Hedging and Options Strategies in Cattle Feedlot Risk Management. The Journal of Futures Markets 8 (2/ April): 142-156. SCI Sparks Companies, Inc. 1992. British Columbia Beef Industry Review. Report (April). Statistics Canada. 1995. Agricultural Profile of British Columbia. Statistics Canada Part 2 Cat. 95-394. Thomas, Verl, M. 1986. Beef Cattle Production - An Integrated Approach. Lea & Febiger, Philadelphia (1986). Bibliography 161 Von Neumann, J. and O. Morgenstern. 1947. Theory of Games and Economic Behavior. Princton University Press. Whitson, R. E., D. J. Barry and R. E. Lacewell. 1976. Vertical Integration for Risk Management: An Application to a Cattle Ranch. Southern Journal of Agricultural Economics 2: 45. Yager, William A., Clyde R. Greer and Oscar R. Burt. 1980. Optimal Policies for Marketing Cull Beef Cows. American Journal of Agricultural Economics 62 (3/August): 456. 162 Appendix 4 Spread Sheet Model Page EXCEL SPREAD SHEET MODEL 163-165 CASH FLOW COEFFICIENT MATRIX 166 Appendix 4 163 § 8 8 ; s § r- r- r» C\J OJ C\J r-.r--.r--LO LO LO CO CO CO www & & & S> CO 0) CT) CO o o ci ci O ) CD CD i - CO LO CO CO LO LO CO CO CM CM 8! $ 3 LO LO LO o o o o d d S LO S o o o o d d o o o o o o s I ? r-- S cp co co Si 8 8 N S $ CO CO CO o o o o ol CM co co|j sir 8 Sl 8 Rl 8 5 31 S CO o co cvi c j | 8 8 8 CM CM CO CM I LO >N 0)1 ° S Ti s r o o col co I n J n J R J n j i T j a j f l J t i j Q o o o o o o o o o o o o o o o o c o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o 2 0 0 0 0 0 0 0 0 0 0 0 0 0 o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o O ^ O V O JQ ^coificoiricoio'-T-; s LO N in s in CO CJ> CO O ) CO °i °? r-: °i O CO O CO o y >u I s I s vo J 3 8 2 ffi 8 S. LO >N tri <N = <P 5 <P S <P f 3 SJ 3 3! S O CO O CO Z N CO N CD ~<N iri ™. iri E N CD S CD - . C O • CD ' CM lO CM CO N CO 8 CO CO LO CO OR: O O O O O O O O * N o o o o o o o o O O O O O O O O O O O O O O O O S CO N O in co r-» iri <N °? P cp t- o in T m CM • 3 °- 2 cS CM S- ^ irj K ^ N CD oo n O O O O O O O O O O O O O O O O CM w CM m m i -CO CD h; O CM CO CO rt CO o co in co in co s in w in w a q co cp T - o in 1 CO T CO CM ' S 3 w 5 W S N CO CO CO CO V O ) CO O CO O CO 9 T f CO N CD N CO CO CM in" w iri N . iri *P fe <? te <? °P 7 O O O O O O O O O O O O O O O O W w O O Z z 5 5 Appendix 4 164 Appendix 4 165 Appendix 4 166 3= O v 3 (ft Q. a if 8 * LL (0 f O) O ^ O) r- W 5 »- CM S TT 5 N f PJ <- (D N v 7 i i i 1 CJ s CO 5 CO Q s s &> o o CO co CO CO ci ci O) O) (D (D 1 T - OO CO CO 1 y cn n N N to C J C O C O C O C O ' r t C O P J C J C J C O ( o t o N w w n n s s o nnooQ'-T-TfTt,-MNoioioiggnnQ ncococoowriwcviri o o r-O) CD s ? CO If) (O CO CJ r-» r-; oo "* in § i e d d • o o o o o o o o o o o o o o o o o o 8 o CO r-.r-.co $ $ 3 cn co co co co ^ m m S o o o o o o o o o o o o o o o o o CO III » «P 2 3 25532222522 2 s 2 * -•g I 5 5 5 5 5 5 5 w c i e y w c y COCOfOCOCOCOCOCOCOCOCDCO CO CD Ol CJ CD CM CM Ol S C J T— LO CO CO C J S) Sf $ Q to in LO LO Lo O) CM CM • cj i- m S3 si a co in io o o o odd T - O) CM CM cn • w i - m ft 8 a 8 5 S m in in o o o d d d d O N O l S N t O C O O ) cococxj'-ojncoi-m m I , a s o o o o o o o G c S o S 5 4 - » c O >< UL U CO W s Rl O u o 10 03 o 9 f II 3 2 3 23S222223522 167 Appendix 5 Production and Model Data Page INITIAL COSTS, SELLING PRICE, CUSTOM FEES 168 FEEDING AND BEDDING SCHEDULE 169 FEED RATIONS 170 CASH FLOW REQUIREMENTS FOR HEDGING ACTIVITIES 171 GROSS MARGIN CALCULATIONS 172-174 MODEL DATA BASE 175-176 ROLFO ERROR FORECASTS 177 RECOVERING VARIANCES-COVARIANCES 178 Appendix 5 O "D Q. a co 0) |1* CM OJ CJ 00 CO CO 00 00 CO C O C O C O cn ai cn 00 00 co 7 < W ^ L O L O ^ 8 5 O Q co O SP o CO in , o cu *t *<t **t I ? I* a. co co in CO 1^ in m in in N ^ r~- (D CD in w w O) K IO Ol O r t K C O Ki CM CM eg 8 § | Q . ^ CD O CO O o cd CO C O C O >. CVJ a co o ca co ca — ca co o p m CL CO CD ™ i2 c ca .c o o o co ,cj> o . . CD C " 5 c s » c to c o «t • 8 •§ 5, w cn „ c5 Appendix 5 169 Date Feedin Wint Month: Feed ing & beed ing Week: g and E erfeeding | 1. 2 4 teddi [Feeder 2. 6 a ng S • Prod 3. 10 12 5ch€ uctioi 4. 14 16 ;dul< 5. 18 20 3 6. 22 24 7. 26 28 8. 30 32 15SS Starter Ration (lbs/day) Growing Ration (lbs/day) 1 Hay bale/200 head/3 day 4 straw bales/200 head/7 day 20 27.5 27.5 L. . An 150S J Starter Ration (lbs/day) Growing Ration (lbs/day) 1 Hay bale/200 head/3 day 4 straw bales/200 head/7 day 20 27.5 27.5 34 L~ An, 15NS Starter R tion (lbs/d y) Growing Ration (lbs/day) 1 Hay bale/200 head/3 day 4 straw bales/200 head/7 day 20 27.5-rKA fc An Supplement hay and bedding bale @ Hay head lbs Cd$ Sept. and Oct.: 0.325 390 7.32 Nov.: 0.300 360 6.75 bale @ Straw head lbs Cd$ Sept.: 0.600 480 6.21 Oct., Nov.: 0.685 548 7.09 Annotation: - Daily feed rations are expressed on a wet matter basis. - As practiced on Clover Farms Ltd. - Cost figures from Clover Farms Ltd. accounting books (1994) Appendix 5 170 (0 c o CO rr Q UJ UJ lis; 1 l If •> o | (3 g | .9 1 I a & 81 1 i U. CO CM co w to ca E i f S e a. — en w <o £ In £ ~ S - 8! co ^ co TJ= M || O > || g OJ CD ... ™ oj -c £ « ti (0 (0 -fc £ 3 => 13 S J3 J3 J3 5 m o *C) 03 0> 3 c i_ ro a> o Q . O £ a E _ S a I I 2| in a 8 8 O u: 0 c CO o 1 CD TJ 0 0 1 2 I N «fc i » 5 « S o f , : £ lO r-o r - n « r s N O ' ^ CO O CN ^  » - a o o ^ co & o JB . . . . i ^ CM to 05 . CM iri £ ^ in £ o <q 5 T f " H CM O .5 U U. u> ±i a 00 a • >» » o CM O „ § 2 o °. g" -a E If § * o £ IS C •— CD I I S cd c ^ M l Appendix 5 171 Cash Flow Requirements for Hedging Activities Feeder Cattle $ Live Cattle $ 650 US 600 US 0 US 0 US 90 CD 90 CD Margins in $/cwt 500 cwt 400 cwt Feeder Cattle $ Live Cattle $ Initial Margin 1.73706 Cd 2.0043 Cd Margin Call 0 Cd 0 Cd Brockerage Fee 0.240516 Cd 0.300645 Cd Most current Exchange Rate: US$/Cd$ 1.3362 Margin Calls: 0%, 100% or 150% of initial margin Annotation: - Information is provided by Douglas J . Taylor, Richardson Greenshields, Vancouver from July 14,1995 - Exchange Rate: The Financial Post, Tuesday, October 17,1995, P. 48 - Initial Margin to be paid when short-hedge is placed. - Expected margin calls are assumed to be spend over the whole hedging period. - The brockerage fee is due when the hedge transaction (place and lift) is completed. Initial Margin Margin Call Brockerage Fee Appendix 5 172 Gross Margin Calculations_($/head)1 15 Sept [15S--] 15 Oct [150--1 15 Noc [15N-] 15. M,iy [15M-] In general: Steers [—$•], Onned [ —O], Custom {—-C} 15SSO 15SSC 1SOSO 150SC 15NSO 15NSC 15MSO 15MSC Gross margins: 117.29 25.58 125.24 24.70 124.35 21.04 Gross margins: -77.26 25.33 Total expenses: (S/head) 177.96 149.98 178.66 150.86 182.26 154.52 Total expenses: ($/head) 167.64 107.47 Break even: ($/cwt sold) 83.87 83.00 83.10 Break even: ($/cwt sold) 88.76 Break even: ($/lb. custom) 0.324637 0.326541 0.334451 Break even: ($/lb. custom) 0.323714 Ration costs: Ration costs: J. Period 1. Period Starter ration Welcome ration Days on: 30 30 30 30 30 30 Days on: 21 21 Intake lbs/day 23.8 23.8 23.8 23.8 23.8 23.8 Intake lbs/day 43.56621 43.56621 Total lbs 714 714 714 714 714 714 Total lbs 914.8905 914.8905 Cost(S)'1 lb. ration 0 020683 0020683 0 020683 0020683 0020683 0 020683 Cost($)/l lb ration 0 017771 0,017771 Cost($)/Total lbs 14.76747 14.76747 14.76747 14.76747 14.76747 14.76747 Cost($)/Total lbs 16.2583 16.2583 Growing ration Finishing ration Days on: 0 0 0 0 0 0 Days on: 9 9 Intake lbs/day 0 0 0 0 0 0 Intake lbs/day 35.32698 35.32698 Total lbs 0 0 0 0 0 0 Total lbs 317.9429 317.9429 Cost($)/1 lb. ration 0 013903 0 013903 0.013903 0 013903 0.013903 0013903 Cost(S)/1 lb. ration 0 0265O6 0.026596 Cost(S) Total lbs 0 0 0 0 0 6 Cost($)/Total lbs 8.455901 8.455901 Total cost in period 1 14.76747 14.76747 14.76747 14.76747 14.76747 14.76747 Total cost in period 1 24.7142 24.7142 2. Period 2. Period Starter ration Welcome ration Days on: 0 0 0 0 30 30 Days on: 0 0 Intake lbs/day 0 0 0 0 27.5 27.5 Intake lbs/day 0 0 Total lbs 0 0 0 0 825 825 Total lbs 0 0 Cost($)/1 lb. ration 0.020683 0.020683 0.020683 0.020683 0.020683 0.020683 Cost($)/1 lb. ration 0.017771 0.017771 Cost($)fi"otal lbs 0 0 0 0 17.06325 17.06325 Cost($)/Total lbs 0 0 Growing ration Finishing ration Days on: 30 30 30 30 0 0 Days on: 30 30 Intake lbs/day 30.8 30.8 30.8 30.8 0 0 Intake lbs/day 35.32698 35.32698 Total lbs 924 924 924 924 0 0 Total lbs 1059.81 1059.81 Cost($)/1 lb. ration 0.013903 0.013903 0.013903 0.013903 0.013903 0.013903 Cost($)/1 lb. ration 0.026596 0.026596 Cost($)/Total lbs 12.84601 12.84601 12.84601 12.84601 0 0 Cost($)/Total lbs 28.18634 28.18634 Total cost in period 2 12.84601 12.84601 12.84601 12.84601 17.06325 17.06325 Total cost in period 2 28.18634 28.18634 3. Period 3. Period Starter ration Welcome ration Days on: 0 0 0 0 0 0 Days on: 0 0 Intake lbs/day 0 0 0 0 0 0 Intake lbs/day 0 0 Total lbs 0 0 0 0 0 0 Total lbs 0 0 Cost($)/1 lb. ration 0.020683 0.020683 0.020683 0.020683 0.020683 0.020683 Cost($)/1 lb. ration 0.017771 0.017771 Cost($)/Total lbs 0 0 0 0 0 0 Cost($)/Total lbs 0 0 Growinq ration Finishinq ration Days on: 30 30 30 30 30 30 Days on: 30 30 Intake lbs/day 34 34 34 34 34 34 Intake lbs/day 35.32698 35.32698 Total lbs 1020 1020 1020 1020 1020 1020 Total lbs 1059.81 1059.81 Cost($)/1 lb. ration 0.013903 0.013903 0.013903 0.013903 0.013903 0.013903 Cost($)/1 lb. ration 0.026596 0.026596 Cost($)/Total lbs 14.18066 14.18066 14.18066 14.18066 14.18066 14.18066 Cost($)fi"otal lbs 28.18634 28.18634 Total cost in period 3 14.18066 14.18066 14.18066 14.18066 14.18066 14.18066 Total cost in period 3 28.18634 28.18634 4. Period 4. Period Starter ration Welcome ration Days on: 0 0 0 0 0 0 Days on: 0 0 Intake lbs/day 0 0 0 0 0 0 Intake lbs/day 0 0 Total lbs 0 0 0 0 0 0 Total lbs 0 0 Cost($)/1 lb. ration 0.020683 0.020683 0.020683 0.020683 0.020683 0.020683 Cost($)/1 lb. ration 0.017771 0.017771 Cost($)/Total lbs 0 0 0 0 0 0 Cost($)/Total lbs 0 0 Growing ration Finishina ration Days on: 30 30 30 30 30 30 Days on: 30 30 Intake lbs/day 34 34 34 34 34 34 Intake lbs/day 35.32698 35.32698 Total lbs 1020 1020 1020 1020 1020 1020 Total lbs 1059.81 1059.81 Cost($)/1 lb. ration 0.013903 0.013903 0.013903 0.013903 0.013903 0.013903 Cost($)/1 lb. ration 0.026596 0.026596 Cost($)/Total lbs 14.18066 14.18066 14.18066 14.18066 14.18066 14.18066 Cost($)/Total lbs 28.18634 28.18634 Total cost in period 4 14.18066 14.18066 14.18066 14.18066 14.18066 14.18066 Total cost in period 4 28.18634 28.18634 5. Period Starter ration Supplement hay: Days on: 0 0 0 0 0 0 Hay bale/head 0 0 Intake lbs/day 0 0 0 0 0 0 Cost($)/bale 22.51125 22.51125 Total lbs 0 0 0 0 0 0 CosHSVsuppl. hay/head 0.00 0.00 Cost($)/1 lb. ration 0.020683 0.020683 0.020683 0.020683 0.020683 0.020683 Appendix 5 173 C o s t ( $ ) / T o t a l l b s 0 0 0 0 0 0 Total ration cost ($/head) 109.27 109.27 G r o w i n a ration Days on: 30 30 30 30 30 30 Bedding: Intake lbs/day 37 37 37 37 37 37 S t r a w b a l e / h e a d 0 0 T o t a l l b s 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 C o s t ( $ ) / b a l e 1 0 . 3 5 1 0 . 3 5 C o s t ( $ ) / 1 lb . ration 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 Cost($Vbeddina/head 0.00 0.00 C o s t ( $ ) / T o t a l l b s 1 5 . 4 3 1 8 9 1 5 . 4 3 1 8 9 1 5 . 4 3 1 8 9 1 5 . 4 3 1 8 9 1 5 . 4 3 1 8 9 1 5 . 4 3 1 8 9 T o t a l c o s t in p e r i o d 5 1 5 . 4 3 1 8 9 1 5 . 4 3 1 8 9 1 5 . 4 3 1 8 9 1 5 . 4 3 1 8 9 1 5 . 4 3 1 8 9 1 5 . 4 3 1 8 9 Medicine and Vet.: ($/head) 6. Period a.) process.,brand. (Arrival) 5 . 7 5.7 G r o w i n g r a t i o n b.) medication (on feedyard) 7 7 Days on: 30 30 30 30 30 30 c.) miscellaneous 1.5 1.5 Intake lbs/day 40 40 40 40 40 40 up-front payments (custom) 16 T o t a l l b s 1 2 0 0 1 2 0 0 1 2 0 0 1 2 0 0 1 2 0 0 1 2 0 0 Total ($/head> 14.20 -1.8 C o s t ( $ ) / 1 l b . r a t i o n 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 Cost ($)n "ota l l b s 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 S u m m e r r a t i o n Death loss: ($/head) Days on: 0 0 0 0 0 0 Percentage: 2 % unit=day 1 1 1 1 1 1 Total death loss ($/head) 15.27 0.00 T o t a l d a y s 0 0 0 0 0 0 CostiSh'day 028 0.28 028 028 028 0.28 Transport slaughter ($/h?ad) 28.89 C o s t ( $ ) / T o t a l d a y 0 0 0 0 0 0 T o t a l c o s t in p e r i o d 6 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 Total expenses: 167.64 107.47 7. Period F i n i s h i n g w e i g h t ( l b s / h e a d ) G r o w i n g ration HO: 700-1050lbs,SO: 700-1121 1075 Days on: 30 30 30 30 30 30 W e i g h t g a i n to b e p a i d ( l b s / h e a d ) Intake lbs/day 40 40 40 40 40 40 HC: 350lbs, SC: 425lbs 375 T o t a l l b s 1 2 0 0 1 2 0 0 1 2 0 0 1 2 0 0 1 2 0 0 1 2 0 0 Shrinkage: (%) 4 % C o s t ( $ ) / 1 l b . r a t i o n 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 Animal weiaht sold (lbs sale): 1 0 3 2 3 3 2 C o s t ( $ ) / T o t a l l b s 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 B r e a k e v e n ($ / lb . s o l d ) 0 . 8 8 7 6 2 8 S u m m e r r a t i o n B r e a k e v e n ($ / l b . c u s t o m ) 0 . 3 2 3 7 1 4 Days on: 0 0 0 0 0 0 unit=day 1 1 1 1 1 1 Total feedstuff: T o t a l d a y s 0 0 0 0 0 0 Welcome ration (Total lbs) 9 1 4 . 8 9 0 5 9 1 4 . 8 9 0 5 C o s t ( $ ) / d a y 0 . 2 8 0 . 2 8 0 . 2 8 0 . 2 8 0 . 2 8 0 . 2 8 Finishing ration (Total lbs) 3 4 9 7 . 3 7 1 3 4 9 7 . 3 7 1 C o s t ( $ ) / T o t a l d a y 0 0 0 0 0 0 T o t a l h a y ( l bs ) 0 0 T o t a l c o s t in p e r i o d 7 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 T o t a l b a r l e y ( l bs ) 2 2 2 5 . 9 3 1 2 2 2 5 . 9 3 1 8. Period T o t a l s u p p l e m e n t ( l b s ) 1 4 6 . 0 9 1 1 4 6 . 0 9 1 G r o w i n g r a t i o n T o t a l s i l a g e ( l bs ) 2 0 4 0 . 2 4 2 0 4 0 . 2 4 Days on: 30 30 30 30 30 30 Intake lbs/day 40 40 40 40 40 40 H a y ( b a l e ) 1 2 0 0 l b s 0 . 0 0 0 0 . 0 0 0 T o t a l l b s 1 2 0 0 1 2 0 0 1 2 0 0 1 2 0 0 1 2 0 0 1 2 0 0 B a r l e y (bu ) 4 8 l b s 4 6 . 3 7 4 4 6 . 3 7 4 C o s t ( $ ) / 1 lb . r a t i on 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 S u p p l e m e n t ( t o n n e ) 0 . 0 6 6 0 . 0 6 6 C o s t ( $ ) / T o t a l l b s 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 S i l a g e ( t o n n e ) 0 . 9 2 5 0 . 9 2 5 S u m m e r r a t i o n S t r a w ( b a l e ) 8 0 0 l b s 0 . 0 0 0 0 . 0 0 0 Days on: 0 0 0 0 0 0 unit=day 1 1 1 1 1 1 Gross margin: T o t a l d a y s 0 0 0 0 0 0 Init ial c o s t ( $ / h e a d ) , N e t l b s : 7 4 8 . 4 0 C o s t ( $ ) / d a y 0 . 2 8 0 . 2 8 0 . 2 8 0 . 2 8 0 . 2 8 0 . 2 8 T o t a l E x p e n s e s ( $ / h e a d ) : 1 6 7 . 6 4 1 0 7 . 4 7 C o s t ( $ ) r T o t a l d a y 0 0 0 0 0 0 Tot. costs, no shrinkage ($): 9 1 6 . 0 3 1 0 7 . 4 7 T o t a l c o s t in p e r i o d 8 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 1 6 . 6 8 3 1 3 A n i m a l w e i g h t s o l d ( l b s ) : 1 0 3 2 3 3 2 9. Period in ( cw t ) 1 0 . 3 2 G r o w i n a r a t i o n S e l l i n g p r i c e : Days on: 0 0 0 0 0 0 Owned: S/cwt; C. F.: S/lb. 8 1 . 2 7 6 2 5 0 . 4 Intake lbs/day 0 0 0 0 0 0 Total selling price ($/head): 8 3 8 . 7 7 0 9 1 3 2 . 8 T o t a l l b s 0 0 0 0 0 0 Gross margin: -77.26 25.33 C o s t ( $ ) / 1 lb . r a t i on 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 Total feedcost (no grazing) 1 0 9 . 2 7 1 0 9 . 2 7 C o s t ( $ ) / T o t a l l b s 0 0 0 0 0 0 S u m m e r r a t i o n Days on: 30 30 30 30 30 30 unit=day 1 1 1 1 1 1 T o t a l d a y s 3 0 3 0 3 0 3 0 3 0 3 0 C o s t ( $ ) / d a y 0 . 2 8 0 . 2 8 0 . 2 8 0 . 2 8 0 . 2 8 0 . 2 8 C o s t ( $ ) / T o t a l d a y 8 .4 8 . 4 8 . 4 8 . 4 8 . 4 8 .4 T o t a l c o s t in p e r i o d 9 8 .4 8 . 4 8 .4 8 . 4 8 . 4 8 .4 10. Period G r o w i n a r a t i o n Days on: 0 0 0 0 0 0 Intake lbs/day 0 0 0 0 0 0 T o t a l l b s 0 0 0 0 0 0 C o s t ( $ ) / 1 lb . r a t i o n 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 0 . 0 1 3 9 0 3 C o s t ( $ ) A " o t a l l b s 0 0 0 0 0 0 S u m m e r r a t i o n Days on: 30 30 30 30 30 30 unit=day 1 1 1 1 1 1 Appendix 5 T o t a l d a y s 3 0 3 0 3 0 3 0 3 0 3 0 C o s t ( $ ) / d a y 0 . 2 8 0 . 2 8 0 . 2 8 0 . 2 8 0 . 2 8 0 . 2 8 C o s t ( $ ) / T o t a l d a y 8 . 4 8 .4 8 . 4 8 .4 8 . 4 8 . 4 T o t a l c o s t in p e r i o d 1 0 8 . 4 8 .4 8 . 4 8 . 4 8 . 4 8 . 4 Supplement hay: H a y b a l e / h e a d 0 . 3 2 5 0 . 3 2 5 0 . 3 2 5 0 . 3 2 5 0 . 3 0 . 3 C o s t ( $ ) / b a l e 2 2 . 5 1 1 2 5 2 2 . 5 1 1 2 5 2 2 . 5 1 1 2 5 2 2 . 5 1 1 2 5 2 2 . 5 1 1 2 5 2 2 . 5 1 1 2 5 CostfSVsuppl. hav/head 7 . 3 2 7 . 3 2 7 . 3 2 7 . 3 2 6 . 7 5 6 . 7 5 Total ration cost ($/head> 1 4 5 . 5 7 1 4 5 . 5 7 1 4 5 . 5 7 1 4 5 . 5 7 1 4 9 . 2 3 1 4 9 . 2 3 Bedding: S t r a w b a l e / h e a d 0 . 6 0 . 6 0 . 6 8 5 0 . 6 8 5 0 . 6 8 5 0 . 6 8 5 C o s t ( $ ) / b a l e 1 0 . 3 5 1 0 . 3 5 1 0 . 3 5 1 0 . 3 5 1 0 . 3 5 1 0 . 3 5 Costf4Vbeddina/head 6 .21 6 .21 7 . 0 9 7 . 0 9 7 . 0 9 7 . 0 9 Medicine and Vet.: ($/head) process.,brand. (Arrival) 5 . 7 5 . 7 5.7 5.7 5.7 5 . 7 medication (on feedyard) 7 7 7 7 7 7 miscellaneous 1.5 1.5 1.5 1.5 1.5 1.5 up-front payments (custom) 16 16 16 Total r$/head) 1 4 . 2 - 1 . 8 1 4 . 2 - 1 . 8 1 4 . 2 - 1 . 8 Death loss: ($/head) ( N O . o f d e a d s * i n i t i a l v a l u e / N O . o f r e m a i n i n g h e a d s ) Percentage: 2 % Total death loss (S/head) 11.98 0 . 0 0 1 1 . 8 0 0 . 0 0 1 1 . 7 5 0 . 0 0 Total expenses: 1 7 7 . 9 6 1 4 9 . 9 8 1 7 8 . 6 6 1 5 0 . 8 6 1 8 2 . 2 6 1 5 4 . 5 2 1 F i n i s h i n g w e i g h t ( l b s / h e a d ) SO: 450-950lbs 950 950 950 W e i g h t g a i n l b s / h e a d ) SC: 450-950lbs 500 500 500 Shrinkage: (%) 4 % Animal weiaht sold (lbs sale): 9 1 2 4 6 2 9 1 2 4 6 2 9 1 2 4 6 2 B r e a k e v e n ($ / lb . s o l d ) 0 . 8 3 8 7 1 4 0 . 8 2 9 9 9 6 0 . 8 3 0 9 7 3 B r e a k e v e n ($ / lb . c u s t o m ) 0 . 3 2 4 6 3 7 0 . 3 2 6 5 4 1 0 . 3 3 4 4 5 1 Total feedstuff: Starter (Total lbs) 7 1 4 7 1 4 7 1 4 7 1 4 1 5 3 9 1 5 3 9 Growing (Total lbs) 7 6 7 4 7 6 7 4 7 6 7 4 7 6 7 4 6 7 5 0 6 7 5 0 Summer (Total can$) 1 6 . 8 1 6 . 8 1 6 . 8 1 6 . 8 1 6 . 8 1 6 . 8 T o t a l h a y ( l bs ) 5 1 1 . 3 8 5 1 1 . 3 8 5 1 1 . 3 8 5 1 1 . 3 8 6 2 1 . 6 3 6 2 1 . 6 3 T o t a l b a r l e y ( l bs ) 1 0 4 0 . 8 9 3 1 0 4 0 . 8 9 3 1 0 4 0 . 8 9 3 1 0 4 0 . 8 9 3 1 1 9 7 . 9 6 4 1 1 9 7 . 9 6 4 T o t a l s u p p l e m e n t ( l bs ) 3 9 3 . 9 4 4 3 3 9 3 . 9 4 4 3 3 9 3 . 9 4 4 3 3 9 3 . 9 4 4 3 3 7 3 . 8 3 9 9 3 7 3 . 8 3 9 9 T o t a l s i l a g e ( l bs ) 6 8 3 1 . 7 8 2 6 8 3 1 . 7 8 2 6 8 3 1 . 7 8 2 6 8 3 1 . 7 8 2 6 4 5 5 . 5 6 6 6 4 5 5 . 5 6 6 H a y ( b a l e ) 1 2 0 0 l b s 0 . 4 2 6 0 . 4 2 6 0 . 4 2 6 0 . 4 2 6 0 . 5 1 8 0 . 5 1 8 B a r l e y (bu ) 4 8 l b s 2 1 . 6 8 5 2 1 . 6 8 5 2 1 . 6 8 5 2 1 . 6 8 5 2 4 . 9 5 8 2 4 . 9 5 8 S u p p l e m e n t ( t o n n e ) 0 . 1 7 9 0 . 1 7 9 0 . 1 7 9 0 . 1 7 9 0 . 1 7 0 0 . 1 7 0 S i l a g e ( t o n n e ) 3 . 0 9 9 3 . 0 9 9 3 . 0 9 9 3 . 0 9 9 2 . 9 2 8 2 . 9 2 8 S t r a w ( b a l e ) 8 0 0 l b s 0 . 6 0 0 0 . 6 0 0 0 . 6 8 5 0 . 6 8 5 0 . 6 8 5 0 . 6 8 5 Gross margin: Ini t ia l c o s t ( $ / h e a d ) , N e t l b s : 5 8 6 . 9 5 5 7 8 . 2 9 5 7 5 . 5 8 T o t a l E x p e n s e s ( $ / h e a d ) : 1 7 7 . 9 6 1 4 9 . 9 8 1 7 8 . 6 6 1 5 0 . 8 6 1 8 2 . 2 6 1 5 4 . 5 2 Tot. costs, no shrinkage ($): 7 6 4 . 9 1 1 4 9 . 9 8 7 5 6 . 9 6 1 5 0 . 8 6 7 5 7 . 8 5 1 5 4 . 5 2 A n i m a l w e i g h t s o l d ( l b s ) : 9 1 2 4 6 2 9 1 2 4 6 2 9 1 2 4 6 2 in c w t 9 . 1 2 9 . 1 2 9 . 1 2 S e l l i n g p r i c e : Owned: $/cwt; C. F.: $ / l b . 9 6 . 7 3 2 5 4 0 . 3 8 9 6 . 7 3 2 5 4 0 . 3 8 9 6 . 7 3 2 5 4 0 . 3 8 Total selling price ($/head): 8 8 2 . 2 0 0 8 1 7 5 . 5 6 8 8 2 . 2 0 0 8 1 7 5 . 5 6 8 8 2 . 2 0 0 8 1 7 5 . 5 6 Gross margin: 1 1 7 . 2 9 25.58 1 2 5 . 2 4 2 4 . 7 0 1 2 4 . 3 5 2 1 . 0 4 | | Total feedcost (no grazing) 1 3 4 . 9 8 1 3 4 . 9 8 1 3 5 . 8 6 1 3 5 . 8 6 1 3 9 . 5 2 1 3 9 . 5 2 A s r e a s o n e d , i n t e r e s t c o s t s a r e n o t i n c l u d e d Appendix 5 175 tu « = N * J cu CO C o « ID CO Q) o s - J CO | co 9 o co i_ c o O o s O i_ CD "D CD CD CO CA 2 a 3 CO 3 Q U. c >. 51 CO OQ a.*C cu CO « • « 1 ^ o o < CO ^ fl) CD 65 i _ Q (A S | g <+-> 3 ,® ^ CD CO OQ o O Q o o o o o o o o o o c o T f c o LO c n c o o o LO CM LO T f CM T f c5 T f o o o o o o CD c v i T— CO T f CM 00 00 c n c n CM CVI LO Q c o CO CO CO CO CJ) CJ) c n o 0 3 0 3 5 o CO 8 8 CM CM CM CM c n c n c n c n o o c n o CM CM c v i c o X X X X CD CD CD CD CD CD CU CU 3 3 3 3 CO CO CO CO cn cn cn cn oo cn o CM CM CM co x x x x CD CD CD CD CD CD CD CD 3 3 3 3 T f T f T f T f LO LO LO CJ> cn cn cn cn cj) cn r— co cn o r— co cn CVI CVI CVI CO CM CM CM X X X X X X X CU CU CD CD CD CU CU CU CU CD CD CD CU CU 3 3 3 3 3 3 3 C M C M C V I C M C O C O C O C O T f T f T f T f L O L O L O cncncncncncncncncncncncncncncn m c o n o i / ) N c j j < D ^ T - c o j S i n c \ l o ) CM T - CM T - 7 - C M i - i - " 1 - 1 -O O O O co oo eg i - -a- LO co oo o LO T-8 i - 8 8 8 8 i o CD CO CD CO O ) LO f— CD CD CD CO i - CM 00 T f T f T f CO CO CO CM y- y- CM CM CM CM CO CO CO CO T f T f T f T f cn cn JJ3 92 g> g> 92 CJ> gj 92 92 92 9! CO cn co CO CJ) CD 92 CJ) CD 92 cn CO CO CO CO CO CO CO CO CO CO CO CO CO CO x X x x X x x X x x X x x x cu CD cu CD CD CD CU CD CD CD CD CD CD CD cu cu CD CD CD CD CU CD CD CD CD CD CD CD 3 3 3 3 3 3 3 3 3 3 3 3 3 3 T f T— o CM y— co co CM co LO CO T f CM T f o T f 00 O T f CO CM CO c> CD* cd 1^  T f T f y^ O T f o T f cn o CM y— CO 00 i— CO 1- LO CM CJ) T f T f i — CO r-- LO CO CO CM i— CM o o T— CM 5> cn cn cn o o o O O o o Q o LO Q LO LO LO Q o T f LO cvi o co 03 oo s 00 CM LO CD LO o LO O) co co o CD co 00 oo h~ CM CM CO co co oo oo CM CM CM CM CO CO CO CO •q-cn 92 92 92 92 92 CJ3 9? 92 92 92 92 CO T f LO CO CO LO CO CO 53 co CM CM CM CM CM CM CM CM CM CM CM CM X X. X. X. X. c^ X. XL XL XL X CD CD CD CD CD CD CD CD CD CD CD CD CD CD cu cu CD CD CD CD CD cu CD CD 3 3 3 3 3 3 3 3 3 3 3 3 CM CM CM CVI CO CO CO CO 92 92 92 cn 92 92 92 92 92 92 92 92 CD CD co sp. co CD CD CD co co co CD .— CO LO CM r-- co CO CO o l-~ CM CM CM CM CM s CO 8 CO CM CD O) CO CO oo oo LO CM CM CO I-; cvi CO d CM r-«: oi 10 \i CM O) o o CO O) CO CO o CJ) o cvi o CJ) CM co LO CM T— CM CO co LO CD CD cn 00 03 O) O) O) O) CJ) O) O) o o o o LO o CO 8 o 00 8 8 8 o 8 o LO o o CD o CO O) cn CO LO o o CM co co oo 00 CM CM o CO 00 00 00 1^  1^  l-~ 00 00 CO 00 y— CM CM CM CM CO CO CO CO 92 92 9? 92 92 92 92 92 92 92 92 92 co- f5 93 O) co CO CJ) co CO cn co CO CO co CO co co co CO co CO CO X X X X X X X X X X X X CD CD CD CD cu CD CD CD CD cu CD CD cu CD CD CD CU CD CD CD cu cu CD CD 3 3 3 3 3 3 3 3 3 3 3 3 1— .SP -5 CM CM CO CO CO 92 92 tz 92 92 92 92 92 O) 92 O) 92 O) O) O) cn o> Si CJ) co CO S3 o CVI CM T — CM CVI at 9 3 § 3 < O O cu Is c . S = « 2^ o O CD U CD Ot-CA CD « cu P CD J ^ v. cn E s < ^ T5 P 52 a u. .C OQ OQ CD • c CD : CD 2 CO •> o .LLZ. O •4—' CO »— fl) CD § 2£ o = O CO 8 8 CM 8 o CO o CM o o 8 o 00 o co o CO LO oo O) O) LO CJ) CO co CO CO o co o CO r~ 00 00 LO CM CO CO O) 00 O) o o o o o o O o CM CM CM CM CO CO CO CO T f o> p» 92 92 CJ) 92 92 92 O) 9! 92 CM CO LO Si CO LO Si CO LO co CO CO CO co CO co CO co co CO co X X X X X X X X X X X X cu cu cu cu cu 0 CD CD cu cu cu cu cu cu cu cu cu CD CD CU cu cu cu cu 3 3 3 3 3 3 3 3 3 3 3 3 CM CM CM CM CO CO CO CO TI- T f 92 92 92 92 92 92 92 92 92 92 CD 9? CO 00 CO co CO 00 CO CO 00 CO SO co CO o cn co CO o oo to Si en CM CM co CM CM o o o o o o o o o o Q o o o o LO 5> t^  Ti- co LO CO s LO LO . — CM en co CO CM LO O) CO CO CM oo 1^  cn O) LO l~~ LO 1— CO co T f o o •"3- LO CM CM CM CO CM CM cvi CM CO co co co •>* T f O) O) O) 92 O) O) 92 92 92 CJ) 92 92 9! O) 92 9! Si co CM CO Si co Si co T|-? • t M- T f X X X X X X X X X X X X X X X X CD CD cu cu CU cu cu cu cu CD CD CD cu cu CD cu CD CD cu cu CU CD cu cu cu CD CD CD cu cu CD cu 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 **• LO . — i^  oo y— o •<t O) 1^  ID oo LO cn o co i^  CJ) LO LO o 00 cb CM cri CD O) ci LO CO CM T— LO T— CO LO CM LO O) i— CJ) CM o cn Ti- 00 LO CD r-~ .  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S 0) <n o .2 co If c S, > o z (4) o 01 .v 3 CL CO CO Q CO E co Q . CO CO Q O 01 3 < CO £ ^  o O CO CO ,_ CQ -g _ 05 co ,? CD co "D CD o :*= .. o D) < C i-•- CD C $ o 6 O z en s a 3 CQ 3 Q li- .c >. S>| CQ C Q 5^ z D ) i o CO (A 2 £ 3 5 3 a LL .5 = 1^ CO o o O o O o Q O O o o Q m m 95 CO CM CM Tt in O CO CM co rt CO o CO a> CO in CO o CO r-- C& CO O) CO r-- Tt CJ) CO CO CO o T — 5 O 03 a> CJ) O) 1 CM CM CM CM CO CO CO CO Tt Tt Tt Tt 9? gs 92 92 g> 9! g> gj 9? g> g> ro co r~ CO O) CO 55 03 CD CO cn co co CO CO CO co rt co m co co rt XL x x X x\ x XL x J * : X XL XL cu CD cu CO cu CU CU a> cu CU CU cu CD d) cu cu cu cu cu cu cu cu cu cu 3 3 5 3 5 3 3 5 3 CM CM CM CM CO CO CO CO Tt Tt Tt Tt O) O) ro CJ) g> cn O) O) CJ) o O) O) 92 TO 92 9? gj gj 9? 3) 9! 3; ro ro . •* , — co CO o m c3 cn CO co T— CM , _ CM CM T— , — CM Q O O O Q O Q O O Q O O B o i n c o f f i c o c o i D N c o c o N rtCOCMCO-r-lOr-T-COCOCO'i--- O O i - CJ) O O CM T - O CM CM CM m r--Tt — CO CM O ) CO CO Tt CM •t- T - y- CM CM CM ro ro ro ro ro ro C O N C O l O C D S • ' Tt Tt Tt Tt J £ ^ ^ cu CU CU CU cu cu cu cu 3 3 3 3 Tt Tt j * j * CU cu cu cu 3 3 CM 00 CO CO CO Tt ro ro ro ro ro ro co in co s co in Tt Tt Tt J C X\ X\ CU CU CU cu cu cu 3 3 3 Tt cu cu cu cu 3 " •* Tt x x\ - CU _ cu 3 5 Tt Tt Tt ro ro ro CD S CO Tt Tt Tt X\ X\ XL cu cu cu cu cu cu 3 3 3 S N N C D O ) T - o r a C M c o c o c M i n o o i s c D i n cxiea^r^iricjJ-r^cMr^ n o n o j ^ c o o o N i n i o c o c o > - c 6 < t o * u ) C B C O Q Q C O T f t i r i c O O > O ) O O I - I - T - T - O •* CM ^ T - CM rt CM CM CJ) CJ) h~ cj) rt co in rt CM o o o CO it) U) CO o * O m S co c o c o in CM CO 8 S ^ cj) in S s co co . § co co co co CO in 8 m 8 o CO CM CO CJ) CM co co in in co CM CM CM CM co CO CO CO CJ) g> g; g> a> 9! 9J 9? CJ) 92 92 92 Si CO m CM CO in CM n m co CO rt co co co rt CO CO co rt CO ^ XL j£ XL XL XL XL XL X cu cu cu cu cu CO cu cu CU cu cu CO cu cu cu cu cu CU cu CU CU cu CO cu 3 3 3 3 3 3 3 3 3 3 3 3 CM CM CM CM CO CO CO n ro ro gj gj g> g> g> ro gj 92 CJ) 92 CO CO co co CO CO CO CO CO 00 SO CO CO i — CO m o> CD CO o CO in ca cn CM "~ CM co CM CM rt co O) CM CM o CJ) in o in in CO CO rt CO 00 o CM CO O) ci ri cd d ^ i< CO co in" CM CJ) CM O) rt m oo 00 CO m rt CM co o cn cn o co CO co Y— 00 00 m CO o m co CO CO CO 00 CO CJ) CJ) cn o o o o o o in c o in o in in o in 8 m CM in c o 00 00 o 7862. o in 00 CM O) 7862. CM CM m 00 c o r-^  CO CO CO 7862. O o O CJ) 7862. CO o o 00 gj T — 92 92 5 CM 9! CM 92 CM ro CM g> n g> n 92 n 92 CO 9? in cS t^  CO in CO co m •st r--•sf 00 M-week X cu cu 3 X cu cu 3 X cu cu 3 X cu I X cu cu 3 X CO cu 3 X cu cu 3 X cu cu 3 X CO cu 3 X CD CO 3 X cu CO 3 92 92 92 92 CM 92 CM 92 CM 92 CM 92 rt 92 n ro n 92 n 92 CO in CM ro CO ?5 CM co IS CM CO 3. a. s u co v ft cc = p> 0) Si (0 co f 1 o cu ^ « cu P S in Q O _ «^ O) 3 < to _ - c ? S cu > t o CO ° 5 cu CA 2 a >« cn ca C Q c o 0 1 Q ° CD ^1 r s ; o £ CO Je .3 21 •—. in o 2 S. < 3 W 3 Q > . l i . C 03 = <a ^ co C Q o O o o o Q o o o o o o O o o o 00 00 in in O 55 CM CJ) co m CM o m Tt CO CM cn O) CO CO o cn o Tt oo m Tt CM rt rt co o o CM co o r-- cn o O) cn CO CO 00 00 cn cn 00 CO 5 00 CM CM CM CM CO m CO rt Tt Tt Tt Tt ro 92 9! ro 9! ro g> 92 ro g> 92 ro 9! 92 CO 00 O ) CO °5 cn CO CO cn CO °S cn co co rt m co rt rt CO co CO co rt co co rt m X X X X X X X X X X X X X X X X cu cu CU cu cu cu cu cu cu cu cu cu cu cu cu cu cu cu cu cu cu cu cu cu CO cu cu CD cu CU cu CD 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 T— CM CM CM CM rt CO CO CO Tt Tt Tt Tt 92 cn cn o> 92 cn cn cn cn cn 92 cn O ) ro 92 92 9! ro ro 92 ro 92 92 92 92 92 9! ro 92 92 ro 92 Sl cn CD co Tt T— CD CO o in cn co CM CO CM CM CM CM o 8 o CO R 8 o cn 8 O CO 8 o CM 8 o Tt 8 o CM o co in Tf o> CO Tt co C  . — Tt oo Tt CM Q o rt rt CM Tt co y— CO rt CO O o o o cn cn ro cn 1 1 1 CM CM CM CM rt rt CO CO Tt Tt Tt Tt ro ro 92 92 ro 92 ro 92 92 92 92 ro ro gj 00 cn o T— 00 cn o . — CO cn o T— 00 cn o T— i — CM CM 1— CM C\J T— CM CM T CM CM X X X X X X X X X X X X X X X X cu CO CO CO cu cu CO cu cu cu cu CO cu cu cu cu CU cu CU CO cu cu cu CU cu CU CU cu cu CU cu cu 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 CM oo Q co co co r— . — CD o o in o CM Ti- in 5 in CO CD CO CM CO CM cn CO ed ci Tt CM in C\i ^ CO in O ri 00 ri co cn oo oo cn CM Tt CO CD CM rt f~ m co O m n n 00 n CO CO o CM CO -- cn co CM CM o co 00 CO 00 00 5 Q CO CO 1^ co co oo oo oo co oo 00 cn cn cn 5 5 O) cn CD m o in o m iQ Q O !Q in in m o m o O Tf co CO o Y— CO co CO rt cn cn Tt CM CM Tt CO co CM o Tt CM CM . — O rt in o co CO  O o CM o Tt Tt Tt Tt in Tt Tt in co o t-- h~ £ CM CM CM CM CO rt rt rt Tt Tt Tt Tt 92 gi CJ) cn 92 Tt cn CD 92 cn CJ) C3> 03 92 Tt 03 Sl n Tt in CM ?3 IS CM rt T? 25 Sl ?3 25 rt CO rt CO rt co CO m CO CO rt co rt rt CO rt X X X X X X X X X X X X X X X X CO CO CO cu CO CO CO CO CD cu CD CD cu CD cu CO CU 0 cu cu CO cu cu CO CD cu cu CD cu CD cu cu 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 T— CM CM CM CM co co CO CO Tt Tt Tt Tt a> CJ) 92 92 cn 92 92 cn g> 92 ro 92 ro g> cn 9! SO CO 00 CO CO CO CO CO 00 CO CO oo co SS go in cn co CO o r~ Tt cn CO CO o CO in Sl 03 CM CM T — CM co CM CM CO CM CO in n CM in ^_ Y— o Tt Tt Tt cn CJ) O 00 CM m q Tt ro in o CO CO 00 CM 00 00 rt ri ci CO in in ri co Tt CO in in CO o Ti- co co oo in 00 o t— r-~ m CD 03 ro o cn CM CM co oo CM 00 i — oo rt CM K CO CO in n t Tt CM Tt Tt Tt CO CO Tt CO oo CO 00 00 00 CO 00 00 cn cn cn cn o> cn cn cn o m m o in o in o m in o in o in o m m cn Tl- cn O) cn cn in Tt CO CM o CM Tt 00 in CM CM o Tt T— in in co in Tl- Tt O) o o cn Tt Tt Tt Tt o o 00 r-- r-- CO CO t". r-- CO CO CM CM CM CM CO CO rt rt Tt Tt Tt Tt ro 92 g> ro 9? ro 92 92 92 9! g> g> ro ro CO cn o co cn o . — S3 cn o co cn o y— . — i— CM CM T— T— CM C\J r— r— CM CM T— T— CM CM X X X X X X X X X X X X X X X X cu CO CO CU cu cu cu cu CD CD cu CD CU cu CD cu cu cu cu CU cu cu cu cu cu CD cu CU cu cu cu cu 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 . — •r— t— CM CM CM CM rt CO co n Tt Tt Tt Tt ro 92 92 9? 92 92 cn 92 9? 92 92 92 cn 92 9? 92 it in in in Jt in i£2 i£2 in in in in in o5 co m o Tt o5 co o Tt Sl ro co co CM CM CM CM T- CM Appendix 5 111 Rolfo Error Forecasts September: October: November: May: (Ps-f°)/f° (t'-fyf (Ps-f°)/f° (f1-f°)/f° (Ps-f°)/f° (f1-f°)/f° (ps.f0)/f0 (f'-f°)/f° 1 -0.09496 -0.00735 -0.06952 0.024242 0.033159 0.139499 -0.1722 -0.07657 2 -0.08145 -0.00244 -0.01581 0.04669 -0.01738 0.12439 -0.15715 -0.06168 3 -0.10959 0.015727 -0.02871 0.069609 -0.00654 0.13723 -0.15013 -0.04272 4 -0.05083 0.006199 0.00826 0.083891 0.005574 0.140032 -0.13945 -0.0646 5 0.022373 0.167549 0.070133 0.151098 0.132995 0.197974 -0.03819 0.05529 6 0.031086 0.165193 0.112032 0.145292 0.134999 0.180691 -0.03952 0.048843 7 0.031683 0.160253 0.126281 0.142199 0.085135 0.164244 -0.02287 0.046729 8 0.060624 0.158954 0.13967 0.17548 0.060309 0.153756 0.009701 0.06558 9 -0.1513 -0.08346 -0.02161 -0.0249 -0.04723 0.03513 -0.02691 0.040791 10 -0.11694 -0.0689 -0.02132 0.020269 -0.06824 0.001214 -0.05013 0.036369 11 -0.0634 -0.05353 -0.04041 0.023341 -0.08538 -0.0306 -0.06656 0.037025 12 -0.0549 -0.04314 -0.03542 0.015671 -0.10678 -0.03073 -0.05018 0.067901 13 -0.16805 0.029288 14 -0.16508 0.022761 15 -0.15655 0.021661 16 -0.14852 0.042196 Variance-Covariance Matrix for Stacked Rolfo Error Forecasts Means: (ps-f°yf° (f1-f°yf° Fall: May: -0.00648 -0.09636 6/29/92 0.016804 Variance-Covariance Matrix: P s-Fall f1 Fall Ps-May f1 May P s-Fall f1 Fall Ps-May f1 May 0.006144 0.005995 -0.00064 0.000357 0.005995 0.007421 -0.00218 -0.00053 -0.00064 -0.00218 0.004243 0.002174 0.000357 -0.00053 0.002174 0.002378 Appendix 5 178 Recovering Variances-Covariances S a m p l e V a r i a n c e C o v a r i a n c e M a t r i x (Adjusted where more observations were available.) (Stacked Rolfo Error Forecast) 15SSQ1 15SSH1 15QSQ1 15QSH1 15NSQ1 15NSH1 15MS01 15MSH1 15SSQ1 | 0.0061441 0.005995 0.006144 0.005995 0.006144 0.005995 15SSH1 150S01 150SH1 15NS01 15NSH1 15MS01 15MSH1 0.005995 0.007421 0.005995 0.007421 0.005995 0.007421 0.006144 0.005995r"0.006144| 0.005995 0.006144 0.005995 0.005995 0.007421 0.005995 0.007421 0.005995 0.007421 0.006144 0.005995 0.006144 0.0059951 .^006144| 0.005995 0.005995 0.007421 0.005995 0.007421 0.005995 0.007421 -0.00064 -0.00218 -0.00064 -0.00218 -0.00064 -0.00218 0.000357 -0.00053 0.000357 -0.00053 0.000357 -0.00053 -0.00064 -0.00218 -0.00064 -0.00218 -0.00064 -0.00218 0.004243I 0.002174 0.000357 -0.00053 0.000357 -0.00053 0.000357 -0.00053 0.002174 0.002378 B i a s : I 21 Feeder Cattle P s(Sep) f1(Sep) Average: 96732.54 104638.3 corresponding biased f°'s: f°(Sep) 104638.3 P s(Oct) 96732.54 f1(Oct) 104638.3 f°(Oct) 104638.3 P s(Nov) 96732.54 f1(Nov) 104638.3 f°(Nov) 104638.3 Live Cattle P s(May) 81276.25 f1(May) 91628.06 f°(May) 91628.06 V a r i a n c e C o v a r i a n c e M a t r i x (Recovered for f1 & P s) ^(Sep) P s(Oct) f^Oct) P s(Nov) f^Nov) Ps(May) f^May) Pa(Sep) | 67270845| 65636151 4770094 65636151 4770094 65636151 -8.8E+07 3424974 P s(Sep) f1(Sep) P s(Oct) f1(Oct) P s(Nov) f1(Nov) Ps(May) f1(May) 65636151 4770094 65636151 4770094 65636151 81258753 65636151 81258753 65636151 81258753 656361511 67270845| 6/29/92 week 27/92 79710 81258753 65636151 81258753 65636151 81258753 65636151 4770094 65636151[67270845! 65636151 81258753 65636151 81258753 65636151 81258753 -2.1E+07 -8.8E+07 -2.1E+07 -8.8E+07 -2.1E+07[ -5070206 3424974 -5070206 3424974 -5070206 -8.8E+07 -2.1E+07 95215.94 -2.1E+07 -8.8E+07 -2.1E+07 3424974 -5070206 3424974 -5070206 3424974 -5070206 35622463| 18248593 18248593 19963561 Appendix 6 179 Optimal Farm Plans Solution Sheets Identification BASE CASE IB HEDGING STRATEGY IS BINDING TO CATTLE PLACEMENT 1A NO HEDGING ACTIVITIES ARE PROVIDED 1C CHANGING BIAS (0.025) 2B CHANGING BIAS (0.05) 2C CHANGING BIAS (0.075) 2D MARGIN CALLS: 100% 3B MARGIN CALLS: 150% 3C Appendix 6 180 ffl c CD E cu u « Q. 0 01 c T) c m O c (fl >• CD CJ C '5> T3 CU I l i i i i CO m O cu cn co CQ cn c ra Q_ E i _ CO LL "ro E a. O = S — o co 3 [J ; = S » j ; E \o3sg L» E f ! 3 S f ^ 4 21 12 g I • » — ° 2 ^ o s S o J 1111 o S z cc ® o 2 •*f CO CM CM o CM CO ^ CD co i n i r i cd o o c o c o oi i r i c n c o CD CM i r i CM CD i n i - CO oi CM c o c o CD CM d 1- CM CO o c o m CD CD o> 8 o o o o o o CM CM O CD o * » CD CD CO CO c o r-O) Oi o o at o CM CO o o o o o o CO CO CD CO t n CD Oi CO CM CM o o h- CM CM CM Oi CD CO CO i n c o CM CM CM i n c o m Oi CM <-i n c o J c o c o J CM CD co co co oi i - CM CO CD I CM CM [ CO CO a c ?5 O C T ; • -a o y o O s T3 c P a l He? o o o o o o o o o o o o o o o o I O O CM CM CM I O CO j CD O | CM CO | Appendix 6 181 UJ « I! «I a. cc o o o o n o" in CM <N CO CO CO CO CO CO CM in CM CO CM CO m eo co eo T- CO O J eo oo cn y- CD eo co CJ co co eo *-co o> co co m m eo co m co in O J OO CM in co Appendix 6 182 ICQ CD n .2 (0 > CO •o CO TJ C TO X O) £ c •« (0 c o o o (0 ro O o" 3 o 5 o o o o o 5 (5 O O O O O O O O O O C M o o o o o o o o o o o e o r ^ g o o o o o o o o o c n t f r * . r-» r-- m o o o o o o o o o o ^ o o c o o in >t co CO N lO o o o o o o o o o o c n c o m co o O O O O O O O O O O C O O ) C*. IN. 00 CO O) * » CD O in o eg O O O O O O O O O O C O C D T -CM »- Tj" Q O O O O O O O O O C J CO CO o o o o o o o o o o o o> O) m o o c o o o c o o o o in in co m in CO O) Ol CD O) ' - m m N o n co co - * 3 3 m co eo T-en o m i n ^ m i o c o m o i n i n c o - r j - i f c o c o 00 -r- i t CO O) CO o m co t» v t o CM w co m m cn m o CM co o CO N CD 3 3 3 3 CO CO co m co •>->— CO O t 1 Tf N O i f i m eo m T-T - n in « r«- co rt T - o c o c n r - o o r - -m ^ - O ' - m c o c M c o e n c o c o c o - r - c o o c o t t t t r - c n m m ID N co O O) TJ" ? in ••- r-f in ^ m m o> CM co O) eo o o co m oo co co in o co CM in eo m co co t CO CD o cb o t - T j - T } - T < D c o m m ' - ( O O O l W ' - N t r c M t D t D ' v t e D 01 m IM N o _ " 0 ) ' - n ( D f t O ) C M f c o c o o o j c D r - r - -O) CO CO O) i - m CM O) h~ CO ^~ eo o co Ti-en co o co m co co oo o in ^ * - C 0 0 ) C 0 O » - O ^ m c M c o - e r o m o o o ) o i o n i M o i T r o ) ^ ? CD CO O CO CM T -f Tf f W N Tf ' - O l O C O C O ' - O C O m co in •*t O) CO O) co in r- o . _ , m m c n c o c o t T j - T j - T r ^ t c o m c o t c o m m m m S O) ifl CM CM CM CO S 2 CO CD CO T-00 00 O CM o ^ 5 5 cn CB n to ^ s — m co h» m o v Tf n f in in in 8 ~ CD s rg s O ) C O C O C T > T - t n C M C 0 ( D i - t M N T f o i c n n T j - o i n » - T * T t m c o l o n c O ' f ^ ' j T t T t T - w C\l s o — — in co cn co in cn eo eo O) co o o> co o> CM o ^ - m c n m o i n c o r (O r Ifl Ol ^ O c o c o c M c o c o e n c n c o cn in 3 3 CO O) O i — CO O CO f-co co m T* CM T~ CM O CM CD O) CM C") i t h« S ^ U) s m o co CM co r~- co m o Tf m t- CM eo tj- Ti- TJ-cS (S co eo co cn CD Tt CO Tf CO CM r ^ c D c o o o c o c o T i - o c o n i - f O N ' - t f ' - i D i n Tt O CO TJ- CD CM CO m eo o co o m CM co co ~ CO CO K t CM h- co CJ m * -c n c M c o c O T i - T j - T f T f r - M n « in (D K at T- i- ~ O O O O O O O U O O O O £ CO o 00 CO CO (0 E E 3 CO > ro k . ro Q. E o o c o O O CO CM CO CO CM t-~ CO CO i n T f « u E o J£ Cfl OJ d T t cn d T t T f O cri CM CO T f i r i o Cvi CO CD Q. ^ DC CO CM CO T t CO r~ CO 0 0 c c o o o t^ . CO CO T- T t T f CO O) CO T f 3 CO E — d d d CO cri CM o> CO i n CO i r i T f CP k_ o o o o 0 ) CO CO f~ f-- CO i n T f T f T f oc a c *'-o o o r-- CJ CO r>- CO i n cn r~ CO r -i o OJ CD m f - o CO 0 0 o o 6 TJ 0 0 t~- CO o d T f Cvi cd cri a? CO c 3 o I d CJ T f CO OJ CO CO CO CM o CO CO f- i n CO o X TJ at o CO CO O p cn O) CD CO CO o E o a> c TJ n d d *-' •"- d d d d d d O n X cc CM o CJ CM CO CO 0 0 CO CO o O) o CO CO CO CO f- f - CO o = TJ d d d d d d d d d d X IX • CD 0 0 O) CO •* i n CM 0 0 CO OJ m T f 1 CO O) T— CO CM o CO i n CO T— s d z p CM B I -E «2 > z o o o O) CO CD CO CO i n T O) CO o o o i n CO CM f~. cn o r -1 6 E o o o CO CO CM 0 0 m o 0 ) 3 i n i n i n T t T t T t T t T f CO CO CO CO CVI z o o o o o o o CO T t OJ CM CVI cn o o _ CO CO O CD CO CO CO >» CD c o 13 ca Cvi cvi CO oj 1 - E o o o o CM i n OJ m T f CO f- CO o Totah 1 Con-tract CD d 0 > T t CO T f i n CO T f 0> 12.3 13.9 cn o o o CM o T f i n CO CO a> T f CO co 0 0 CO CO co T f T f CO CO C •a OJ OJ T f CO CO o ° d 1 $ '— T— T— z 6 II o o o o o o o o o o O o o TJ c o o o o o o o o o o o o o s o o o O o o in o in o in o °°. U J p in o" in o in o CVI in f»" o CM" in u> I CD GC in ID CD oo CO CO CO cn O ) O ) Appendix 6 183 „ n w _ w *- g £ 5 I S w ° a. s o fc ^ 1 f o g CO $ y o i c 8 —- m co i n oS i r i cn co ->3- cn cvj cd m co T -i r i ^ CM co co cd i r i co t n CO TJ-cri cd co co i n co o CM I* ICO o eo m co co co ^ 8 - CM > cJ) E O 3 B Q> z o " x ti k £ « oSBg S. A E ? CI) 3 O S « O - £ r-. cn m »* co co CO O co i n o cn o cn cn co oo co r-cn cn o o cn o CM co o co o cn o cn CO CM cn co i n co cn co CM CM r» CM CM CM CM cn co co m co CM CM co r*» | co co | CO CO I c cu 0) u Q 0 at c "•5 c m en >. at cu 4 - « CQ CO O) c "5i •o cu 1 CO c ra 0 . E CO l i . ra E ! ^ Q. o 2 » o 2 3 S l o l l co M co cn m co I co oo I cn CM I r» co l § 1 * J D) C « o » o 2 cn cn sdjg'd CO CO tv :CO d o I f i f O CO cn o CM co Us Appendix 6 184 o m CO CO CO CO CO CO CM CO CM CO r- T -"* CD » t CM co in co co CM CO CM CO CM CO "tf CM o h - CO cn co CO o CM O CO co r-o o 0 o "tf CO 01 o •t- o CO CO 0 01 cn o cn "tf CO CO CO "tf CO " t f m CO CM cn cn o CO m CM CM h-co co co co cri cd co cn co co CD is CD Is 1 X  oi 1 LL 1 Appendix 6 185 [~S 5 o o o o 13 5 o o"~ l o o o o o o o o o o 5 CO co to l o o o o o o o o o o c M r ^ o i l o o o o o o o o o o c n r - c M 0 0 ) 0 Tf CO CM N (D U) l o o o o o o o o o o c o r - t n • — LO to CO O) N N in N n l o o o o o o o o o o Ol CM f ) o o o o o o o o o o c o c n c o • — co cn co O O O O O O O O O O I O - - -CM "— tf-O O O O O O O O O O i Q l o o o o o o o o o o ^ -O O CO O o O CO CO O Ifl N N LQ CO Ol B * W) o co m F: 3 LO m 2 S t f t f CM i n m - n - Tf eo r -CO T- f-co en o in O) 3 3 CD tf n »- CM m co to m cn in o CM O N ID N O l t t O LO LO O LO to CO O 2 CO CM ^ ^ ? t o to O en in 8 8 CO CO to to CD *-co o T r ^ r T f T j - ^ t h - o i n CO LO f- to "- o m "-cn co co to r~~ o o h-8 3 3 3 "- LO CO i -*- CO CO CM CO CO O CO CO t f CO cn LO LO Cf) 0) ja .2 *c CO > CD TJ 55 •o c CO X JZ O) CC c "5 1-CO c O o O CO CO o T- r-m oi CM to o o tr co in N n T in cn t f Tf Tf s t m to - - . C M i o c o t f T f c o c o o r ^ t o o c o C O t O t f T f T f T f t f t f t O C O L O L O I »- to co cn CM o o h- oi O) CD CO CT) Tf I 0$ CO T- CM i n CM O) t f CM CO CO t f CO S O ^ CO f (O n co t Tf m oj L O C M t f t f c o c o o t M c n r ^ f ^ t o t f t f t f t f T f t r c o r ^ t f T r I oi N n CO O CO t f to CM LO tf O cn o co CM oi tf to CO O CO "- o . m to o i tf cn ^ _ CM tf ^ tf to tf Tf ( O C \ | i - O L O C O C O - - O C O l e n t o o c o c o t n t r c o m CM K CM i L O c o c o c o t f o i c n c o h - c O L o r ^ o K O LO T- t f O l CO 01 to i - in t f t f T f T f t f c o m c o t t f o to ci cn cn 3 3 S CO Ol to i - t— T- CO CO O CM co co Tf r-* m - -co r- m en m _ t f CO t f to to cvi m m m m r*. s o m CN CM CM CM CO t f CO O LO T- t f s co n f Tf Tf Ol S CM S CD oi co co en i -CO CM N Tf _ T f o t o - i - t f T f L o c o m o i c o i o CM r*. cn CM co m oo co cn to cn co o I LO CO CO t f t f t f T co to m I c n t o c n c g * - ' - T - o o " - O l t f L O O l L O O L O C O t O C M t O C O O l O I C O ^ o i L O - ^ t f T f i n t o CM CO tf tf Tf tf tf T~ LO CO CO CO Ol I CM o CM to cn co tf r^ - h- tr in O CO CM Ol f- CO . . _ to O t f Tf LO CD I ^ C M C O t f t f T f t f T f S 5 CO CO (O s to Ol S CO CM I r ^ c o t o o o c D c o T f o t o r - . c o c M 1 — — — -~ - — ~ Tf LO T - LO CO T- Ol CO CM I . _ . Tf ^ w in t f o c O T - i n c o o t o o L O T f t D C M C O T - C M C O C O t O t O O l C M C O C O T f t f T f t f t O C M cn T- T~ T-2 2 r Ic £ C B w < B C Q C w ( Q ( Q ( B < B ( ( J ( v ' CO o CO CO CO CO E E 3 CO CD > CO I— CO Q. E O u c o o O) CO CM -a- 00 . 00 CO CM LO T f rce UIO, JC to to f~ CM d CM CO d CO CM CO •cr CO d cn CM o d CO w 0 . DC d co" CM CO CO 00 CO c 1_ c J£ o o Tf r~ CO CO CM CO CO CM CM T f 3 CO E r? d d oi CO oi CM oi CM oi CO Tf Q) k- o o o O) o> CO CO r~ CO LO T f T f T f DC CL o c T~ o o Tf r- CM T — CM CM CM r- CO CO r-i O CM CO •» O) CO Tf o 6 TJ CO torn d CO r- a> d LO CM CO oi a? d> c 3 U torn d CM LO CM CO CO CO 00 o o o o LO LO LO CO LO o -UIO TJ O) o f~ CO CO 00 CO f~ f~ CO o -UIO ine TJ 0) CD d d d d d d d d d d d o n X CC CO o o o o LO LO LO CO L0 o 8) o CO CO 00 00 CO o = TJ d d d d d d d d d d d X CC • CO r~ o cn CO CO r- LO 00 T f r- T f CO i — O) CO CM o CO co CO No. ( > y- ^~ C\l •* -o 1- No. ( 45 z o o CO O) 00 O) co CO •tf CO f~ di o o CO LO CO CM CM CO o T f CO r~ t 1 E o o O) o> 00 CO CO OJ CO CM o O) 6 3 LO LO T f •cf CO CO CO CO CM - z o o o o o o o O o O o o o o >» C act CO o act i= E o % o o CO CM CO CM CM 00 T f T f cn o Con-tract d d O) CO O O CO CO o Toti Fall Con-tract 1 •"t CO CO o o CNJ r- CO 00 T f O) L0 CO TJ m cu CO CO CM o CO i d 1 CM CM •>* CO CO o ^ 1^ z 6 £ o o o O o o o o o o o o o T3 C o o o O o o o o o o o o o o o o o o o i n o i n o i n o AO UJ u f o i n o t o o i n N-" o c i i n CD i CD DC i n CD CD CO CO eo CO o t O) o Appendix 6 186 c '5) XJ z a O •s i f O 3 z o 1^  S I O o ° . a. S2 E co S 3 2 £ 3. •» — K . • 4 S o t -o h » J m i a J: SS — ° 7 C S £ 3 ° — w U> c o 3 O >. cn c ri E » o 2 o 3 z cc 5 1 3 2 III ro o , ~ cn c rc I© » O 2] s d 11 i t a ca cc H i ! > Q St 35 *d c S 3 " i 'nil in CO CO r- CD CJ CO tr i r-" co in cn co iri co CD in in co ci co CM CM I CD o co in 2 K I cn co I r- co CD CD Is- CD o o o o o o CM CM - O OJ TH CM H I I Tf CO co r» co - I O CM | CD Tf Tf CO 1 Tf CO in Tf CO CM CM y- CO CO *-in r-~ CM CM - - o o o cn o CM CO O O o o o o CO CO O CO co r -cn GO CM CM CO CO CO CO CM CM r- CM y- in *- CM CM CO I OJ CO co m CM GO i S CM CO GO It o o o o o o o o o o o o o o 6 6 pj-p o""6 O : p ; 6 6 co CO CO CO CM CM O) CO r - o CM CO o o o o o o 6" in o o o o o o Appendix 6 187 o CQ B 1 1 SI o o o o o © CD CO CO CO CO CO CM CD LO 5 CM CO CM CD CO CD - I Appendix 6 188 I O O o o o o £3 £5 £5 o P in 1 — N CM O) CO »- O cn co r*. lOOOOOOOOOOTfCO 3 £ l o o o o o o o o o o c o c n r - -• — to co co co cn co m m l o o o o o o o o o o c o e n c o 1 - ^- o o o o o o o o o o o c M c n e o 1 - CO CO r» CO O h-l o o o o o o o o o o c M c n c o 1 — cn m o o o o o o o o o o o r - c o 1 — 0.(0 0 r*. co co co co in l o o o o o o o o o o c o r - v i n 1 — o co m m co oo w cn co l o o o o o o o o o o m r r c v j o o o o o o o o o o l o t f o o t o o o i n o o I o in in ••- cn t— C J m in CM in I o cn cn co en cn Tt o m m r» Tf CM o co co • T} T} T- - - CO in co oo * -- - o Tf CO CO CO -- <T> t*~- en CM co in r-Y— CO Tf m co i -eo co CO i -m co CO •>-co en Tj- TT cn o in co m m Tt m m co w cn O) h- cn cn o Tt to in co Tf Tf - -CO CO CO TT TT CM Tt Tt co o m cn Tt t t co *- CM m CO m in c i in o CM I cn m m 00 CO CO ID N O) 3 3 3 CO Tf CO Tf Tf r*— o LO I CM T- Tf r- co co Tt i - o c o i n r ^ o o f * . ? s s m oo CM oo CO O 00 eo TT oo T f T f T t T t r ^ c n i n m ID S CO ? in Tf in o co o o Tt co in I c o r - T t m i n c n c M t o c o c o c o c M i n c o T t T t t o c o o r ^ — _ w c o c o T f r f T f T t T f T f i o c p i n i n . C O C D C n C M ' - C M T r C M C O C O T f C O o o r ^ r ~ ~ o ) i n c \ i r ~ - 0 ' - < O T f < o | e n c n c o c n T t c n » - c o c D T t T t c n c M c% co i n c M T t T f t o c o o c M c n h - r ^ COTtTfTj-Tl-M-TfCO" — — I c o ^ c M t O T - e o c n e o o e n r - e o - ^ i n i n c M c o T t o c o o c O T t T t c n o e o c M e n c o » - i n c M T t T f c o c o o c o — COCOTtTfTfTtTtTtin m co co Tt cn T-S 3 (O CO CD cn co o co in co co co r- o m * -cn co co Tt in Tt co in i - CM o c n c n c o f * c o m r - o T t c n c o c n ' » - i n » - i n Tt Tt Tt CO 10 CD Tt CO I m m w in h- m • — r-. cn in CM m co I CM CM CM co co* Tt T> 5 ch cn co co Tt - U) (D N lO Tt Tf CO Tf CO T— T— CO O CM N m m cn LO -in eo O) N Cv| S O o co oo co i — in o> CM r- Tf cn Tt O m y- Tf Tf m CO CO Tf TT TT Tf cn co cn CM i- i-t- cn Tt in cn in — co oo CM co co cn ^ cn in i - Tt Tt CM CO Tf Tf Tf I CM o CM co cn i -co Tt r>. r>. Tt in • Tt o co CM cn co in o Tf Tf CM CO Tf Tf Tf N C O C O O O C O C O T t O C D f f i O N ' - T r ' - c o i n o c o ^ - i n c o o c o o i n , . C O C M C O ' - C M C O C O C O C D l e n c M C O c O T t T t T t T f c o c M in CM cn CM CO CO r-m cn O) CO CD e  cn CD cnCO CO CD O m Tf CD Tf in CO cn CO CO m cn CM CM CM o cn 00 in CO CO CO s cn CM o o Tt CO O CD in Tf CD Tf ? CO cp CO Tf CO CM in CM r-r*. s CO 3 CD CO CO cn CO CO CO O r-in in m Tf D Tf 3 CO CM o Tf CM CM o r- co CM r- ^ Tf in ^ w to cn co CM I T - CM C O in t o s co o i i -O O O B B B Q Q I t n f l ' o o o o o o o o o o u £ CO u "*>* CO '•5 CO CO E E 3 CO CD > CO i _ CO Q. E o o c o O o i n O ) CO T f cn CO 00 CM T f o E *t m CO O cn CO CO f~ 0J o o CO CM O ) cd d CO cri d CO CO 0- £ cc co cri CM CM T f CO f - CO c w c o O o r - o CO O ) CM CO T f CM CO T f 3 » E ~ d d d cb d CO o> i r i CO CM CO d T f % >- o o o o an O ) CO r - r~ CO CO m i n T f CC CL o c •'~ o o o CO CO r - 0J O ) y~ r^ _^ CO r~. i O o o r- m CD CO CM CO CM 00 o 6 TJ co t= CO CO i n CO o> CM cri cri CP c Cu d oj i r i CM CO o o o o o o o O o o A TJ O l o o o o o o o o O o o E o ine TJ <D CO d d d d d d d d d d o 43 x cc o o o o o o o o o o 8> o o o o o o o o o o o = TJ d d d d d d d d d d X a CO CO o O J CO i n CO CO cn T f CO T— o> CM r- CO T— cn m CO y— Tota No.( farm ANI O J o o o O co y— o m CM CO CO r» o o o CO T f i n 00 CO cn cn o r » t 3 E o o o O ) 00 r - CO T f CO m CO cn 6 3 i n i n i n •tf •* T f T f T f T f CO CO CO CM z o o * o o o o o o o O o o o o o 75 >. C t> o CO o CO 1- S u * o o o o o o o o o o o o o 75 _ c o o CO o CO i- U _ o o o o o r-» CO f - i n CM r~ CO TJ CD O J CO m f - CO CO CO 1 No. i ? CM CM CO i n co CO cn ^ o 1- No. 1 o o o o o o o o o o o o o TJ £ o o o o o o o o o o o o o a> o o o o o o in o in o in o CO LU peel Rett in o in o " in o CM" in h." o " CM" in CD peel Rett in (O CD CO CO CO CO O l o> O l O l Appendix 6 189 OQ CM M M m CO 0) o 'SZ CL CO a> • 3 LL. C a> % JO CO < m a> c '5) c CO o CO c ra a E i _ ra Li-ra E a O > i O 3 z o ITS i £ g a . A E « (0 O - I * 3 I S 4 S ITS a > • z ^ £ o < - s ^ — ° Z = S > a = 8 z o c o - •- = s CD • A , CO T3 o £ 1111 o z CC 11 5 s o £ o n o S o » o S CD I .—. •fii •All CD Tf Tf CO CM CJ O O O O CO O f- Is-CO LO CO CO CD CO O CD O Tf CD CD O O O O r- co CO CO r- CD CO CO CO CD Ol o o o o 2 s CO 3 CO LO o o o o h- CD co tri CO LO r- CD co oi CO CO LO TT CD d CM CO CM CM CM CM CO CO CO LO CO CD CO * -CO CO T — LO r--CM CM T - O o o CD O CM CO O O O Tf O CD CO CM LO CD CO o CD CO CM CM CO LO Tf CO CO Tf CM CM CM M l T - CO I O CO If CM T -co in LO CD CM d CM CO I I CD CO I I CO LO CM CO I ""- CM II ID CO | O O O O O O o o o o o o o o o o o o i o d •p||:0; d d o o o o o o o o CO CO CO LO CM CM 8 CO I a i i T3 | X A Appendix 6 190 . 1 E L3 I I S o o o o o o cn OJ c*. co CO CO OJ CD w in co in OJ cn 5 £ 8 C L O •5 c in o I c § ? H X A Appendix 6 191 m CM o o o o o o o 5 toFT h> CM O) CO i - O o> co r*. oooooooooTftnr--U) S (D CO Tf CO o o o o o o o o o c o c n r * -CO CD CO CO Ol CO N to LO OOOOOOOOOCO OOOOOOOOOOCMCD — 1 " ( D O S co o r-OOOOOOOOOCMCDCD O) IO Tf S CO CO CO CD IO O) CM o o o o o o o o o r ^ O T f LO CO CO LO T - LO LO O CM loooooooooor^r^co 1 ~ CO LO f-CO LO o CM T - Tf OOOOOOOOOCOCO £ s lOOOOOOOOOOO^CD O CO i — O 8 • 3 8 I T- T- O LO LO CD O LO LO CO CO CO LO LO Tf ) O) Is-L  L  CO CO CO CO CO LO LO o r- to LO LO Tf CO CO Tf CO CO O CD CD CO CO CO »- «- LO  CO CO O LO Tf CM T - CM T-co t - cv co CM Tf Tf CO O T - CO T- 1- T- CO O 3 3 3 3 CM Tf Tf CO O CD S LO CD LO CO CO CO CM CO LO CO S CO T- T-y— co o Tf Tf r~- o T - LO 00 CO ^ CO T - CO CO CO 0) £1 ra CO > 0) TJ CO TJ c CO X cn be c ra CO c o o o CO CO o O T - CM i - C M C O T f L O C O r - C O C D n c o M C A c n n t o c o u o i M O 0) o .52 CO it CO E E 3 CO a> > CO l_ CO Q. E O o c o o o> in oo C O 00 O ) C O oo f - C M T f CD O E JC to 0 ) C M C O m O L O CM' o C M cn C O C O C O 1 -oi I-. d C M C O c 0) Q. £ CC L O iri C M C M C M T f C O ?I 00 c o o T f C M o T - f~ C M C O T f C M C O T f 3 o u E d d L O L O 1 - d C O i r i 00 C M C O d T f IS o o o cn <j> 00 C O f- f - C O C O L O L O T f DC a z c ~^ " I — o o C O C O r~ co O ) f - C O f~ i o CM C O T f cn C O co C M co C M C O o 6 TJ « E C O o C M C M cn C M oi oi # CD C o o *~ T f C O C D 1 - C M C O C O f-ao cn C O o o O o o o A TJ 0> o C O co C O T f o o O o o o E o o CD C T3 CD d d d d d d d d d d d a Z CC T f 00 Ol 00 o o o o o o O) o C O C O T f o o o o o o = TJ CD CO d d d d d d d d d d d X CC • C O L O 00 I - C O C O L O C O C O cn T f JS ? C O ^ T f C M T f o o cn L O C O r- 6 z 43 > z o o O in C O o L O o in C M C O C O r— o o C O r~ in o 00 C O cn cn o f-s 6 CO o o 00 00 f - C O C O T f 00 i  C O cn 3 L O L O T f T f T f T f T f T f C O C O C O C M 1- z o 3 * o o C O o o o o o o o o o O otal >  a C o n a d r-S o o o 00 f~ C D L O o o o o o O otal i 75 c o ts & 00 d d C O C M in C M cn d i- L L o o o o L O 00 o L O C M r- C O TJ CD C O C O cn 00 0 ) L O f - C O 00 C O otal 6 i IS CO T~ C M C M C O L O C O C O cn z o L L o o o o o o o o o o o o o TJ c    O          X LU £ u 3 o i n o © o i n CO o " o i n o o i n CN o i n i n hT © o i n o f o i n CO ID ci CD CC i n CD CO r~ 00 OO CO CO cn cn o> a Appendix 6 192 •b 8 5 » CD J Z 3 o CO CO cd co m co co cvi oi CM co CO LO ci co co y- Ol oi CM eo co 01 CO LO Tf CO CM LO CO oi to" CM CM t i l l CO o CO LO to CO CD I Ol Ol I Ol Tf Tf CO CM CM O o I r-. co m Tf oo oo o o i 0 Tf 01 oi co oo co r». O) oi Tf CO in Tf i - co CM CM O CD I CO CM co in to *-CM CM CO o CM r-co T -CM CM S DC I © I ^ > • O ) C « i ra T 3 o r o T5 Z CC , CO j . I l i! 1 I c i i l CM CO Ol CO co m CM GO r- CM to 00 O n r cn £ —1 O T J O O « O O O c o o o o !• a z nil CO 00 to m CM CM Ol CO o CM CO 8 « o cn i C i T5 c i o o o o o o o o o o o o o o o o O O o i n "tf Tf A Appendix 6 193 CO TJ C i 8 C _ o o o o o o o o o o © o o in CM CM O O O O O © © in co co o o o o o o * - CM o in o o O CM r- co o h-CM r*» *- m CM i * -o co T - r-CM CO CO CO co co cn o o> co r- r-CO Tf CM * -Tf Tf co r-y- CJ> co r--o oo co oi oo r-o oi co co co eo CM CM CO CM tn O ) CM r-co co CO CM oo »-CO CO O CO to r*. r-. in cn CO CM » -CO CO CO CM o ml CD CD CO CO CM CM CM CO CO CM cn oo to CO to CO CM CM Appendix 6 194 I o o £5 o o o o o £5 o~~ S W CO OJ CO f -O O O O O O O O O C M C M i n CO to O O O O O O O O O * - C M t 0 CO O CO CO o to N LO Lf) o o o o o o o o o O O O O O O O O O O C M h -l o o o o o o o o o o O ' - r -1 " OJ tO Tf CO LO CO UJ (O OJ o o o o o o o o o c o c o r -LO CO LO O O O O O O O O O C O LO S l o o o o o o o o o o c M h . c n »— LO CO o o o O O OJ O O CM tO CO LO f- 1- Tt l o o o o o o o t o o o r - c o c M I CM CO T— O I i - * LO o i i n LO O O) O) S O) O) " 3 8 °? 3 3 CO Tf 3 3 "J 3 f CM O CM O LO to to I o r~- CO co to to CO Tf Tf Tf CV Tf CO O) — CO Tf CO t— LO CO cn to s Tf _ LO I LO CO LO " s CO Tf Tf to r-I — CO I S CO S CO CO 3 Tf CO CM LO u j cn LO o CM ID S Ol 3 3 Tf Tf Tf r-. O LO • • - o c o L o r - o o r * O J ' - L O C O C M C O CO CO CO T- CO O CO tO tO IP- CO CO Tf CO Tf Tf Tf t>. cn LO LO m r*. co o o Tf — — — co to to m . - - CO O CO CO I LO CO CO CO Tf tO i - CM O CO o ' — CM CO OJ CO co to o r-Tf Tf Tf tO I m m in K) s i - m y- r*. cn LO CM LO co I CM CM CM CO c? TT ? 5 l o j c o c o c n * - L O O J t o i n c o Cf) f W N I cn CD en CM »- — T - c n T f i n c n i n o L o c o c o c M t o c o c n e n c o I CM O CM CD _. co Tf r- h- Tf m r-Tf LO CO to CO co cn s s CO S CO Tf m to co cn £3 Tf Tf Tf Tf Tf CD m Tf o cn CM a _ co in m c n c M » - c M T f C M c o e o T f c o *- — — C M O O ' — C D T f C O i - co to Tf Tf en CM ID lO O (M (J) S N Tf Tf Tf tO |-» Tf Tf • " D ' - t M l D T - a J t D n O ' - O N ~ " — • - • - C M t O T f o t o c o e n o co CM cn Tf en T -CD CD O to CM Tf Tf Tf Tf LO f» Tf Tf 0 in co eo i - o eo Tf to LO -- CM t>. CM 01 n s n w s o cn CD en m * - in Tf Tf eo in to Tf co CO O) ID i -C0 CO O CM cn OJ co co Tf r» m —- m co i-» in cn m Tf Tf eo Tf m co CM co co co m CO Tf CM co eo to r-co i - in Tf CM OCDtOTfOCOh-CDCM ... . - Ni-t'-COlON'-V TJ- o co »- i n t o o t D O L O L o - ^ m I ~ (OLO--I3) CM CO CM Tt m to r» co cn CO CO CO CQ o o o o o o o u o o o o = CO o CO CO CO E E 3 CO CD > CQ i -CO a . E o a c o O CO T f T f CO T f cn CO 00 N . CM T f <D UIO. cn O O J r~ r~ cn cd CO r- r- CM O UIO. M o CO CO CD cri d CO c co CL £ LO CO * ~ CM CM T f CO CO c (0 o o o r- co LO 05 CM CO T f CM CO Tf 3 CD o E d d f-" c j r-' o i 00* LO CO cvi CD d T f Re' Pen tfro o c o o cn O ) 00 CO l-» f~ CD CO i n LO Tf o o o O ) T f cn CO f~ cn x- CO f~ t * 05 T t CO o r~ t o co CM cd CM CO o 5 TJ e ^~ o CO o> cn CM cri cri as CD C o § *~ cvj cri T f CO O J CO cn o cn CO CO o O o o o o X TJ §> o q CO C J o o o O o o o o E o CD C •a a> S d d d d d d d d d d u 3 X cc CM o cn CO CO o o o o o o 0) cn o CO CO CM o o o o o o o o = "DCD OD d d d d d d d d d d d X CC CO CO CO CO T f LO LO CO 00 O ) T f CO o> LO CM O cn 1^  i n CO Tota No. i farm ANI o o CO CO o cn T f o LO CM 00 CO N . o o CO T t r~. o CO 00 CD o> o r~. S d M o o CO CO r~ r- t o Tf CO LO CO cn o 3 LO LO T f T f T f T f T f T f T f CO t o CO CM 1= z o 3 o o LO o O o O o o o o o o otal CO otal >» ca c o Z S d i - S O o o r~ LO CO _^ o o o o o o on- CO LO cn CO T f I "5 on-o CO d d d d d LL o o o CO cn LO 10 f~ LO CM f - CO CD 10 cn r~ CO 00 LO r~ CO 00 CO otal TH i— CM CM t o L o CO CO en otal 6 * V CD ~^ z o LL o o o o § o o o o o o o o Tt £ o o o o o o o o o o o o 0) o o o o o ca i n o i n o i n o 00 UJ i n o i n © i n o c j i n h-" o CN i n ID i cc i n CO CO f* f* CO CO CO CO cn O l o> at Appendix 6 195 o c 5> n S o M i s 4 S m j z = I - 3 g i = s — LO , 1 e V S § § s o o 2 £ to o a i > cn c « o v o s S •() S i i ! 1 > = z cc in! CO . J I o 2 1| £ 2 co fi CO oc i f i ! ' CO TJ C i B C _ , OT Tf Tf CO CJ CM O O o o o o o o CD O r*- r-co LO N- co CO CO CO co CD I s -O i OS o © o o o o Tf CO LO Tf T - CO o o o o o o T - CO CO T-LO r-CM CM § § Tf Tf T - O o o cn o CM CO o o o o o o o o o o o o o o cri cri CO CO LO CM oi d CM CO O Tf O LO o cn CO CM o o o o o o o o o o co r-CD CO CM o o o o o o o o o o s s LO CO cri co CM CM CO CO CO CO r- r-CM CM CO o CM r-CO T~ CM CM Is o o o o CM CO 01 CO CO LO CM GO I"- CM CO GO o o o o o o o o ;;o o o o CO 00 CO LO CM CM 1? s CM C-> 8 CO la o * - CM CM TT CO CO o : e a> c I X<v A Appendix 6 196 3 o o o o o o o o o" LO CN CN O O O O O O r- r*-o o co co CO oo co CO co co LO Ol o> r -co co CO CM co * -CO CO Oi CO CM T -CD CO CO CM 00 CO CO CO CO co CM r-h- r-T - O tt r-CM CM CO CO CM Ol 00 00 00 CO oo CO CO a, 3 cn c c m o C cn Appendix 6 197 Q CM CO jD £X ro *c ro > 0) XJ to •o c (0 x O) c '5 to c o o 5 o Li. C to (0 o o o o o o o o o o LO Tf •st co O O O O O O O O O O C O O O O O O O O O O O C M O C O O O O O O O O O O O C M O o o o o o o o o o O CM 3 CO O) ID r~- T-LO CD O O O O O O O O O O O T f O l O Q N N 1 J 3 S O T> T- CD N- CM * - CO o o o o o o o o o o e o T f t o o o o o o o o o o o S 3 LO Ol o o o o o o r - o o O C O O O O O O C O O O C O L O C O O O CO o O CO 3 3 f» T-CO LO CO O) o to CO CO o cn cn O LO LO O CO CO LO U l Ol O l 3 3 CO LO tg T- CM T— r— co cn tn Tf CO O Lf) O • T— •»— 1 CM O LO LO t-o oi cn 3 3 S en Tf Tf co CO LO LO Ol IO co o r» co r- oi O Tf CO CO CO T-CM Tf Tf S S 2 LO 3 LO »-3 LO O CO LO - - CD »-. . . CO CD r -h - C O C O T f T f T f T f T f T f T- CO LO Tf Tf Tf LO LO 00 o co co ••- Tf O CO O CO 00 O LO CO co o r— Tf S O CO CO r-» o o LO CO CM CO y- CO O 00 c D f - - c o T f L O T - r - - t o o o T f c o i o O O l Tf Tf Tf LO CO f*- Tf LO LO Ol CO CM LO CO Tf Tf LO CO CO Tf Tf Tf CO LO Tf o i - CO to CM CO Ol CO CO O r» UJ c j f J Tf Tf Tf C0 CO LO LO O O f- f-Ol Ol s co tn Tf cn 3 3 CM Tf CM CO CO CM r» o * - to y- CO CD CO CO -Tf Tf Tf CO CO . cn CM ( M O S S y- CO y- CM CO y-o s co T- LO cn co o co Tf Tf en CD r - LO CM • * * y~ CO CO Tf CO O i— O f— Tf o LO to cn CM O) Tf O) * -O tD CM Tf T-Tf Tf Tf LO f*. 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CD r » f - CM o> 1^ - 0 0 f -CO c o 1 - LO CO CO O J 0 0 o 0> ro LO CO O ) CM 1^ CO CM o i o i d CM Tf" LO CM CO CO o o o O o O o O O o o o o o O o O o O o o d d d d d d d d d d d 0 0 o o o o o o o o o o o o o o o o o o o o o d d d d d d d d d d d CO f~ CM ^ CO LO CO 0 0 T f 0 5 T— t T— c o CO O ) LO CO 1 1 CM ' o o CO CO y_ CO o LO CM 0 0 CO r -o o o 0 0 o T f LO 0 0 0 0 O ) o> o f -o o o> 0 0 0 0 1 - CO T f CO LO CO c n LO LO T f T f T f T f T f T f T f CO CO CO CM o o o o o o o o o o o o O o o r ~ o o o o o o o o o o O d o o CO CO _^ CO r ~ - LO CM l - ~ CO LO T f CO LO CO 0 0 CO CM CM CO i n CO 0 0 o> o o o o o o o o o o o o o o o o o o o o o o o o o o o CD o o o n o i n o i n o i n o a i n o " i n © i n o c i i n N T o C4 i n co" m CO CO 1^ f* CO oo CO CO Ol Ol O) CO Appendix 6 198 m CO 0) c '5) k. CO S Ol c c co (A c a a. IQ (Q E 4 - « J> a. g O 5 « s j ; s * 31 s to ° 5. 2 • 4 S | ca s o " » ^ S o 7 <= S — 3 s < Z 8 ^ — © Z C S — 3 9 o c o ! - 3 S *• * E M " D B S O o 2 i a. <!> E a » R o a> (/> O - £ > oi 4 t; cu o o s s » o S 1111 si z cc I i l l « TJ O tt o o to 2 O O c i l l ! till O CM CO Tf Tt CO CD O f - r-. co m N - CD m T T oo CO Tt CO m Tt y- CO •rt eo i n Tt i - co CM OJ O o o o 5 S O J 5 T- o O J S cy CO o o o o OJ OJ CO CO CM CO h - eo r- O y- CM O O J O CO O O J CO CM CO CO a i Tf OJ oo CO CD T - CO CM i -00 CO lO CO O) 00 CM CM h - CD c i co r - co CO CM CO CM CO CO CO CO CO r - r -CM CM o 8 i n CD i - 00 i n CM O CM CO CM i n eo CM CM CM CO T- OJ CM CO OJ h -O eo CM CM CD 00 CM OJ CO CO CO 3 eo CM lO y-y- CO 1- OJ r - co co d i n co CO 00 CM CM ro co | cn CM | r - oo j h - co CD o CM CO c i 0> § E SI a I I CL s D) C "a c lis •5 si cn e , 5i | X A Appendix 6 199 o o o o o o o o s § un co co co o oj ou CM O CO CO CO CM CD IM CO CO CM 01 CO CO o o Tf CO o cn GO co LO co cn co LO co co cn Jill Appendix 6 200 o o o o o o o r- o CO LO co co o o o o o o o o o o o c o o c o to cn f LO O CO •t- LO CO o o o o o o o o o c o r - i n - - LO CM CM Tf CO OOOOOOOOOOtDLOO Q O Tf Tf O O o> O O CO CO r-o r- r-- co QOOOOOOOOOTfCOh-O LO CO LO S O O CO sow o o o o o o o o o cn o o OOOOOOOOOCMCOTf CO CO LO LO CO O Tf O — CM i -OOOOOOOOO'— COCO o cn o S uS cS o o o o o o o o o o o r-. i -cn CM co co cn Tf OOOOOOOOOlO CM CO CO co o co T- CO CO OCMOOCOOOOOOCOCOTf 8 8 3 3 y- y- CM f- y~ LO LO — — — en cn IS s LO CO cn cn IS s to S LO Tf T- 1 LO Lo r? 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E o o c O 0 O T f CD LO O LO ^_ T f 0 E CO CO Tf • O LO LO f - CO if 0 CO CO 0 CM i r i T f CO d CO c L. 0 a CC CO *~ *~ CO CO f - c o 00 c O O O CO r~ LO cn T - O O 0 T f 3 a> u E — O O O CO O ) CM CO CO LO c r i CD Tf to 0 O O O cn CO 00 r^  CD LO T f T f T f rc a c T _ T " ^~ 0 O O O LO CO CM Tf CM T f f~ i •cr r~ O O Tf CO CO O t S TJ & c CO cn •~ i r i CO CD cri s s 0 c O 2 0 CM Tf CO , ~ CM CO CO 00 CO 00 CO CO CO CO cn O 0 X TJ o> 0 q q q q cn O ) cn CO CO 0 fc o O C TJ 0 c l d d d d d d u J5 X cc CO CM CM CM r~ CO 0 0 0 D) 0 CO CO CO CO r~ CO CO 0 = TJ d d d d d d d d d d X CC • CO r~ t o CO CO CO T f CO CM LO LO T f CO 0 CO CM 0 r~ LO CM Tota No.( farm ANI CM CM " " 0 0 cn CO LO 05 T f cn T- LO LO r^  0 0 CO LO CD 0 CO 00 cn T f LO t-~ a co E 0 0 cn O ) CO r~ CO CM 00 T f CM O cn 6 3 LO LO T f T f T f T f T f T f CO CO CO t o CM f- z O 0 & O 0 0 LO CO CO CO CM cn f : CO 0 0 CM CO CO CO f -"5 •5 >• a C O t s CO O cvi CO d 1- E O O 0 0 CO CM f~ CM c o 10 00 CO T f 0 +-CO O T f CM CD LO T f CM CM Fall Cor trac 0 CM CO Tf CD cri CM CO O 0 0 CM LO CM O r-- LO cn CO CO "3 0 T f CO CO CO CO CM CO otal T J CM CM Tf CD CO 0 otal d $ ^~ T _ •~ r- z O LL O 0 0 0 O O O O 0 0 0 O 0 TJ c O 0 0 0 O O O O O 0 0 O 0 x CD 3 O 0 0 O O'S O'O i n O i n 0 i n O CO UJ i n 0 i n 0 " O'S O'O o f i n 0 CM" i n CD SL IX i n CD CO f~ CO CO 00 CO 01 cn at Ol Appendix 6 201 o. _ 73 i _ ro S o> c U) c n £ o in c ra Du E i _ CO U. ra E is a. 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