Hedging net firm income for Florida dairy producers : A case study with an application of the conditional value at risk PDF
Preview Hedging net firm income for Florida dairy producers : A case study with an application of the conditional value at risk
HEDGINGNETFIRMINCOMEFORFLORIDADAIRYPRODUCERS:ACASE STUDYWITHANAPPLICATIONOFTHECONDITIONALVALUEATRISK By MICHAELJOHNZYLSTRA ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAFNPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2004 Copyright2004 by MichaelJohnZylstra Tomyparents. ACKNOWLEDGMENTS IamgratefulfortheguidanceIreceivedfrommysupervisorycommitteechair,Dr. RichardL.Kilmer. Mydiscussionswithhimwereinstrumentaltothedevelopmentand fundingofthisresearchproject. HisperseverancekeptmegoingwhenIhadalmost succumbedtocompletefrustration. Thepatienceandflexibilityheawardedmeinthe developmentofthisdissertationweregreatlyappreciated. Iamthankfulforthetimehe tooktometiculouslyreviewmywork;andforhishelpfulcomments. Iwouldalsoliketoacknowledgethesupportofmycommitteemembers. Dr. RonaldH.Wardprovidedmuchofthetechnicalandtheoreticalsupportformyresearch. Hewasthesourceofnumeroushelpfulideasfortheeconometricmodelingused. My discussionswithDr.StanislavUryasevhelpedmetoselectandimplementthe conditionalvalueatrisk. Hisenthusiasmforhisworkisrefreshing. Alloftheproducer revenueandexpensedatausedinthisdissertationweremadeavailablebytheDairy BusinessAnalysisProject(DBAP). Dr.AlbertdeVriesofferedconsiderablesupport workingwiththeDBAPdatasets. Finally,IcanonlyhopethatmydiscussionswithDr. P.J.vanBloklandwillhelptogroundthisresearchwithintherealmofpracticality. Anumberofotherindividualscontributeddirectlyandindirectlythroughtheir helpfulcomments. IwouldliketothankDr.ClydeSchoolfieldoftheStatistics departmentforhishelpfulcommentsregardingbinomialtrees. Myconversationswith Dr.Schoolfieldhelpedgreatlyinthedevelopmentofamodelingmethodologythatwas sensitivetotheintricaciesofthedairyindustry. SherifKandil(adoctoralstudentinthe IV MechanicalandAerospaceEngineeringDepartmentandaclosefriend)introducedmeto Tecplot. SherifprovidedinstructionandthengrantedaccesstohislabsothatIcould createsomeofthecontourgraphspresentedinthisdissertation. VladimirBoginskiand SergeySarykalin(mycomradesintheIndustrialandSystemsEngineeringDepartment) providedmewithassistanceusingCPLEXandimplementingtheconditionalvalueat risk. IregretthatIwillnotreapthefullbenefitofourdiscussionsuntilIcontinuework onimplicationsforfurtherresearch. Dr.GeorgeWang(oftheCommodityFutures TradingCommissioninWashington,DC)madeseveralcommentsonliquidityriskthat havekeptmeupatnight,questioningtheresultsreportedinthisdissertation. His commentsonthedairymarketswerehelpful,andfortunatelywillkeepmeworkingafter IleavetheUniversityofFlorida. FinallyIwouldliketoacknowledgethemuch-appreciatedfinancialsupportI receivedfromtheUnitedStatestaxpayers(viatheUSDANationalNeedsFellowship Program);theFloridadairyfarmers(viatheFloridaDairyCheck-OffProgram);andthe FoodandResourceEconomicsDepartmentattheUniversityofFlorida. TABLEOFCONTENTS Page ACKNOWLEDGMENTS iv LISTOFTABLES x LISTOFFIGURES xi ABSTRACT xiii CHAPTERS 1 COMPLEXITIESOFRISKMITIGATIONFORFLORIDAPRODUCERS 1 DairyProductUtilization 1 MilkPricing 1 ImpactofPolicyShifts 3 RecentPolicyChanges 3 Short-versusLong-RunImplications 4 ProblemStatement 5 ResearchObjectives 5 2 LITERATUREREVIEW 7 BusinessRisk 7 ProductionRisk 7 PriceRisk 9 OtherSourcesofRisk 9 FinancialRisk 10 Fanners'DegreeofConcernaboutDifferentTypesofRisk 10 RiskBalancing 11 RiskEfficiencyModels 14 ExpectedValue-Variance 14 EmpiricalApplicationsofExpectedValue-Variance 16 AdvantagesandDisadvantagestoUsingtheExpectedValue-Variance 18 ValueatRiskandConditionalValueatRisk 19 EmpiricalApplicationsofExpectedValue-Variance 20 AdvantagesandDisadvantagestoUsingExpectedValue-VaRandExpected Value-cVaR 21 DairyRiskMitigatingTools 22 VI 1 MilkFutures 22 MilkOptions 23 SummaryofWhatWasLearned 23 COMPATIBILITYOFTHEVARIANCE,VALUEATRISKAND CONDITIONALVALUEATRISKWITHEXPECTEDUTILITY MAXIMIZATIONANDCOHERENCY 25 Introduction 25 ExpectedUtility 25 SimpleLotteries 26 CompoundLotteries 27 VonNeumannMorgensternAxioms 28 Completeness 28 Transitivity 28 Continuity 29 Independence 29 ExpectedUtilityForm 30 ExpectedUtilityProof 30 CertaintyEquivalence 32 RiskPremium 33 RiskAversion 34 ExpectedUtilityandHedging 35 ExpectedUtilityMaximizingHedgeGivenaCashPosition 37 ConsistencyoftheVarianceRiskMeasurewithExpectedUtility 38 QuadraticUtility 38 NormallyDistributedReturns 39 Meyer'sLocationScale 39 ConsistencyofValueatRiskandConditionalValueatRiskwithExpectedUtility Maximization 40 NormallyDistributedReturns 40 First-andSecond-DegreeStochasticDominance 41 ConsistencyofValueatRiskandConditionalValueatRiskwithCoherency 42 SubadditiveandPositiveHomogeneity 42 MonotonicandTranslationInvariance 43 SummaryofWhatWasLearned 46 CONCEPTUALMONTECARLOMODELFORGENERATINGMONTHLYNET INCOMESCENARIOSFORAFLORIDADAIRYPRODUCER 48 ProducerRevenue 49 BlendPriceRevenue 49 MilkProduction 51 MilkPrices 52 MilkUtilization 56 VI StochasticOverorderPremium 59 MilkIncomeLossContract(MILC) 60 OtherRevenueSources 61 ProducerExpenses 62 ProductionExpenses 62 InterestExpenses 63 ProducerNetIncome 63 OptimizationProblem 64 5 RISK-NEUTRALVALUATIONOFAMERICANCLASSIIIMILKOPTIONS USINGBINOMIALTREESANDTHEGENERATIONOFSTOCHASTIC CLASSIIIPRICES 65 Risk-NeutralValuation 65 RelationshipbetweenU,D,andVolatility 67 ImpliedVolatilities 68 ValuationofAmericanandEuropeanOptions 69 MilkPrice-Supports 74 PutCallParity 77 ObservableandUnobservableComponentsofClassIIIMilkFutures 78 CalibrationofUnobservedComponents 79 Implementation 82 6 PRECURSORY,IMPLICIT,ANDEXPLICITMODELRESULTS 86 Introduction 86 PrecursoryResultsDerivedforModelDevelopment 86 Utilization 86 MilkProductionPerCow 87 HedgingStrategyandClosingBasis 89 ImplicitModelResults 93 MilkPrice-Support 93 Past,Present,andFutureImpliedPriceVolatilities 94 ExplicitModelResults 96 7 SUMMARY.CONCLUSIONS,IMPLICATIONS,ANDDIRECTIONFOR FUTURERISKMITIGATINGRESEARCHINTHEFLORIDADAIRY INDUSTRY 104 Introduction 104 Summary,ConclusionsandImplicationsRegardingModelParameters 104 MilkUtilization 104 MilkProduction 105 Summary,ConclusionsandImplicationsRegardingModelAssumptions 106 vm HedgingStrategy 106 PriceFloor 108 Summary,ConclusionandImplicationsRegardingModelResults 109 MilkIncomeLossContract 109 Productionrisk Ill CapitalStructure Ill DirectionsforFurtherRisk-MitigatingResearchontheFloridaDairyIndustry 112 APPENDIX A STOCHASTICMILKUTILIZATIONINFLORIDA 115 Introduction 115 EconometricModeltoPredictMilkUtilization 116 B PRODUCTIONRISK 123 FloridaMilkProduction 123 EconometricModelUsedtoPredictMilkProductionPerCow 124 ForecastingMilkProductionandProductionRisk 125 C MILKPRODUCTIONEXPENSESFORFLORIDADAIRYPRODUCERS 128 DairyBusinessAnalysisProjectData 128 EconometricEstimatesofExpenseVariation 129 LISTOFREFERENCES 135 BIOGRAPHICALSKETCH 139 IX LISTOFTABLES Table page 4-1 Historicalcorrelationsbetweenstochasticvariables 64 6-1 Averageminimumriskfuturesandoptionshedgeratiosandcorresponding conditionalvalueatrisk(calculatedfrombootstrapsample) 98 A-l Restrictedordinaryleastsquaresmilkclassutilizationparameterlabels,variables, andestimates 120 A-2 Milkutilizationdata(January2000throughDecember2003) 121 B-l RestrictedordinaryleastsquareparametereEstimatesandtheirstatistical significance 125 C-l ChangesinMilkProductionCostsDueToChangingProduction 134
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