Optimal_execution_of_portfolio_transactions_Almgren_Chriss.2001

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1、OptimalexecutionofportfoliotransactionsRobertAlmgrenDepartmentofMathematics,UniversityofToronto,100St.GeorgeStreet,Toronto,OntarioM5S3G3,CanadaNeilChrissICorBrokerageInc.,500FifthAvenue,Suite415,NewYork,NewYork10110,USATheauthorsconsidertheexecutionofportfoliotransactionswiththeaimofminimizinga

2、combinationofvolatilityriskandtransactioncostsarisingfrompermanentandtemporarymarketimpact.Inthespaceoftime-dependentliquida-tionstrategies,theef®cientfrontierconsistsofstrategieshavingthelowestexpectedexecutioncostforagivenlevelofuncertainty;withalinearcostmodelthisfrontiercanbeexplicitlyconst

3、ructed.Itisthenpossibletoselectparticularoptimalstrategieseitherbyminimizingaquadraticutilityfunctionorbyminimizingvalue-at-riskVaR).Thelatterchoiceleadstotheconceptofliquidity-adjustedVaR,orL-VaR,whichexplicitlyconsidersthebesttradeoffbetweenvolatilityriskandliquidationcosts.1.INTRODUCTIONThis

4、paperconcernstheoptimalexecutionofportfoliotransactions,transactionsthatmoveaportfoliofromagivenstartingcompositiontoaspeci®ed®nalcompositionwithinaspeci®edperiodoftime.BertsimasandLo1998)havede®nedbestexecutionasthedynamictradingstrategythatprovidestheminimumexpectedcostoftradingovera®xedperi

5、odoftime,andtheyshowthatinavarietyofcircumstancesonecan®ndsuchastrategybyemployingadynamicoptimizationprocedure;buttheirapproachignoresthevolatilityofrevenuesfordierenttradingstrategies.Thispaperworksinthemoregeneralframeworkofmaximizingtheexpectedrevenueoftradingor,equivalently,minimizingthec

6、osts),withasuitablepenaltyfortheuncertaintyofrevenueor1cost).Westudyvarianceoftradingcostinoptimalexecutionbecauseit®tswiththeintuitionthatatrader'sutilityshould®gureinthede®nitionofoptimalin1Thisgeneralframeworkarisesinmarketmicrostructuretheory,butwithadierentpurposeinmind.Theuninformeddiscr

7、etionarytradertradesanexogenousendowmentoveranexogenouslyspeci®edamountoftimetomaximizepro®tsAdmatiandP¯eiderer1988);theinformedstrategictradertradesovermultipleperiodsoninformationnotwidelyavailable,againtomaximizepro®tsKyle198