金融机构管理Chap010.docx

金融机构管理Chap010.docx

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金融机构管理Chap010

ChapterTen

MarketRisk

ChapterOutline

Introduction

MarketRiskMeasurement

CalculatingMarketRiskExposure

TheRiskMetricsModel

∙TheMarketRiskofFixed-IncomeSecurities

∙ForeignExchange

∙Equities

∙PortfolioAggregation

HistoricorBackSimulation

∙TheHistoric（BackSimulation）ModelversusRiskMetrics

∙TheMonteCarloSimulationApproach

RegulatoryModels:

TheBISStandardizedFramework

∙FixedIncome

∙ForeignExchange

∙Equities

TheBISRegulationsandLargeBankInternalModels

Summary

SolutionsforEnd-of-ChapterQuestionsandProblems:

ChapterTen

1.Whatismeantbymarketrisk?

Marketriskistheuncertaintyoftheeffectsofchangesineconomy-widesystematicfactorsthataffectearningsandstockpricesofdifferentfirmsinasimilarmanner.Someofthesemarket-wideriskfactorsincludevolatility,liquidity,interest-rateandinflationaryexpectationchanges.

2.Whyisthemeasurementofmarketriskimportanttothemanagerofafinancialinstitution?

MeasurementofmarketriskcanhelpanFImanagerinthefollowingways:

a.Provideinformationontheriskpositionstakenbyindividualtraders.

b.Establishlimitpositionsoneachtraderbasedonthemarketriskoftheirportfolios.

c.Helpallocateresourcestodepartmentswithlowermarketrisksandappropriatereturns.

d.Evaluateperformancebasedonrisksundertakenbytradersindeterminingoptimalbonuses.

e.Helpdevelopmoreefficientinternalmodelssoastoavoidusingstandardizedregulatorymodels.

3.Whatismeantbydailyearningsatrisk（DEAR）?

Whatarethethreemeasurablecomponents?

Whatisthepricevolatilitycomponent?

DEARorDailyEarningsatRiskisdefinedastheestimatedpotentiallossofaportfolio'svalueoveraone-dayunwindperiodasaresultofadversemovesinmarketconditions,suchaschangesininterestrates,foreignexchangerates,andmarketvolatility.DEARiscomprisedof（a）thedollarvalueoftheposition,（b）thepricesensitivityoftheassetstochangesintheriskfactor,and（c）theadversemoveintheyield.Theproductofthepricesensitivityoftheassetandtheadversemoveintheyieldprovidesthepricevolatilitycomponent.

4.FollowBankhasa$1millionpositioninafive-year,zero-couponbondwithafacevalueof$1,402,552.Thebondistradingatayieldtomaturityof7.00percent.Thehistoricalmeanchangeindailyyieldsis0.0percent,andthestandarddeviationis12basispoints.

a.Whatisthemodifieddurationofthebond?

MD=5÷（1.07）=4.6729years

b.Whatisthemaximumadversedailyyieldmovegiventhatwedesirenomorethana5percentchancethatyieldchangeswillbegreaterthanthismaximum?

Potentialadversemoveinyieldat5percent=1.65=1.65x0.0012=.001980

c.Whatisthepricevolatilityofthisbond?

Pricevolatility=-MDxpotentialadversemoveinyield

=-4.6729x.00198=-0.009252or-0.9252percent

d.Whatisthedailyearningsatriskforthisbond?

DEAR=（$valueofposition）x（pricevolatility）

=$1,000,000x0.009252=$9,252

5.Whatismeantbyvalueatrisk（VAR）?

HowisVARrelatedtoDEARinJ.P.Morgan’sRiskMetricsmodel?

WhatwouldbetheVARforthebondinproblem（4）fora10-dayperiod?

Withwhatstatisticalassumptionisouranalysistakingliberties?

Couldthistreatmentbecritical?

ValueatRiskorVARisthecumulativeDEARsoveraspecifiedperiodoftimeandisgivenbytheformulaVAR=DEARx[N]½.VARisamorerealisticmeasureifitrequiresalongerperiodtounwindaposition,thatis,ifmarketsarelessliquid.ThevalueforVARinproblemfouraboveis$9,252x3.1623=$29,257.39.

Therelationshipaccordingtotheaboveformulaassumesthattheyieldchangesareindependent.Thismeansthatlossesincurredononedayarenotrelatedtothelossesincurredthenextday.However,recentstudieshaveindicatedthatthisisnotthecase,butthatshocksareautocorrelatedinmanymarketsoverlongperiodsoftime.

6.TheDEARforabankis$8,500.WhatistheVARfora10-dayperiod?

A20-dayperiod?

WhyistheVARfora20-dayperiodnottwiceasmuchasthatfora10-dayperiod?

Forthe10-dayperiod:

VAR=8,500x[10]½=8,500x3.1623=$26,879.36

Forthe20-dayperiod:

VAR=8,500x[20]½=8,500x4.4721=$38,013.16

ThereasonthatVAR20（2xVAR10）isbecause[20]½（2x[10]½）.Theinterpretationisthatthedailyeffectsofanadverseeventbecomelessastimemovesfartherawayfromtheevent.

7.Themeanchangeinthedailyyieldsofa15-year,zero-couponbondhasbeenfivebasispoints（bp）overthepastyearwithastandarddeviationof15bp.Usethesedataandassumetheyieldchangesarenormallydistributed.

a.Whatisthehighestyieldchangeexpectedifa90percentconfidencelimitisrequired;thatis,adversemoveswillnotoccurmorethanonedayin2