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TopicWeightings
FALevelI
SessionNO. Content Weightings
StudySession1 Ethics&ProfessionalStandards 15
StudySession2-3 tative ysis 12
StudySession4-5 Economics 10
StudySession6-9 FinancialReportingand ysis 20
StudySession12
PortfolioManagementandWealth
nning
7
StudySession10-11 CorporateFinance 7
StudySession13-14 EquityInvestment 10
StudySession15-16 Fixed e 10
StudySession17 Derivatives 5
StudySession18 AlternativeInvestments 4
FrameworkPortfolioManagement
PortfolioManagement
R40PortfolioManagement:AnOverview
R41RiskManagement:AnIntroduction
R42PortfolioRiskandReturn:PartI
R43PortfolioRiskandReturn:PartII
R44BasicofPortfolionningandConstruction
Reading
42
PortfolioRiskandReturn:PartI
HPR
Averagereturn
Arithmeticmeanreturn:unbiasedestimatorofthetruemean
Geometricmeanreturn:compoundannualrate
Money-weightedrateofreturn:IRR
Otherreturnmeasures
Grossreturn:totalreturnbeforemanagementandadministrationfees
Pretaxnominalreturn
After-taxnominalreturn
Realreturn
Leveragedreturn:thegainorlossasapercentageofaninvestor’scashinvestment.(realestate)
Assetclasseswiththegreatestaveragereturnsalsohavethehigheststandarddeviationsofreturns.
Liquidityshouldbeconsideredwheninvest,especiallyinemergingmarketsandforsecuritiesthattradeinfrequently.
Anindividualinvestment: n
ExpectedReturn E(R)PiRi
i1
n
P1R1P2R2LPnRn
VarianceofReturn Var=2[RiE(R)]2Pi
i1
[RE(R)]P
i1
StandardDeviationofReturn SD=
Covariance
Correlation
Theportfoliostandarddeviationformula
Theriskofaportfolioofriskyassetsdependsontheassetweightsandthestandarddeviationsoftheassetsreturns,andcruciallyonthecorrelation(covariance)oftheassetreturns.
Thelowerthecorrelationbetweenthereturnsofthestocksintheportfolio,allelseequal,thegreaterthediversificationbenefits.
Two-assetportfolio:
σp2=w12σ12+w22σ22+2w1w2COV1,2
=w12σ12+w22σ22+2w1w2σ1σ2ρ1,2
Riskandreturnfordifferentvaluesofcorrelation
E(R)
ρ=-1
ρ=-0.5 ρ=0 ρ=+0.5
ρ=+1
E(R) GlobalMinimumVariancePortfolio
EfficientFrontier
(AllEfficientportfolio)
InefficientPortfolios
IndividualSecurity
Minimumvariancefrontier
Portfoliothathavetheloweststandarddeviationofallportfolioswithagivenexpectedreturnareknownasminimum-varianceportfolios.Togethertheymakeuptheminimum-variancefrontier
Portfoliosthathaveminimumvarianceforeachgivenlevelofexpectedreturn
Globalminimum-varianceportfolio:Theportfolioontheefficientfrontierthathastheleastrisk.
Efficientfrontier
Thoseportfoliosthathavethegreatestexpectedreturnforeachlevelofriskmakeuptheefficientfrontier.
Allriskyassetsarecontained
Efficientportfolio:well-diversifiedorfully-diversified
Riskseeking
Referstothefactthatinvestorissaidtoberisklovingorriskseeking.
Riskseekinginvestors:
Preferhigherrisktolowerriskforagivenlevelofexpectedreturns
Willacceptles pectedreturnbecauseoftheextrautilityfromtherisk
Thegamblehasanuncertain e,butwiththesameexpectedvalueastheguaranteed e.Thus,aninvestorchoosingthegamblemeansthattheinvestorget tra"utility"fromtheuncertaintyassociatedwiththegamble.
RiskNeutral
Aninvestorisindifferentaboutthegambleortheguaranteed e
Riskneutralityinvestorcaresonlyaboutreturnandnotaboutrisk,sohigherreturninvestmentsaremoredesirableeveniftheycomewithhigherrisk.
Riskaversion
Referstothefactthatindividualspreferlessrisktomorerisk.
Risk-averseinvestors:
Preferlowertohigherriskforagivenlevelofexpectedreturns
Willonlyacceptariskierinvestmentiftheyarecompensatedintheformofgreaterexpectedreturn
E(R)
Higher
Utility
Lower
Risk
Theoptimalportfolioforaninvestor
Atthepointofwhereaninvestor’s(highest)risk-returnindifferencecurveistangenttotheefficientfrontier.
E(R)
GlobalMinimumVariancePortfolio
X
Y
I2
I1
I2
I1
EfficientFrontier(AllEfficientportfolio)
InefficientPortfolios
IndividualSecurity
Optimalportfolio
Thehighestindifferencecurvethatistangenttotheefficientfrontier
Differentinvestorsmayhavedifferentoptimalportfolios
Reading
43
PortfolioRiskandReturn:PartII
Two-fundseparationtheorem:
Combiningariskyportfoliowitharisk- asset
Allinvestors’optimumportfolioswillbemadeupofsomecombinationofanoptimalportfolioofriskyassetsandtherisk- asset.
CAL
Thelinerepresentingthesepossiblecombinationsofrisk- assetsandtheoptimalriskyassetportfolio.
Ris
As
withWAntheRis
Risk-Asset
PortfolioInvestediAsset
E(RP)WAE(RA)WBE(RB)
P
P WAA
E(R)
CAL
A
Indifference
Curve
CALB
B
CALC
C
RiskyPortfoliosandTheirAssociatedCapitalAllocationLinesforDifferentinvestors
Ifeachinvestorhasdifferentexpectationsabouttheexpectedreturnsof,standarddeviationsof,orcorrelationsbetweenriskyassetreturns,eachinvestorwillhaveadifferentoptimalriskyassetportfolioandadifferentCAL
TheMarketPortfolio
IsthetangentpointwheretheCMLtouchestheMarkowitzefficientfrontier.
Consistsofeveryriskyassets
Theweightsoneachassetareequaltothepercentageofthemarketvalueoftheassettothemarketvalueoftheentiremarketportfolio.
Capitalmarketline
Wheninvestorsshareidenticalexpectationsaboutthemeanreturns,varianceofreturns,andcorrelationsofriskyassets,theCALforallinvestorsisthesameandisknownasthecapitalmarketline(CML):
E(RP
)RF
E(RM)RF
P
M
Themarketportfolio
ExnationoftheCML
InvestmentusingCMLfollowapassiveinvestmentstrategy(i.e.,investinanindexofriskyassetsthatservesasa forthemarketportfolioandallocateaportionoftheirinvestableassetstoarisk- asset.)
Differenc weentheCMLandtheCAL
Unsystematicrisk(orunique,diversifiable,firm-specificrisk):
Theriskthatdisappearsintheportfolioconstructionprocess
Systematicrisk(ormarketrisk):
Theriskthatisleftcannotbediversifiedaway.
Totalrisk=systematicrisk+unsystematicrisk
Riskvs.NumberofportfolioAssets
σ
Totalrisk
Unsystematicrisk
MarketRisk
Systematicrisk
Numberofsecuritiesintheportfolio
SystematicRiskisRelev Portfolios
Oneimportantconclusionofcapitalmarkettheory:
Equilibriumsecurityreturnsdependonastock’soraportfolio’s
systematicrisk,notitstotalriskasmeasuredbystandarddeviation.
Oneoftheassumptionsofthemodel:
Diversificationis ,becauseinvestorswillnotbecompensatedforbearingriskthatcanbeeliminatedatnocost.
Beta:thesensitivityofanasset’sreturntothereturnonthemarketindexinthemarketmodel.Astandardizedmeasureofsystematicrisk.
Covi,mkti 2
(i
)
i,mkt
mkt mkt
Assetcharacteristicline(regressionofassetexcessreturns marketassetreturns)
AssetExcessReturn(Ri-Rf)
AssetCharacteristicLine
BSlopeCovim
i
MarketExcessReturn(Rm-Rf)
Returngeneratingmodels:multifactormodels
Macroeconomicfactors:GDPgrowth,inflation,orconsumerconfidence
Fundamentalfactors:earnings,earningsgrowth,firmsize,andresearchexpenditures
Statisticalfactors
E(Ri)RF
Marketmodel
i,1E(Factor1)i,2E(Factor2)...i,kE(Factork)
Asinglefactormodel
Theonlyfactoristheexpectedexcessreturnonthemarketportfolio(marketindex)
E(Ri)Rf i(E(RM)Rf)
AssumptionsoftheCAPM
Investorsarerisk-averse,utility- izing,rationalindividuals.
Marketsarefrictionless, ludingnotransactioncostsandnotaxes.
Investorsnforthesamesingleholdingperiod.
Investorshavehomogeneou pectationsorbeliefs.
Allinvestmentsareinfini ydivisible.
Invstorsarepricetakers.
CapitalAssetPricingModel
)
Securitymarketline(SML)
)
Marketportfolio
RFR
mkt
Systematicrisk
TheEquationofSML: E(Ri)=Rf+βi[E(RM)-Rf]
Howtojudgeifastockisproperlyvalued
E(R)
Appropria yvalued
undervalued,buy
SML
Overvalued,Sell
Beta,SystematicRisk
DifferencesbetweentheSMLandtheCML
SML
CML
Measureofrisk
Usessystematicrisk(non-diversifiablerisk)
Usesstandarddeviation(totalrisk)
Application
Toolusedtodetermheappropriateexpected(benark)returnsforsecurities
Toolusedtodetermheappropriateassetallocation(percentagesallocatedtotherisk-assetandtothemarketportfolio)fortheinvestor
Definition
Graphofthecapitalassetpricingmodel
Graphoftheefficientfrontier
Slope
Marketriskpremium
MarketportfolioSharperatio
Evaluaterelativeportfolioperformance(risk-adjustedreturns)
Sharperatio=RPRf
P
P2
M
P1
P1 P2
M
TheSharperatioforanyportfolioalongtheCMListhesame.
TheM-squared(M2)measureproducesthesameportfoliorankingsastheSharperatiobutisstatedinpercentageterms.
M(R
M2(R R)
P f
E(R)
R)
M(R R)
M f
Notes:
TheM-squared(M2)measureproducesthesameportfoliorankingsastheSharpratiobutisstatedinpercentageterms.
M2andSRfornotwell-diversified
P
P
P p f
M2
RM M
R
P
P
Rf
P M
Treynormeasure&Jensen’salpha(systematicrisk)
f
Treynormeasure=RPR
P
(RR)(R R)
P P f P M f
E(R)
Slope=treynormeasureforPortfolioP
RP
RM
P
SML
Jensen’salpha
Rf
P
1
Comparisonoffourmeasures
Jensen’salpha和M-squared是可以根据大小来判断投资业绩
wearenotonlyabletodetermherankofaportfoliobutalsowhich,ifany,ofourportfoliosbeatthemarketonarisk-adjustedbasis
Sharperatio和Treynormeasure需要再和其他的组合的指标进行比较
torankportfolios,theSharperatioorTreynorratioofoneportfoliomustbecomparedwiththeSharperatioorTreynorratioofanotherportfolio
Fornon-diversifiedportfolio,SharperatioandM-squaredare
appropriate
Forfullydiversifiedportfolio,JensenAlphaandTreynorareappropriate
Reading
40
PortfolioManagement:AnOverview
Portfolio
Definition:evaluateindividualinvestmentsbytheircontributiontothe
riskandreturnofaninvestor’sportfolio.
Diversificationallowsaninvestortoreduceportfolioriskwithout
necessarilyreducingtheportfolio’ pectedreturn.
Duringperiodsoffinancialcrisis,correlationstendto rease,whichreducesthebenefitsofdiversification.
Thetypesofinvestmentmanagement s
Individualinvestors
DCpensionn:theindividualmakestheinvestmentdecisionsandtakesontheinvestmentrisk.
DBpension n:befundedby contributionsandhaveanobligationtoprovidespecificbenefitstoretirees.
Endowment:afundthatisdedicatedtoprovidingfinancialsupportonanongoingbasisforaspecificpurpose.
Foundation:afundestablishedforcharitablepurposestosupportspecifictypesofactivitiesortofundresearchrelatedtoaparticulardisease.
Bank
Insurance
Investmentcompanies
Mutualfunds
Sovereignwealthfunds:poolsofassetsownedbya ernment.
Characteristicsofdifferenttypesofinvestors
Investor
RiskTolerance
InvestmentHorizon
LiquidityNeeds
eNeeds
Individuals
Dependsonindividual
Dependsonindividual
Dependsonindividual
Dependsonindividual
DBpensions
High
Long
Low
Dependsonage
Banks
Low
Short
High
Payinterest
Endowments
High
Long
Low
Spendinglevel
Insurance
Low
Long—lifeShort—P&C
High
Low
Mutualfunds
Dependsonfund
Dependsonfund
High
Dependsonfund
nningstep:
ysisoftheinvestor’srisktolerance,returnobjectives,timehorizon,taxexposure,liquidityneeds, eneeds,uniquecircumstances;
IPS:detailstheinvestor’sinvestmentobjectivesandconstraints;specifyanobjectivebenark;updatedatleasteveryfewyearsandanytimetheinvestor’sobjectivesorconstraintschangesignificantly.
Executionstep:assetallocation;top-downysis&bottom-up
Feedbackstep:
monitorandrebalancetheportfolio;
Measureportfolioperformance.
Reading
41
RiskManagement:AnIntroduction
Risk
Exposuretouncertainty
Manydecisionmakersfocusonreturn,whichisnotsomethingthatiseasilycontrolled,asopposedtorisk,orexposuretorisk,whi ayactuallybemanagedorcontrolled
Riskexposure
Theextenttowhichanentity’svaluemaybeaffectedthroughsensitivitytounderlyingrisks.
Riskmanagement
Riskmanagementistheprocessbywhichanorganizationorindividualdefinesthelevelofrisktobetaken,measuresthelevelofriskbeingtaken,andadjuststhelattertowardtheformer;withthegoalofizingthe’sorportfolio’svalueortheindividual’soverallsatisfaction,or
utility.
Itiscomprisesallthedecisionsandactionsneededtobestachieveorganizationalor alobjectiveswhilebearingatolerablelevelofrisk.
Notaboutminimizingrisk.
Riskmanagementframework
Risk ernance
Riskidentificationandmeasurement
Riskinfrastructure
Definedpoliciesandprocesses
Riskmonitoring,mitigation,andmanagement
Communications
Strategic ysisorintegration
Risk ernanceisthetop-levelfoundationforriskmanagement, ludingriskoversightandsettingrisktolerancefortheorganization.
Riskidentificationandmeasurementisthetativeandqualitativeassessmentofallpotentialsourcesofriskandtheorganization’sriskexposures.
Riskinfrastructurecomprisestheresourcesandsystemsrequiredtotrackandassesstheorganization’sriskprofile.
Riskpoliciesandprocessesaremanagement’scomplementtorisk ernanceattheoperatinglevel.
Riskmitigationandmanagementistheactivemonitoringandadjustingofriskexposures,integratingalltheotherfactorsoftheriskmanagementframework.
Communication lud skreportingandactivefeedbackloopssothattheriskprocessimprovesdecisionmaking.
Strategicrisk ysisandintegrationinvolvesusingtheserisktoolstorigorouslysortoutthefactorsthatareandarenotaddingvalueaswellas
orporatingthis ysisintothemanagementdecisionprocess,withtheintentofimproving es.
Risk ernance
Risk ernanceisthefoundationforriskmanagement.
Risk ernancereferstoseniormanagement’sdeterminationoftherisktoleranceoftheorganization,theelementsofitsoptimalriskexposurestrategy,andtheframeworkforoversightoftheriskmanagementfunction.
Employingariskmanagementcommittee,alongwithachiefriskofficer(CRO),arehallmarksofastrongrisk ernanceframework.
Riskmanagementcommitteeprovidestopdecisionmakerswithaforumforregularlyconsideringriskmanagementissues.
Risktolerance
Attheernancelevel,thedutyisgenerallynottoselecttheseactivities—ajobthatusuallyfallstomanagement—buttoestablishtheorganization’sriskappetite.
Certainrisksorlevelsofrisksmaybedeemedacceptable,otherrisksdeemedunacceptable,andinthemiddlearerisksthatmaybepursuedinarisk-limitedfashion.
Saiddifferently,risktoleranceidentifiestheextenttowhichtheentityiswillingtoexperiencelossesoropportunitycostsandtofailinmeetingitsobjectives
Whenyzingrisktolerance,managementshouldexaminerisksthatmayexistwithintheorganizationaswellasthosethatmayarisefromoutside.(“inside”viewand“outside”view)
Therisktoleranceshouldbechosenandcommunicatedbeforeacrisis,andwillserveasthehigh-levelguidanceformanagementinitsstrategicselectionofrisks.
Ifahastheabilitytoadaptquicklytoadverseeventsmayallowforahigherrisktolerance.
Riskbudgetingistheprocessofallocatingfirmresourcestoassets(orinvestments)byconsideringtheirvariousriskcharacteristicsandhowtheycomb omeettheorganization’srisktolerance.
Theprocessofriskbudgeting sthefirmtoconsiderrisktradeoffs.
Thegoalistoallocatetheoverallamountofacceptablerisktothemixofassetsorinvestmentsthathavethegreatestexpectedreturnsovertime.(Thereturnperunitofriskisthehighest.)
Theriskbudgetmaybeasinglemetric,suchasportfoliobeta,valueatrisk(VaR),portfolioduration,orreturnsvariance.
Ariskbudgetmaybeconstructedbasedoncategoriesofinvestments,suchasdomesticequities,domesticdebtsecurities,internationalequities,andinternationaldebtsecurities.
Anotherwaytoallocateariskbudgetistoidentifyspecificriskfactors,suchasinterestraterisk,equitymarketrisk,andforeignexchangeraterisk.
Financialrisksrefertotherisksthatarisefromeventsoccurringinthefinancialmarkets.Examplesare:
Marketrisk
Arisesfrommovementsinstockprices,interestrates,exchangerates,andcommodityprices
Creditrisk
Theriskth ounterpartywillnotpayanamountowed
Liquidityrisk
Theriskthat,asaresultofdegradationinmarketconditionsorthelackofmarketparticipants,onewillbeunabletosellanassetwithoutloweringthepricetolessthanthefundamentalvalue
Liquidityriskcouldalsobecalledtransactioncostriskandismostassociatedwithawideningbid-askspread.
Non-financialrisksarisefromactionswithinanentityorfromexternalorigins,suchastheenvironment,thecommunity,regulators,politicians,rs,andcustomers.Examplesare:
Operationalrisk
Thisistheriskthathumanerrororfaultyorganizationalprocesseswillresultinlosses.
Solvencyrisk
Thisistheriskthattheorganizationwillbeunabletocontinuetooperatebecauseithasrunoutofcash.
Regulatoryrisk
Thisistheriskthattheregulatoryenvironmentwillchange,imposingcostsonthefirmorrestrictingitsactivities.
ernmentalorpoliticalrisk(ludingtaxrisk)
Thisistheriskthatpoliticalactionsoutsideaspecificregulatoryframework,suchasreasesintaxrates,willimposesignificantcostsonanorganization.
Legalrisk
Thisistheuncertaintyabouttheorganization’posuretofuturelegalaction.
Modelrisk
Thisistheriskthatassetvaluationsbasedontheorganization’s yticalmodelsare orrect.
Tailrisk
Thisistheriskthatextremeevents(thoseinthetailsofthedistributionofes)aremorelikelythantheorganization’s ysisindicates,
especiallyfrom orrectlyconcludingthatthedistributionof esisnormal.
Accountingrisk
Thisistheriskthattheorganization’saccountingpoliciesandestimatesarejudgedtobe orrect.
Individualsfacemanyofthesameorganizationalrisksoutlinedherebutalsofacehealthrisk,mortalityorlongevityrisk,andpropertyandcasualtyrisk.
In ctionbetweenrisks
Risksarenotnecessarilytbecausemanyrisksariseasaresultofotherrisks;riskin ctionscanbeextremelynon-linearandharmful.
Riskdriversarethefundamentalglobalanddomesticmacroeconomicandindustryfactorsthatcreaterisk.
Metrics
Standarddeviationisameasureofthevolatilityofassetpricesandinterestrates.Standarddeviationmaynotbetheappropriatemeasureofriskfornon-normalprobabilitydistributions,especiallythosewithnegativeskeworpositiveexcesskurtosis(fattails).
Betameasuresthemarketriskofequitysecuritiesandportfoliosofequitysecurities.Thismeasureconsiderstheriskreductionbenefitsofdiversificationandisappropriateforsecuritiesheldinawell-diversifiedportfolio.
Durationismeasureofthepricesensitivityofdebtsecuritiestochangesininterestrates.
Derivativemeasures,suchasdelta,g ,vega,andrho.
Tailmeasuressuchasvalueatrisk(VaR),CVaRandexpectedlossgivendefault(LGD).
VaRistheminimumlossoveraperiodthatwilloccurwithaspecificprobability.
CVaRistheexpectedvalueofloss,giventhatthelos ceedsaminimumamount.(calculatedastheprobability-weightedaveragelossforalllosse pectedtoexceedaminimumamount)
Subjectiveandmarket-basedestimatesofrisk
TwomethodsofriskassessmentthatareusedtosupplementmeasuressuchasVaRandCVaRarestresstestingandscenario ysis.
Stresstestingexaminestheeffectsofaspecific(usuallyextreme)changeinakeyvariablesuchasaninterestrateorexchangerate.
Scenario ysisreferstoasimilarwhat-if ysisofexpectedlossbut orporateschangesinmultipleinputs.
Methodsofriskmodification:
Riskpreventionandavoidance
Notengageintheactivitywiththeuncertain e.
Riskacceptance:self-insuranceanddiversification
Self-insuranceisobtainedbysettingasidesufficientcapitaltocoverlosses.
Anotherformofacceptingrisk,but ngsointhemostefficientmannerpossible,isdiversification.
Risktransfer(insurance)
Risktransferistheprocessofpassingonarisktoanotherparty,often,butnotalways,intheformofaninsurance.
Riskshifting(derivatives)
Whereasrisktransferreferstoactionstakenthatpasstheriskontootherparties,riskshiftingreferstoactionsthatchangethedistributionofrisk es.Riskshiftinggenerallyinvolvesderivativesastheriskmodificationvehicle.
Thedeterminantsofwhi ethodisbestformodifyingriskarethebenefitsweighedthecosts.
Reading
44
BasicofPortfolio nningandConstruction
Theneedforastatement
Understandandarticulaterealisticinvestorgoals,needsandrisktolerance
Ensurethatgoalsarerealistic
Provideanobjectivemeasureofportfolioperformance
MajorcomponentsofIPS
Descriptionof
Statementofthepurpose
Statementofdutiesandresponsibilities
ProcedurestoupdateIPSandtorespondtovariouspossiblesituations
Investmentobjectives
Investmentconstraints
Investmentguidelines
Evaluationofperformance
Appendices:informationonassetallocation
Investmentobjectives:riskandreturn
Riskobjective
Theriskobjectivelimitshowhightheinvestorcansetthereturnobjective
Riskmeasurement:
Absolute:varianceorstandarddeviation
Relative:relateriskrelativetooneormoreben arksperceivedtorepresentappropriateriskstandards(trackingrisk),
Downsiderisk:VAR
Risktolerance:willingnessandability
Situation
Risktolerance
Willingness>Ability
Ability(Education)
Willingness<Ability
ReturnObjective=Willingness
Willingness(Reevaluation)
ReturnObjective=Ability
Ability(Education)
Returnobjectives:absoluteorrelativebasis
Returnmeasurement:totalreturn(balanc weencapitalgainsande),inflation-adjustedreturn(real)
Totalreturn:balanc weencapitalgainsand e
Statedreturndesirevs.Requiredreturn
Consistentwithriskobjective
Investmentconstraints
Liquidity—forcashspendingneeds(anticipatedorunexpected)
Timehorizon—thetim weenmakinganinve
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