定量方法與投資組合管理

SS12–Portfolio

PortfolioPortfolioManagement:AnPortfolioRiskandReturn:PartPortfolioRiskandReturn:PartBasicsofPortfolio 2ImportanceofthePortfolioapproach:評估各種資產(chǎn)對整個資產(chǎn)組合投資特ImportanceoftheUnlessthereturnsoftheriskyassetsareperfectlypositivelycorrelatedriskisreducedbydiversificationacrossassets只要風(fēng)險 雞蛋放在同一子里，在金 Reducerisk:portfolio能提供相應(yīng)的expectedreturn,同時減少其Diversificationratio分散比率，把包含n個 43小，說明分散化效43A.ImportanceoftheImportanceoftheRisk‐returnNotnecessarilydownsidePortfoliodiversification只在經(jīng)濟與市場正常運作時能降低風(fēng)險，但在severemarketturmoil時就不能提供downside

B.Typesof 6C.StepsinthePortfolioManagement nningUnderstanding 'sPreparationofan statementTheExecutionAsset PortfolioTheFeedbackPortfoliomonitoringandPerformancemeasurementand

D.PooledMutualfund(共同基金 e與netassetvalue(NAV)open‐endfund(開放式基金):可以接近凈資產(chǎn)(NAV)netassetvalue(NAV)=asset–close‐endfund(封閉式基金能在secondary D.PooledTypesofmutualMoneymarket投資于highqualityshort‐termcorporatedebt,federal debt,stateandlocal ernmentdebtBondmutual主要投資于bondandpreferred

D.PooledTypesofmutualStockmutualStockmutualfund分成activemanagedfundandpassivemanagedfund(indexfunds)。這兩種stockmanagedfund的activelymanagedfund的managementfeeactivelymanaged 頻繁，要 Hybrid/balance即投資bonds,又投資 D.PooledOtherinvestmentExchangetradedfund 或債券。這與indexfund很類“in‐kind”creationandredemptionof 票。好處是能使marketpriceofETFclosetoNAV，另外也有ataxadvantage

D.PooledOtherinvestmentSeparayManagedAccountSMA根據(jù)的investmentobjectivesrisktoleranceandtaxsituation等建立獨立賬戶進行投資。SMA與mutualfund的不同之處在于SMA的資產(chǎn)是直接屬于singleinvestor的(考慮tax的影響)。ETF的優(yōu)點提供一個最有效率的diversification(tracking可以shortedorbetterriskmanage，因為有對應(yīng)的指數(shù)的futures和投資者可以了解ETF的結(jié)noloadandbid‐askspread,efficientoperatingexpensedividendreinvestedimmedia D.PooledOtherinvestmentHedgeThecommonobjectiveofhedgefundisthattheystriveforabsoluteHedgefundsareexemptfromSECregulation，形式以partnershipLLC,offshorecorporationHedgefundstypicallylimittheamountofleveragethatcanbeBuyoutandventurecapitalBuyout通常使用highleverage將上市公司或上市公司部分業(yè)務(wù) Venturecapital投入到處于start‐upphase的中小公司，為其提供，以幫助公司快速發(fā)展壯大。最后公司上市，在二級市場退出。VC的投

PortfolioPortfolioManagement:AnPortfolioRiskandReturn:PartPortfolioRiskandReturn:PartBasicsofPortfolio PortfolioRiskandReturn:PartMajorReturn金融資產(chǎn)通常包括2種類型的return1)周期性的dividendorinterestpayment;2)價格的上升或下跌(capitalgainorloss)MajorreturnHPR(holdingperiodArithmeticormeanArithmeticreturnhasstatistical A.MajorReturnMajorreturnGeometricmean注意Geometricmeanreturn比arithmeticmeanreturn更能準(zhǔn)確反映出資者的總體回報可以反映”buy‐and‐hold A.MajorReturnMajorreturnMoney‐weightedreturnorinternalrateof考慮投資期內(nèi)的cashadditionandAnnualizedPortfolioA.MajorReturnOtherreturnGrossandnetGross在扣除managementexpense,custodialfee,taxes等費用前的return。Grossreturn是已扣除掉tradingexpense的。Grossreturn便于比較不同基金經(jīng)理的investmentskill。Net扣除掉所有上述費用后的return，是投資者最為關(guān)注的凈回Pre‐taxandafter‐taxnominalCapitalgain分為short‐termcapitalgain和long‐termcapitalgainlong‐termcapitalgain打的稅比較低，通常是flat‐taxratee(dividendorinterest)istaxedas 以個人的邊際稅率打稅(progressivetaxrate)

A.MajorReturnOtherreturnRealNominalreturn(r)通常包括3部分rrF:real :inflationrateRP:riskpremiumRealreturn通常用于測量不同通脹率時期的真實回報，也用于比較在不同國家投資的真實回報，因為匯率通常會受到通脹率Leveraged是買入futurescontracts（保證金）;另一種是借錢投資。（融B.Mean,VarianceandCovarianceofAssetBasedonHistoricalExpectedreturnforanindividualE(R)=P1?R1+P2?R2+P3?R3+…….+Pn?P:Probability發(fā)生此收益率的可能性)R:Return(收益率)；E(R):期望收益率VarianceforanindividualExpectedreturnforaE(Rp)=W1?E(R1)+W2?E(R2)+……+Wn?

B.Mean,VarianceandCovarianceofAssetBasedonHistoricalCorrelation注意1)當(dāng)ρ=+1時，代表正相關(guān)，兩種資產(chǎn)收益率同向變當(dāng)ρ=‐1時，代表負(fù)相關(guān)，兩種資產(chǎn)收益率反向變當(dāng)ρ=0時，代表兩種資產(chǎn)收益率無linear C.CharacteristicsofMajorAsset主要的三類資產(chǎn)：stocksbondsandTreasuryHistoricalmeanreturnandexpectedHistoricalreturn是過去真實賺到的回報，expectedreturn是投資者預(yù)期在將來能賺到的回報，兩者并不一定相等。只能說我們預(yù)expectedreturn會等于averagehistoricalreturn思考：關(guān)于股權(quán)投投資者需風(fēng)險的角C.CharacteristicsofMajorAssetHistoricalmeanreturnandexpectedNominalreturnandriskmajorasset

C.CharacteristicsofMajorAssetHistoricalmeanreturnandexpectedRealreturnandriskmajorasset 2.C.CharacteristicsofMajorAssetHistoricalmeanreturnandexpectedRealreturnandriskmajorassetRisk‐returntrade‐off:positiverelationshipbetweenexpectedandreturn.Higherexpectedreturn,higher

D.RiskRisk假定你有2種選擇你肯定獲得50risk選擇(2),代表risk選擇(1)或(2)都行，覺得兩者無區(qū)別，代表risk選擇(1),代表riskPortfoliomanagementtheory假定投資者都是riskaverseRiskMinimizetheriskforthesameamountofizethereturnforthesameamountof2.D.Risk*IndifferenceIndifferencecurvesareconvexbecauseofdiminishingmarginalutilityofreturn(orwealth)–(why?)

E&F.PortfolioStandardStandardDeviationoftwoAssetsstandarddeviationofaportfolio決定于各種資產(chǎn)的比例，standardCorrelationcoefficient對portfoliostandarddeviation的影Whenρ=1,thereisnodiversificationifcorrelationcoefficientislessthan1(ρ<1),thatcanreducetheportfoliostandarddeviation.Thehighercorrelationbetweentwoassetsreturn,thehigherportfoliostandard 2.E&F.PortfolioStandard*Relationshipbetweenportfolioriskand

2.G.Minimum‐Variance,EfficientFrontiersofRisky*Minimum‐variancefrontier（risk‐returntrade‐offρ= 2.G.Minimum‐Variance,EfficientFrontiersofRisky*Efficientfrontiersofriskyasset,globalminimumvariance

2.G.Minimum‐Variance,EfficientFrontiersofRiskyAsset,GlobalMinimum‐VariancePortfolio*EfficientAportfolioisconsideredtobeefficientifnootherportfoliooffersahigherexpectedreturnwiththesameriskorifnootherportfolioofferslowerriskwiththesamereturn。 隨著risk增加，efficientfrontier的slopecoefficient越來越 2.H.CapitalAllocationLineandOptimal*Capitalallocationline上面所討論的efficientfrontier上的portfolios所包含的都是risky當(dāng)在portfolio中加入 asset時，efficientfrontier就會變成條直線(capitalallocation

H.CapitalAllocationLineandOptimalCapitalallocationtwo‐fundseparationCAL線與efficientfrontier的切點，決定了optimalportfolioofriskyasset,所有投資者不管他們的riskpreference,andinitialwealth是如 asset和optimalportfolioofriskyasset. asset對于所有投資者utility都一樣，因為variance= H.CapitalAllocationLineandOptimal*Optimalinvestor如果再將投資者的riskpreference考慮進來，indifferencecurve與CAL線的切點就得到最適合投資者的optimalinvestorportfolio PortfolioPortfolioManagement:AnPortfolioRiskandReturn:PartPortfolioRiskandReturn:PartBasicsof nning 3.PortfolioRiskandReturn:Part3.A.ImplicationsofCombiningaRisk‐ AssetwithaPortfolioofRiskAssets asset的standarddeviation=0，并且與riskyasset的correlation=0，因此將risk‐ asset與portfolioriskyasset合并組成新的portfolio時，canresultabetterrisk‐returntrade‐off。這種組合就是capitalallocationline(CAL)。當(dāng)其中一種資產(chǎn)是 asset時，上式變成

A.ImplicationsofCombiningaRisk‐ AssetwithaPortfolioofRiskAsset 3.B.CapitalAllocationLineandCapitalMarket由于每個投資者都有不同的expectations(例如不同的expectedreturn，standarddeviationandcorrelation)，從而每個投資者都有不同的optimalriskyassetportfolio和不同的capitalallocationlineCAL)。當(dāng)我們假定所有的投資者都是homogeneityofexpectations時，不同的CAL就變成唯一的capitalmarketline。*CapitalMarketLineE(RmRf叫marketrisk

3.B.CapitalAllocationLineandCapitalMarket*Capitalmarket 3.B.CapitalAllocationLineandCapitalMarketB.CapitalAllocationLineandCapitalMarketMarket asset與portfolioM的組合。因為portfolioM有最高的sharperatio,所以所有的投資者都會投資于這個組合中。這個組合也必然包括了所有的riskyasset，并且是 ydiversified，因而是marketportfolio。LendingandBorrowing 表示 Market Borrowing:表示以國債利率借入錢，然后投資到MarketPortfolio C.SystematicRiskandNonsystematicSystematic也叫nondiversifiablerisk或者marketrisk，反映的是 風(fēng)險，也就是說所有資產(chǎn)都必須承受的風(fēng)險，無法避免。Systematicriskfactors包括interestrates,inflation,economiccycles,politicaluncertaintyandwidespreadnaturaldisasters。Nonsystematic也叫uniquerisk,diversifiablerisk或者firm‐specificrisk，反映的是單獨 diversifiablerisk。Nonsystematicriskfactors包括failureofdrugtrial,majoroildiscoveriesorairlinecrash。Totalrisk=Systematicrisk+Nonsystematic注意Nonsystematicrisk是無需被補償?shù)模驗閚onsystematicrisk可通portfoliodiversification去掉，即zeroreturnfordiversifiableriskSystematicrisk是需要有對應(yīng)的return作為補償?shù)?，接?systematicrisk時就必須要有更高的return作為補償，因為systematicrisk

3.C.SystematicRiskandNonsystematic*RiskVsNumberofportfolio隨著加入portfolio的資產(chǎn)數(shù)量越來越多，unsystematicrisk不斷被分散掉，因此當(dāng)加入的資產(chǎn)數(shù)量到30時，基本上nonsystematicrisk都被分散掉了，剩下的只是systematicrisk。D.Return‐GeneratingReturn‐generatingreturn‐generatingmodelprovidesanestimateoftheexpectedreturnofasecuritygivencertainparameters。常見的return‐generatingmodel是multi‐factormodel。Multi‐factor影響return的因素有多種，例如macroeconomic,fundamentalandstatisticalfactors。Macroeconomicfactor影響return的因素包括economicgrowth,interestinflationrate,productivityemployment,consumerconfidence

D.Return‐GeneratingMulti‐factorFundamentalfactor影響return的因素包括earnings,earningsgrowth,cashflowgenerationsinvestmentresearch,advertisingandnumberofstatisticalfactor通過分析historicalandcross‐sectionaldata來解釋不return之間的相關(guān)性。但有時這種相關(guān)性可能沒有經(jīng)濟意義Marketmodel(Single‐index影響個股return只有一個因素:market E.Betaisameasureofhowsensitiveanasset’sreturnistothemarket,capturesanasset’ssystematicrisk。Positivebetashowsasset’sreturnfollowthemarketNegativebetashowsasset’sreturnisoppositetothemarket asset’sbetaiszero，因為covarianceBeta=1表明資產(chǎn)承受的systematicrisk與marketportfolio一 F.CapitalAssetPricingModelCAPM表明expectedreturn只由一個參數(shù)beta來決定，即systematicrisk決定了expectedreturn。兩種不同性質(zhì)的資產(chǎn)如果有相同的beta時，它們的expectedreturn也都相同。AssumptionsoftheInvestorsarerisk‐aversion, izing,rationalMarketsarefrictionless,includingnotransactioncostsandno nforthesamesingleholdingInvestorshavehomogeneousexpectationsorAllinvestmentsare yInvestorsarepriceF.CapitalAssetPricingModel*SecurityMarketLine(SML):將CAPM圖形化，就得到了

F.CapitalAssetPricingModelCMLVS.CML線反映了totalrisk因為CML是用standarddeviation去衡風(fēng)險的。CML是用于portfoliomanagement決定 SML線反映了systematicrisk。SML是用β衡量單 在Betaofthemarketis1當(dāng)資產(chǎn)的beta大于1，表明其承受的systematicrisk高于marketexpectedreturn(requiredreturn)要高于marketportfolio’sreturn當(dāng)資產(chǎn)的beta小于1時，expectedreturn小于marketreturn 3.F.CapitalAssetPricingModel*理解 1：因為資產(chǎn)分散化是沒有成本的，所以可分散化的風(fēng)險（非系統(tǒng)性的風(fēng)險/公特定的風(fēng)險）Point2：系統(tǒng)性風(fēng)險的大小決定了投資的收益回報，系統(tǒng)性風(fēng)險由資產(chǎn)i和市場組合的相關(guān)系數(shù)決定，反映了資產(chǎn)i的波動與市場波動的Pit 3：現(xiàn)實中PM模型的假設(shè)并不完全成立，分散化是有成本的，并且不是所有的公司特定的風(fēng)險都可以被分散化，所以資產(chǎn)i的風(fēng)險不僅僅由其與市場波動的協(xié)同性所決定；但是，資產(chǎn)的收益與其bta的正相關(guān)性依然有重要的參考價值（why?） 3.G.ExpectedReturnof

3.H.ApplicationofCAPMand 3.H.ApplicationofCAPMand*SecurityB點的預(yù)期收益率高于要求回報率C點的預(yù)期收益率等于要求回報率，因此沒有高估

H.ApplicationofCAPMandEstimateofexpectedPortfolioperformanceSharperatioandTreynorSharpeSharperatio表明承受單位總風(fēng)險(totalrisk)時所取得的超額回報Sharperatio越高越好。TreynorTreynorratio使用的是betariskofportfolio，表明承受單位系統(tǒng)性風(fēng)險(systematicrisk)時取得的超額回報H.ApplicationofCAPMandPortfolioperformanceM‐squaredM2就是thereturnofthemimickingportfolio減去marketreturn，評價的結(jié)果與sharperatio是一致的。如果mimickingportfoliomatchthemarket，M2=0。如果M2>0，表明mimickingportfoliooutperformthemarketM2isbaseontotalrisk。 H.ApplicationofCAPMandPortfolioperformanceJensen’sJensen’salphaisbaseonsystematicrisk。Alpha大于0，表示portfoliooutperformthemarket。

PortfolioPortfolioManagement:AnPortfolioRiskandReturn:PartPortfolioRiskandReturn:PartBasicsof nning Basicsof nningand Statementportfoliomanager為客戶 ’sneed，circumstancesandconstraints，寫一份investment objectivesandconstraints，并以此作為指南為客戶挑選合適的資產(chǎn)進行portfoliomanagement。

MajorComponentsofanIntroduction:describeStatementofStatementofdutiesandProcedurestoupdateInvestmentInvestmentInvestmentguidelines: ,assettypes,EvaluationandAppendices:strategicassetallocationandC.ObjectivesofRis