证券投资风险及风险度量方法

()112AH190134198351,,,1987.2,,,1985.(1).3,,,1987.4,,,1987.15,,,,1994.23XXX2X,{0;∈=−xXxX}{}0;∈=+xXxX−X+X−XρX,{}nmlll=mβββ,,,21Lnlll,,,21Lnααα,,,21Lρ),,,,,(11nnllααρρLL=1()xf()()dxxfxX∫−=,ρρ2ϕ(mmww)ββϕϕ,,,,,11LL=3()()dxxfxX∫+=,ϕϕ42ρρ()dxxfxX))((21∫−=ρρρ()dxxfxX)(1∫−=ρρ()dxxfxXθ∫−=0θx()xfx)(1xρ0θθxFishburnθ=2Markowitzθ=1DomarMusgrave(1944)θθ1θ1θ=031X()22XXΕ−Ε=σMarkovizΕ6Markoviz7Markoviz8()()Ε−Ε=,0,2XXShhXhX≤Porter(1974)Fishburn(1977)h()XΕ2GINIGiniYitzhaki1982Gini9XGINIG()XF()X()()()XFXXG,cov2=YitzhakiGini6H.Markowitz,“PortfolioSelection”,JournalofFinance,(1952)78H.Markowitz,PortfolioSelection,JohnWiley&Sons,NewYork49S.Yitzhaki,”StochasticDominance,MeanVarianceandGini’sMeanDifference”(1982,72)Gini3VARVARValueatRiskVARVARW0R()RWW+=10Rσµc()*0*1W+=RW*RVARVAR=()()µ−−=−Ε*0*R=W*0*0RWW−=−VARW()wfcW*()∫+∞=*WdwwfcVARVARVARVARVARVARVAR2RothschildStiglitz1WW12ΕΕ{()}{()}UWUW12≥102WW12ΕΕ()()WW12=WW1W123WW12εε+=12WW0)1=ΕWε510,,,,,P240,1992WW12()[−∞XG∫∫∞−Xv115FGUFSD0′UFG()()XGXF≤XSSD0,0′′′UUFGX()]0≥∫−dttFtTSD0,0,0′′′′′′UUUFG()()[]0≥−−∞dtdvtFtG()()XXGFΕ≥ΕX12Karamata196913FSD11KrollLevyIncreasingRiskandDecreasingRiskAversion”workingpaper,HebrewUni(1988)12HadarandRussell(1969);RothschildandStiglitz(1970).613HadarandRusell(1969);HanochandLevy(1969);RothschildandStiglitz(1970);Whitmore(1970).HalmLevy,StochasticDominanceandExpectedUtilitySurveyandAnalysisManagementScience1992,Vol.38,No.4Philippe.JorionValue-at-RiskTheNewBenchmarkforControllingDerivativesRiskOkuney.JAComparativeStudyoftheGini’sMeanDifferenceandMean-VarianceinPortfolioAnalysis”,AccountingandFinance28,1988.Markowitz,H.MPortfolioSelectionJournalofFinance7,1952HaimShalitandShlomoYitzhaki,Mean-Gini,PortfolioTheory,andthePricingofRiskyAssets,TheJournalofFinance,5,1984.OKUNEY.JAComparativeStudyoftheGini’sMeanDifferenceandMean-VarianceinPortfolioAnalysis”AccountingandFinance28198820008200147