长期投资决策的风险度及其应用

199922a(,610065),,,,.,.TheRiskDegreeforDecisionMakingofLong2TermInvestmentandItsApplicationXuJiuping(Inst.ofInfo&DecisionMaking,SichuanUnionUniv.,Chengdu610065)AbstractInthispaper,basedonthedescriptionofriskofinvestment,usinginforma2tiontheory,wecandefinetheriskdegreeofinvestmentforthelongrun,anessentialconceptoninvestmentanalysis,andstudyitsproperties.Analyticalmethodsofnetcashvalueareestablishedbythedegreeofriskforthedecisionoflong2terminvest2ment,andanapplicationexampleisdescussed.Keywordslong2terminvestment;riskdegree;methodofnetcashvalue1,.,.,,.,,.,.,.VonNeumannMorgenstern[1]1947(UtilityFunc2tion).1952Markowitz[2](Frontier).1958Tobin[3].E(rp)R2rp,.1959Markowitz[4]Markowitz.,;.,,.1961Cramer[5],(Semiin2a1997825(79670060)©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.terquartilerange).KonnoYamazaki(1991)[6].Markowitz,,,.,1960Stein[7]1968Sclove[8]1988Balakr2ishna[9],1965Massy[10](Pc),1970Marquardt[11](FR),1970HoerlKennard[12,13](Ridge)(GR).1963Sharpe[14]Markowitz(SingleIndexModel).,,B.1972Black,JensenScholes[15](NYSE)19621965B,.Sharpe,B.1987Haugen[16]Markowitz,,(MultipleIndexModel).(),.,,.2.().,.211X=(x1,x2,,xm)Rm,p(xi),p(xi)[0,1],i=1,2,,m,6mi=1p(xi)=1.h(X)C-6mi=1p(xi)lnp(xi)(2.1)X.limp(xi)0p(xi)lnp(xi)=0,,h(X);,h(X).X,h(X),.211h(X)[0,lnm](2.2)Px0,lnxx-1,,ln1möp(xi)1möp(xi)-1-6mi=1p(xi)lnp(xi)-6mi=1p(xi)ln1m=-ln1m=lnm-p(xi)lnp(xi)0,h(x)0212X=(x11,x12,,x1k1,x21,x22,,x2k2,,xn1,xn2,,xnkn),p(xi)xij(j=1,2,,ki),p(yi)=6kii=1p(xij)0,i=1,2,,n,6ni=1p(xij)=1,Xh(X)=-6ni=1p(yi)lnp(yi)-6ni=1p(yi)6kij=1p(xij)p(yi)lnp(xij)p(yi)(2.3)h(X)=h(Y)+6ni=1p(yi)h(Xi)792©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.h(Y)=-6ni=1p(yi)lnp(yi),h(Xi)=-6kij=1p(xij)p(yi)lnp(xij)p(yi)h(X)=-6ni=16kij=1p(xij)ln(xij)=-6ni=16kij=1p(xij)lnp(xij)p(yi)+lnp(yi)=-6ni=16kij=1p(xij)lnp(yi)-6ni=1p(yi)6kij=1p(xij)p(yi)lnp(xij)p(yi)=-6ni=1p(yi)lnp(yi)-6ni=1p(yi)h(Xi)=h(Y)+6ni=1p(yi)h(Xi),,.2131)h(p(x1),p(x2),,p(xm))p(x1),p(x2),,p(xm);2)h(1m,1m,,1m)Cf(m)m,(213),(211),h(p(x1),p(x2),,p(xm))=c6mi=1p(xi)ln1p(xi)(2.4)p(xi)0,6mi=1p(xi)=1,c.(213),xij=1nm,p(yi)=1m,ki=n,i=1,2,,m,f(nm)=f(m)+f(n)(2.5)f(mk)=kf(m)(2.6)m,n1,l,nlmkml+1(2.7),2)f(m),f(nk)f(mk)f(nl+1)(216),lkf(m)f(n)l+1k(2.8)lklnmlnnl+1k(2.9)k,f(m)öf(n)=lnmölnn(2.10)f(m)=clnm(2.11)p(xi),p(xi)=kin,ki0,i=1,2,,m,n=6mi=1ki,6mi=1p(xi)=1,h(p(x1),p(x2),,p(xm))=h1n,,1n,,1n,,1n-6mi=1p(xi)h1ki,,1ki(k1)(km)=f(n)-6mi=1p(xi)f(ki)=clnn-c6mi=1p(xi)lnki=-c6mi=1p(xi)lnp(xi)(2.12)1),(214)p(x1),p(x2),,p(xm).214X=(x1,x2,)p(xi),i=1,2,,6i=1p(xi)=1,8919992©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.1)6i=1p(xi)lni+,h(X)+;2)h(X)+,p(x1)p(x2),6i=1p(xi)lni+.1)m,hm6mi=1p(xi)ln1p(xi)=26mi=1p(xi)lni+6mi=1p(xi)ln1i2p(xi)26mi=1p(xi)lni+6mi=1p(xi)ln6mi=11i26mi=1p(xi)26mi=1p(xi)lni+1e+lnP26h(X)+2)p(x1)p(x2),ip(xi)p(x1)+p(x2)++p(xi)1,i1p(xi),6i=1p(xi)lni6i=1p(xi)ln1p(xi)=h(X)+X=(x1,x2,,xm),p(xi),i=1,2,,m.1)ha(X)C11-aln6mi=1[p(xi)]a(a0,a1)lima1ha(X)=h(X)2)n,0nm,qnC1-6nj=1p(xj)h(X)h(p(x1),p(x2),,p(xm),qn)+qnln(m-n).1),2)h(X)213.3.=6Ti=1Ei(1+r+g)-i(3.1)Eii,r,g.,.(311),g,g.,,.g,,.,,.,g.g,,h.=6Ti=1Ei[1+r+g(h)]-i(3.2)g(h)1)g(h)[0,lnm];2)g(h)[0,lnm],3)h(0)=0.992©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.g,.,.x(i)=(xi1,xi2,,xim)i,x(i)p=(p1,p2,,pm),Iii(i=0,1,2,,T),S=6Ti=0E(x(i))(1+r+gi(h))-i(3.3)I=6Ti=0Ii(1+r)-i(3.4),K=SöI(3.5)K.(313)(315).T=(n1,n2,,nk),p(nj),j=1,2,,k,S=6kj=0p(nj)6nji=0E(x(i))(1+r+gi(h))-i(3.6)I=6kj=0p(nj)6nji=0Ii(1+r)-i(3.7)K=SöI(3.8)(3.6)(3.8).4,1,r=0.06,g(h)=hö101(100)i()01234X(0)Pj0X(1)Pj1X(2)Pj2X(3)Pj3X(4)Pj4xj1-6000165000.540000.430000.625000.7xj232000.345000.520000.410000.3xj3-10000.225000.1I()i600040003000200xj1-110001100000.480000.360000.610000.9xj280000.340000.450000.34000.1xj360000.220000.310000.1xj410000.1I()i11000800030001000xj1-8000160000.380000.4100000.830000.8xj220000.240000.340000.220000.2xj310000.220000.2xj4-10000.210000.1xj5-20000.1I()i8000900050002000EA(X(0))=-6000EA(X(1))=65000.5+32000.3-10000.2=401000119992©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.EA(X(2))=40000.4+45000.5+25000.1=4100EA(X(3))=30000.6+20000.4=2600EA(X(4))=25000.7+10000.3=2050hA(X(1))=-0.5ln0.5-0.3ln0.3-0.2ln0.2=1.03gA(h(X(1)))=0.10hA(X(2))=-0.4ln0.4-0.5ln0.5-0.1ln0.1=0.94gA(h(X(2)))=0.09hA(X(3))=-0.6ln0.6-0.4ln0.4=0.67gA(h(X(3)))=0.07hA(X(4))=-0.7ln0.7-0.3ln0.3=0.61gA(h(X(4)))=0.06S(A)=EA(X(0))+EA(X(1))(1+0.06+gA(h(X(1))))-1+EA(X(2))(1+0.06+gA(h(X(2))))-2+EA(X(3))(1+0.06+gA(h(X(3))))-3+EA(X(4))(1+0.06+gA(h(X(4))))-4=3661.83I(A)=6000+4000(1+0.66)-1+3000(1+0.6)-2+2000(1+0.06)-3=14122.81K(A)=S(A)öI(A)=0.26EB(X(0))=-11000EB(X(1))=100000.4+80000.3+60000.2+10000.1=7700EB(X(2))=80000.3+40000.4+20000.3=4600EB(X(3))=60000.6+50000.3+10000.1=5200EB(X(4))=10000.9+40000.1=940hB(X(1))=-0.4ln0.4-0.3ln0.3-0.2ln0.2-0.1ln0.1=1.28gB(h(X(1)))=0.13hB(X(2))=-0.3ln0.3-0.4ln0.4-0.3ln0.3=1.00gB(h(X(2)))=0.10hB(X(3))=-0.6ln0.6-0.3ln0.3-0.1ln0.1=0.90gB(h(X(3)))=0.09hB(X(4))=-0.9ln0.9-0.1ln0.1=0.33gB(h(X(4)))=0.03S(B)=EB(X(0))+EB(X(1))(1+0.06+gB(h(X(1))))-1+EB(X(2))(1+