第五小組成員：張寶發(fā)段俞西李毅力劉橙劉月張玲劉暢Whyaretypicalinvestorsassumedtopreferportfoliosonindifferencecurveslyingtothenorthwest?為什么典型的投資者被假定認(rèn)為更偏好于“西北”的無(wú)差異曲線上的投資組合？Whyaretheindifferencecurvesofmorerisk-averseinvestorsmoresteeplyslopedthanthoseofinvestorswithlessriskaversion?為什么風(fēng)險(xiǎn)厭惡程度高的投資者的無(wú)差異曲線比風(fēng)險(xiǎn)厭惡程度低的投資者的無(wú)差異曲線傾斜的更陡一些？12.Atthebeginningoftheyear,CornsBradleyownedfoursecuritiesinthefollowingamountsandwiththefollowingcurrentandexpectedend-of-yearprices:securityshareamountcurrentpriceexpectedyear-endpriceA100$50$60B2003540C502550D100100110end-of-periodwealth–beginning-of-periodwealthReturn=-----------------------------------------------------

beginning-of-periodwealth(100*60+200*40+50*50+100*110)-(100*50+200*35+50*25+100*100)rp=-----------------------------------------------------

(100*50+200*35+50*25+100*100)rp=(27500-23250)/23250=4250/23250=18.2795%13.Giventhefollowinginformationaboutfourstockscomprisingaportfolio,calculateeachstock’sexpectedreturn.Then,usingtheseindividualsecurities’expectedreturns,calculatetheportfolio’sexpectedreturn.stockinitialinvesmentvalueexpectedend-of-periodinvestmentvalueproportionofportfolioinitialmarketvalueA$500$70019.20%B2003007.7C100100038.5D960150034.6Ra=(700-500)/500=40%Ra=(300-200)/200=50%Ra=(1000-100)/1000=0Ra=(1500-900)/900=66.7%Rp=40%*19.2%+50%*7.7%+34.6%*66.7%=7.68%+3.85%+23.07%=34.6%=10%*0.1+0*0.25+10%*0.4+20%*0.2+30%*0.05=0.85%14（1）=10.1%(2)=13%*0.5+5%*(-0.5)=17%=0.25*10%*18%=0.004515（1）(2)用雙和法求標(biāo)準(zhǔn)差=15.4%（2）18.GibbyBrockhasestimatedthefollowingjointprobabilitydistributionofreturensForinvestmentsinthestockofLakelandHalfwayHomesandAftonBrewery:LakelandAftonProbability-10%15%0.15100.201050.302000.35OnthebasisofGibby’sestimates,calculatethecovarianceandcorrelationcoefficientbetweenthetwoinvestments.20.Giventhefollowingvarianc-covariancematrixforthreesecurities,aswellasthepercentageoftheportfolioforeachsecurity,calculatetheportfolio’sstandarddeviation.SecurityASecurityBSecurityCSecurityA459SecurityB-211312SecurityC112215179

XA=0.50XB=0.30XC=0.20公式：書上151頁(yè)6.3a和6.4a

21題Theportfolio’sexpectedreturnE(A)=（-10%*0.3）+0*0.2+10*0.3+20*0.2=4%E(B)=10%*0.3+10%*0.2+5%*0.3+（-10%*0.2）=4.5%E(C)=0*0.3+10%*0.2+15%*0.3+5%*0.2=7.5%E(p)=20%*4%+4.5%*50%+7.5%*30%=5.3%Standarddeviation

公式見(jiàn)書上153頁(yè)和154頁(yè)σA=[(-10﹪-4﹪)2×0.3＋﹙0－4％﹚2×0.2+﹙10％-4％﹚2×0.3＋﹙20％-4％﹚2]?=11.136％σB=[﹙10％-4.4％﹚2×0.3+﹙10％－4.5﹚2×0.2＋﹙5％-4.5％﹚2×0.3＋﹙－10％－4.5％﹚2×0.2]?＝7.57％σC＝[﹙0-7.5％﹚2×0,3＋﹙10％-7.5％﹚2×0.2＋﹙15％-7.5％﹚2×0.3＋﹙5％-7.5％﹚2×0.2]?=6.021％σρ﹦[0.22×﹙11.136％﹚2＋0.52×﹙7.57％﹚2＋0.32﹙6.021％﹚2]?=4.749％公式見(jiàn)書上153頁(yè)和154頁(yè)24題σa=[0.5×0.5×30％×30％＋0.5×0.5×40％×40％＋2×0.5×0.5×40％×30％×0.9]?＝34.1％σb﹦[0.5×0.5×30％×30％＋0.5×0.5×40％×40％]?＝25％σc＝[0.5×0.5×30％×30％＋0.5×0.5×40％×40％＋2×0.5×0.5×40％×30％×﹙－0.9﹚]?＝9.2％a.=20%x20%x1x12%x12%+20%x80%x0.2x10%x12%+80%x20%x0.2x10%x12%+80%x80%x1x10%x10%=0.007744=8.8%b.=40%x40%x1x12%x12%+40%x20%x(-1)x12%x15%+40%x40%x0.2x12%x10%+20%x40%x(-1)x12%x15%+20%x20%x1x15%x15%+20%x40%x(-0.2)x15%x10%+40%x40%x0.2x15%x10%+20%x40%x15%x10%+40%x40%xx40%x10%=0.002308=4.8%

25c.Assumethatdenotestheproportionoftheportfolio’sinitialinvestedinsecurityA,and1-denotestheproportionoftheportfolio’sinitialinvestedinsecurityB.SOx12%x12%+(1-)x(-1)x12%x15%+()()x1x15%x15%=0=0.556,==0.44426.r=-40%x0.03-10%x0.07+0x0.3+15%x0.1+30%x0.05+40%x0.2+50%x0.25=21.6%Themedianisthemiddleoutcomeofthedistributionwhenthepossiblevaluesoftherandomvariablearearrangedaccordingtosize.Themodeisthemostlikelyvalue.27(p151.6.3a)=1.9×0.05+1.95×0.15+2×0.3+2.05×0.3+2.1×0.15+2.15×0.05=2.025(P165)=[(1.9-2.025)2×0.05+(1.95-2.025)2×0.15+(2-2.025)2×0.3+(2.05-2.025)2×0.3+(2.1-2.025)2×0.15+(2.15-2.025)2×0.05]