第四講資產(chǎn)組合理論(投資學(xué)-廈門大學(xué)金融系,陳善昂)

1、W = 100W1 = 150 Profit = 50W2 = 80 Profit = -20p = .61-p = .4E(W) = pW1 + (1-p)W2 = 6 (150) + .4(80) = 122s2 = pW1 - E(W)2 + (1-p) W2 - E(W)2 =.6 (150-122)2 + .4(80-122)2 = 1,176,000s = 34.293W1 = 150 Profit = 50W2 = 80 Profit = -20p = .61-p = .4100Risky Inv.Risk Free T-billsProfit = 5Risk Premium =

2、 17=ssrsPrE)()()( )()()(22=srEsrsPsssriskyassetriskyassetpw=rf = 7%s srf = 0%E(rp) = 15%s sp = 22%y = % in p(1-y) = % in rfE(rc) = yE(rp) + (1 - y)rfrc = complete or combined portfolioFor example, y = .75E(rc) = .75(.15) + .25(.07)= .13 or 13%E(r)E(rp) = 15%rf =7%22%0PFs ss scE(rc) = 13%Cpc=由于由于rfy=

3、 0, 因此，因此，依規(guī)則依規(guī)則4s ss ss sc= .75(.22) = .165 或或16.5%若若 y = .75, 則則c= 1(.22) = .22 或或 22%若若 y = 1c= (.22) = .00 or 0%若若y = 0s ss ss sE(r)E(rp) = 15%rf = 7% s sp = 22%0PF ) S = 8/22E(rp) - rf = 8%s sE(r)s s9%7%) S = .36) S = .27Ps sp = 22%E(r)s s7%PLenderBorrowers sp = 22% The lender has a larger A wh

4、en compared to the borrowerNumber of SecuritiesSt. DeviationMarket RiskUnique Riskrp = W1r1 + W2r2W1 = 組合中證券組合中證券1的比例的比例W2 = 組合中證券組合中證券2的比例的比例r1 = 證券證券1的期望收益的期望收益r2 = 證券證券2的期望收益的期望收益1=n1iiws sp2 = w12s s12 + w22s s22 + 2W1W2 Cov(r1r2)s s12 = 證券證券1的方差的方差s s22 = 證券證券2的方差的方差Cov(r1r2) = 兩證券收益率的協(xié)方差兩證券收益率

5、的協(xié)方差 1,2 = 兩證券的相關(guān)系數(shù)兩證券的相關(guān)系數(shù)Cov(r1r2) = 1,2s s1s s2s s1 ，s s2 為兩證券的標準差為兩證券的標準差相關(guān)系數(shù)相關(guān)系數(shù) 1,2的取值的取值+ 1.0 -1.0 = 1.0時時,兩證券完全正相關(guān)兩證券完全正相關(guān) = -1.0時時,兩證券完全負相關(guān)兩證券完全負相關(guān)E(rp) = W1r1 + W2r2s sp2 = w12s s12 + w22s s22 + 2W1W2 Cov(r1r2)s sp = w12s s12 + w22s s22 + 2W1W2 Cov(r1r2)1/2s s2p = W12s s12+ W22s s12+ 2W1W2

6、rp = W1r1 + W2r2 + W3r3 Cov(r1r2)+ W32s s32 Cov(r1r3)+ 2W1W3 Cov(r2r3)+ 2W2W3rp = Weighted average of the n securitiess sp2 = (Consider all pairwise covariance measures) = 113%8E(r)St. Dev12%20% = .3 = -1 = -1112 22 - Cov(r1r2)W1=+ - 2Cov(r1r2)W2= (1 - W1)s s22E(r2) = .14= .20Sec 212= .2E(r1) = .10=

7、 .15Sec 1s ss s s s 2W1=(.2)2 - (.2)(.15)(.2)(.15)2 + (.2)2 - 2(.2)(.15)(.2)W1= .6733W2= (1 - .6733) = .3267rp = .6733(.10) + .3267(.14) = .1131p= (.6733)2(.15)2 + (.3267)2(.2)2 +2(.6733)(.3267)(.2)(.15)(.2)1/2p= .01711/2= .1308s ss sW1=(.2)2 - (.2)(.15)(.2)(.15)2 + (.2)2 - 2(.2)(.15)(-.3)W1= .6087W

8、2= (1 - .6087) = .3913rp = .6087(.10) + .3913(.14) = .1157p= (.6087)2(.15)2 + (.3913)2(.2)2 +2(.6087)(.3913)(.2)(.15)(-.3)1/2p= .01021/2= .1009s ss sE(r)EfficientfrontierGlobalminimumvarianceportfolioMinimumvariancefrontierIndividualassetsSt. Dev.ME(r)CAL (Globalminimum variance)CAL (A)CAL (P)PAFPP&FA&