第三次作业答案 Question 1 a. Expected returns Return on Return on State of the economy Probability ecurity Low Growth 0.4 d ium growth 0.5 28% High Growth 48% E(R)=04×(-29)+0.5×28%+01×48%=18% E(Rn)=04×(-10%)+0.5×40%+01×60%=22 b. variances and stand ard deviations σ2(R)=04×(-2%-18%)2+0.5×(28%-18%)+0.1×(48%-18%)=003 a(Rn)=04×(-10%-22%)+0.5×(40%-22%)+0.1×(60%-229)2=0.0716 (R 0.03=17.32% o(Rn)=√0716=2676% c. Portfolio expected returns and standard deviations Portfolio I=90% invested in security I and 10% in security II Portfolio II=10% invested in security I and 90% in security II Return on Return on State of the Economy Probability portfolio I Portfolio ll Low Growth 0.4 -2.8% 9.2% Med ium growth 0.5 38.8 High growth 0.1 49.2% 58.8 E(Rn)=04×(-28%)+05×292%+01×49.2%=184% E(Rn)=04x(-92%)+0.5×388%+0.×588%=216% o(Rn)=√04×(+-28%-184%0)+05×(292%-1849)+01×(49%-1849)=1825% o(Rn)=√04x(-929%-216%)+05×(388%-216%)+0.1×(588%-21.6%)=2580% ◎徐信忠 MBA公司财务学© 徐信忠 MBA 公司财务学 1 第三次作业答案 Question 1 a. Expected returns State of the Economy Probability Return on Security I Return on Security II Low Growth 0.4 −2% −10% Medium Growth 0.5 28% 40 High Growth 0.1 48% 60 E(RI ) = 0.4(− 2%)+ 0.528% + 0.148% =18% E(RII ) = 0.4(−10%)+ 0.540% + 0.160% = 22% b. Variances and standard deviations ( ) 0.4 ( 2% 18%) 0.5 (28% 18%) 0.1 (48% 18%) 0.03 2 2 2 2  RI =  − − +  − +  − = ( ) 0.4 ( 10% 22%) 0.5 (40% 22%) 0.1 (60% 22%) 0.0716 2 2 2 2  RII =  − − +  − +  − =  (RI ) = 0.03 = 17.32%  (RII ) = 0.0716 = 26.76% c. Portfolio expected returns and standard deviations Portfolio I = 90% invested in security I and 10% in security II Portfolio II = 10% invested in security I and 90% in security II State of the Economy Probability Return on portfolio I Return on Portfolio II Low Growth 0.4 −2.8% −9.2% Medium Growth 0.5 29.2% 38.8 High Growth 0.1 49.2% 58.8 E(RPI ) = 0.4(− 2.8%)+ 0.529.2% + 0.149.2% =18.4% E(RPI ) = 0.4(− 9.2%)+ 0.538.8% + 0.158.8% = 21.6% ( ) 0.4 ( 2.8% 18.4%) 0.5 (29.2% 18.4%) 0.1 (49.2% 18.4%) 18.25% 2 2  RPI =  − − +  − +  − = ( ) 0.4 ( 9.2% 21.6%) 0.5 (38.8% 21.6%) 0.1 (58.8% 21.6%) 25.80% 2 2  RPI =  − − +  − +  − =