Question

Consider the following probability distribution for stocks A and B: State Probability Return on Stock A Return on Stock B 0.20 5.0% 8.0% 0.15 7.0% 5.0% 0.40 -8.0% 9.0% 0.10 6.0% -15.0% 0.15 9.0% 6.0%

A) What is the variance of each stock?

B) What is the coefficient of correlation between stock A and B?

C) If you invest 80% of your money in A and 20% in B, what would be your portfolio's expected rate of return and standard deviation?

Answer 1

Мб A B C D E F H I J K L M N O P Q R S 3 A) Stock A a b c d =cbe =c-0.8% State Return(A) - ER(A) ER(A)=Return Probability Return(A) *Probability 0.20 5.00 1.00 0.15 7.00 1.05 0.40 -8.00 -3.20 6.00 0.60 0.15 9.00 1.35 0.80 4.20 6.20 -8.80 5.20 8.20 freeg=bef Square of [Return(A)- Prob Square ER(A)] 17.64 3.53 38.44 5.77 77.44 30.98 27.04 2.70 67.24 10.09 53.06 0.10 Variance of Stock A = 53.06% Stock B 16 17 d=cb e = -5.35% State Probability Return(B) ER(B)=Return *Probability Return(B) - ER(B) 1 0.20 0.15 0.40 0.10 0.15 8.00 5.00 9.00 -15.00 6.00 1.60 0.75 3.60 -1.50 0.90 5.35 2.65 -0.35 3.65 -20.35 0.65 frete R=b Square of [Return(B)- Prob Square ER(B)] 7.02 1.40 0.12 0.02 13.32 5.33 414.12 41.41 0.42 0.06 18 23 ... Sheet16 Sheet17 Sheet18 Sheet19 Sheet20 Sheet22 Sheet24 Sheet23 Sheet21 Sheet25 Sheet28 10:59 PM D 4X ENG 7/21/2019

- IX R33 A 27 28 D E F H I J K L M N O P B C Variance of Stock A = 48.23% Q R S B) Coefficient of Correlation = Covariance of A&B / SD(A) SD(B) SD (A) = Covariance (1/2) SD (A) = (53.06)^(1/2) 7.28% SD (B) = Covariance (1/2) SD (B) = (48.23)^(1/2) 6.94% beef State Return(B) COV(AB) Probability Return(A) 0.20 5.00 0.15 7.00 0.40 -8.00 6.00 0.15 9.00 8.00 5.00 9.00 - 15.00 6.00 Return(A). ER(A) 4.20 6.20 -8.80 5.20 8.20 15.00 Return(B) - ER(B) 2.65 -0.35 3.65 -20.35 0.65 -13.75 2.23 -0.33 -12.85 - 10.58 0.80 0.10 COV(AB) = -20.73 Coefficient of Correlation=-20.73/ 7.28 * 6.93 Coefficient of Correlation = -0.41 54 C) Portfolio Return 55 0 30 ... Sheet16 Sheet17 Sheet18 Sheet19 Sheet20 Sheet22 Sheet24 Sheet23 Sheet21 Sheet25 Sheet28 10:59 PM A D 4X ENG 7/21/2019

... EX R51 H I J K L M N O P Q R S 51 52 Coefficient of Correlation=-20.73/ 7.28 6.93 Coefficient of Correlation = -0.41 53 54 C) Portfolio Return 0.2 0.8%+0.8+5.35% 1.71% Standard Deviation SD * SD Sum Weight Weight 0.8*0.8 0.2 0.2 7.28*7.28 6.93 6.93 33.92 1.92 -0.41)]^(1/2) [33.9241.92+2+0.8*0.2*7.28 6.93 5.41% Sheet16 Sheet17 Sheet20 Sheet22 Sheet24 Sheet23 Sheet21 Sheet25 Sheet28 ... Ei Sheet18 0 Sheet19 9 R 11:00 PM AD6 4x ENG 7/21/2019 13