Consider the following information: Your portfolio is invested 20 percent each i

Question

Consider the following information: Your portfolio is invested 20 percent each in A and C, and 60 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return % What is the variance of this portfolio? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.) Variance What is the standard deviation? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Standard deviation %

Explanation / Answer

A. Calculation of Expected Return

Expected return of Stock A = 37%*0.15 + 22%*0.45 - 4%*0.35 – 18%*0.05 = 13.15%

Expected return of Stock B = 47%*0.15 + 18%*0.45 – 7%*0.35 – 22%*0.05 = 11.60%

Expected return of Stock C = 27%*0.15 + 11%*0.45 – 5%*0.35 – 8%*0.05 = 6.85%

Investment in A is 205, B is 60% and C is 20%

Expected return of Portfolio = 13.15%*0.20 + 11.60%*0.60 + 6.85%*0.20 = 10.96%

B. Calculation of Variance

Portfolio variance = w 2 A * 2 (R A ) + w 2 B * 2 (R B ) + 2*(w A )*(w B )*Cov(R A , R B )

+ w 2 C * 2 (R C ) + w 2 B * 2 (R B ) + 2*(w C )*(w B )*Cov(R C , R B )

+ w 2 A * 2 (R A ) + w 2 C * 2 (R C ) + 2*(w A )*(w C )*Cov(R A , R C )

Portfolio variance = 0.2 2 * 272.03 + 0.6 2 * 383.94 + 2*0.2*0.6*(11.85)

+ 0.2 2 * 128.83 + 0.6 2 * 383.94 + 2*0.2*0.6*16.68

+ 0.2 2 * 272.03 + 0.2 2 * 128.83 + 2*0.2*0.2*(5.64)

Portfolio variance = 309.21

Calculation of Cov(R A , R B )

Probablility

Market

Cond

(P)

Boom 0.15 37 47 23.85 35.4 126.64

Good 0.45 22 18 8.85 6.4 25.49

Poor 0.35 (4) (7) (17.15) (18.6) (111.65)

Bust 0.05 (18) (22) (31.15) (33.6) (52.33)

Total (11.85)

Calculation of Cov(R B , R C )

Market

Probablility

Cond

(P)

Boom 0.15 27 47 20.15 35.4 107

Good 0.45 11 18 4.15 6.4 11.95

Poor 0.35 (5) (7) (11.85) (18.6) (77.14)

Bust 0.05 (8) (22) (14.85) (33.6) (24.95)

Total 16.86

Calculation of Cov(R A , R C )

R A R B R A – E(A)

E(A) = 13.15%

R B – E(B)

E(B)=11.6%

P(R A – E(A))

(R B – E(B))

R C R B R C – E(C)

E(C) = 6.85%

R B – E(B)

E(B)=11.6%

P(R C – E(C))

(R B – E(B))

Probablility

Market

(P)

Cond

Boom 0.15 37 27 23.85 20.15 72.09

Good 0.45 22 11 8.85 4.15 16.53

Poor 0.35 (4) (5) (17.15) (11.85) (71.13)

Bust 0.05 (18) (8) (31.15) (14.85) (23.13)

Total (5.64)

Calculation of 2 (R A )

Probablility

Market

Cond

(P)

Boom 0.15 37 85.32

Good 0.45 22 35.25

Poor 0.35 (4) 102.94

Bust 0.05 (18) 48.52

Total 272.03

Calculation of 2 (R B )

Probablility

Market

Cond

(P)

Boom 0.15 47 187.97

Good 0.45 18 18.43

Poor 0.35 (7) 121.09

Bust 0.05 (22) 56.45

Total 383.94

Calculation of 2 (R C )

Probablility

Market

Cond

(P)

Boom 0.15 27 60.9

Good 0.45 11 7.75

Poor 0.35 (5) 49.15

Bust 0.05 (8) 11.03

Total 128.83

B-2. Calculation of Standard Deviation

Standard Deviation = Square root of Variance = Square root of 309.21 = 17.58

R A R C R A – E(A)

E(A) = 13.15%

R B – E(C)

E(C)=6.85%

P(R A – E(A))

(R C – E(C))

R A P(R A – E(A)) 2

E(A) = 13.15%

R B P(R B – E(B)) 2

E(B) = 11.6%

R C P(R C – E(C)) 2

E(C) = 6.85%

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