Consider the following information: Consider the following information: Your por

Question

Consider the following information:

Consider the following information: Your portfolio is invested 25 percent each in A and C. and 50 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. Omit the "%" sign in your response.) What is the variance of this portfolio? (Do not round intermediate calculations. Round your answer to 5 decimal places.) What is the standard deviation? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Explanation / Answer

where return on portfolio=

rp = wara + wbrb + wc rc

ra is the return and wa is the weight on asset A.

rb is the return and wb is the weight on asset B.

rc is the return and wc is the weight on asset C.

AND

the variance of the portfolio is ^ 2 (rp) = w ^2 a ^ 2 (ra) + w ^2 b ^ 2 (rb) + w^ 2 c^ 2 (rc ) + 2wawb cov(ra,rb) + 2wawc cov(ra,rc ) + 2wbwc cov(rb,rc ),

the standard deviation of the portfolio is (rp) = ( 2 (rp).)^(1/2)

Stock A Scenario Probability Return =rate of return * probability Actual return -expected return(A) (A)^2* probability Boom 0.35 21 7.35 11.15 43.512875 Good 0.2 14 2.8 4.15 3.4445 Poor 0.3 2 0.6 -7.85 18.48675 Bust 0.15 -6 -0.9 -15.85 37.683375 Expected return = sum of weighted return = 9.85 Sum= 103.1275 Standard deviation= Standard deviation of stock A =(sum)^(1/2) 10.1551711 Stock B Scenario Probability Return =rate of return * probability Actual return -expected return(B) (B)^2* probability Boom 0.35 42 14.7 29.7 308.7315 Good 0.2 21 4.2 8.7 15.138 Poor 0.3 -9 -2.7 -21.3 136.107 Bust 0.15 -26 -3.9 -38.3 220.0335 Expected return = sum of weighted return = 12.3 Sum= 680.01 Standard deviation= Standard deviation of stock B =(sum)^(1/2) 26.07700136 Stock C Scenario Probability Return =rate of return * probability Actual return -expected return(C) (C)^2* probability Boom 0.35 30 10.5 17.7 109.6515 Good 0.2 12 2.4 -0.3 0.018 Poor 0.3 -5 -1.5 -17.3 89.787 Bust 0.15 -9 -1.35 -21.3 68.0535 Expected return = sum of weighted return = 10.05 Sum= 267.51 Standard deviation= Standard deviation of stock C =(sum)^(1/2) 16.35573294 Covariance: A and B Probability Actual return -expected return(A) Actual return -expected return(B) (A)*(B)*probability Boom 0.35 11.15 29.7 115.90425 Good 0.2 4.15 8.7 7.221 Poor 0.3 -7.85 -21.3 50.1615 Bust 0.15 -15.85 -38.3 91.05825 Covariance=sum= 264.345 CorrelationAB= Covariance/(std devA*std devB)= 1.00 Covariance: A and C Probability Actual return -expected return(A) Actual return -expected return(C) (A)*(C)*probability Boom 0.35 11.15 17.7 69.07425 Good 0.2 4.15 -0.3 -0.249 Poor 0.3 -7.85 -17.3 40.7415 Bust 0.15 -15.85 -21.3 50.64075 Covariance=sum= 160.2075 CorrelationAC= Covariance/(std devA*std devC)= 0.964551871 Covariance: B and C Probability Actual return -expected return(B) Actual return -expected return(C) (A)*(B)*probability Boom 0.35 29.7 17.7 183.9915 Good 0.2 8.7 -0.3 -0.522 Poor 0.3 -21.3 -17.3 110.547 Bust 0.15 -38.3 -21.3 122.3685 Covariance=sum= 416.385 Correlation= Covariance/(std devB*std devC)= 0.976264316 weight in portfolio stock A 0.25 Stock B 0.5 Stock C 0.25 Expected return= 11.125 weight in portfolio stock A 0.25 Stock B 0.5 Stock C 0.25 Variance= 343.0255109 Standard deviation 18.52094789

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