Consider the following information: Rate of Return If State Occurs State of Prob

Question

Consider the following information: Rate of Return If State Occurs State of Probability of Economy State of Economy Stock A Stock B Stock C Boom 0.17 0.352 0.452 0.332 Good 0.43 0.122 0.102 0.172 Poor 0.33 0.012 0.022 ?0.052 Bust 0.07 ?0.112 ?0.252 ?0.092 Requirement: (A) What is the variance of this portfolio? (Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 5 decimal places. Variance of the portfolio ________ (B) What is the standard deviation of this portfolio? (Do not include the percent sign (%). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places. Standard deviation ______% There are 2 answers to this question (A) and (B)

Explanation / Answer

considering all 3 stocks have equal weights(1/3 each)

then expected return on portfolio E(R) = ((35.2+45.2+33.2)/3)*.17) + ((12.2+10.2+17.2)/3)*.43)+((1.2+2.2+5.2)/3)*.33) + ((11.2+25.2+9.2)/3)*.07 = 14.123333%

hence variance of the portfolio = ((.17*(37.866666-14.123333)^2 + .43*(13.2-14.123333)^2 +.33(2.866666-14.123333)^2 + .07*(15.2-14.123333)^2) = 138.099677%

standard deviation = 11.75%

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