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 State Economy of Economy Stock A Stock B Stock C Boom 66 .09 .03 .24 Bust 34 .13 .19 Required: (a) What is the expected return on an equally weighted portfolio of these three stocks? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) Expected return (b)What is the variance of a portfolio invested 21 percent each in A and Band 58 percent in C? (Do not round intermediate calculations. Round your answer to 5 decimal places (e.g., 32.16161).) Variance of a portfolio

Explanation / Answer

a.

Probability

Stock A

Stock B

Stock C

Average Return

Boom

0.66

0.09

0.03

0.24

0.12

Bust

0.34

0.13

0.19

-0.04

0.093333333

Expected Return = Probability (Boom)*Average Return1+ Probability (Bust)*Average Return1

                                =.66*.12+0.34*.0933 =0.110922

b.

Probability

Stock A

Stock B

Stock C

Return=weightA*ReturnA+weightB*ReturnB+weightc*ReturnC

weight

21%

21%

58%

Boom

0.66

0.09

0.03

0.24

0.1644

Bust

0.34

0.13

0.19

-0.04

0.044

Expected return = 0.16644*0.66+0.044*0.34 = 0.12481

Variance = 0.66*(0.1644-0.12481)^2+0.34*(0.044-0.12481)^2

Variance =0.00325475

Probability

Stock A

Stock B

Stock C

Average Return

Boom

0.66

0.09

0.03

0.24

0.12

Bust

0.34

0.13

0.19

-0.04

0.093333333

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