Your portfolio is invested 30 percent each in A and C, and 40 percent in B . Wha

Question

  

Your portfolio is invested 30 percent each in A and C, and 40 percent in B . What is the expected return of the portfolio? (Do not round intermediate calculations and round your answer to 2 decimal places. (e.g., 32.16))

  

  

What is the variance of this portfolio? (Do not round intermediate calculations and round your answer to 5 decimal places. (e.g., 32.16161))

  

  

  

Rate of Return if State Occurs   State of Probability of   Economy State of Economy Stock A Stock B Stock C   Boom .20 .24 .45 .33   Good .35 .09 .10 .15   Poor .30 .03 - .10 - .05   Bust .15 - .05 - .25 - .09

Explanation / Answer

a)

expected return of stock = sum of (probability of state * return in state)
expected return of stock A = 0.2 * 0.24 + 0.35 * 0.09 + 0.3 * 0.03 + 0.15 * -0.05 = 0.081

expected return of stock B = 0.2 * 0.45 + 0.35 * 0.1 - 0.3 * 0.1 + 0.15 * -0.25 = 0.0575

expected return of stock C = 0.2 * 0.33 + 0.35 * 0.15 + 0.3 * -0.05 + 0.15 * -0.09 = 0.09

expected return of portifolio = sum of ( weight of investment in stock * return of stock)

= 0.3 * 0.081 + 0.4 * 0.0575 + 0.3 * 0.09

= 0.0743 = 7.43%

b1)

variance = 0.3 * (0.081 - 0.0743)^2 + 0.4 * (0.0575 - 0.0743)^2 + 0.3 * (0.09 - 0.0743)^2

= 0.00020

b2)

standard deviation = sqrt(variance)

= 4.47%

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