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 0.15 0.40 0.50 0.30 Good 0.60 0.16 0.10 0.09 Poor 0.20 0.02 0.05 0.03 Bust 0.05 0.18 0.25 0.11 a. Your portfolio is invested 25 percent each in A and C, and 50 percent in B. What is the expected return of the portfolio? (Round your answer to 2 decimal places. (e.g., 32.16)) Expected return % b-1 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 b-2 What is the standard deviation? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Standard deviation %

Explanation / Answer

Given table can be interpreted as follows

A) Expected return of stock = Sum of (Probability * Expected Return for that economy)

So Return of A = 0.15 * 0.40 + 0.60 * 0.16 + 0.20 * -0.02 + 0.05 * -0.18 = 0.14

Similarly Expected return on B = 0.11

and Expected return on C = 0.09

Portfolio return = 25% * 0.14 + 50% * 0.11 + 25% * 0.09 = 11.25%

B) For calculating the variance and standard deviation of this portfolio, we should require correlation or covariance between stocks A, B and C

Economy Prob Stock A Stock B Stock C Boom 0.15 0.40 0.50 0.30 Good 0.60 0.16 0.10 0.09 Poor 0.20 -0.02 -0.05 -0.03 Bust 0.05 -0.18 -0.25 -0.11

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