Consider the following information: a. Your portfolio is invested 24 percent eac

Question

Consider the following information: a. Your portfolio is invested 24 percent each in A and C, and 52 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, e.g., 32.16.) 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 .) b-2 What is the standard deviation? (Do not round Intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g.. 32.16.)

Explanation / Answer

Rate of Return if State Occurs State of Economy Probability of State of Economy Stock A Stock B Stock C Expected Return on Stock A Expected Return on Stock B Expected Return on Stock C Boom 0.15 0.38 0.48 0.28 0.06 0.07 0.04 Good 0.45 0.22 0.19 0.15 0.10 0.09 0.07 Poor 0.30 -0.04 -0.09 -0.06 -0.01 -0.03 -0.02 Bust 0.10 -0.16 -0.34 -0.11 -0.02 -0.03 -0.01 Total 1.00 0.13 0.10 0.08 Expected Return of the Portfolio is = 0.24*0.13 + 0.52*0.10 + 0.24*0.08 0.10 or 10% Stock A Stock B Stock C Deviation from Expected Value Squared Probability of State of Economy Variance Deviation from Expected Value Squared Probability of State of Economy Variance Deviation from Expected Value Squared Probability of State of Economy Variance 0.25 0.06 0.15 0.01 0.38 0.15 0.15 0.02 0.20 0.04 0.15 0.01 0.09 0.01 0.45 0.00 0.09 0.01 0.45 0.00 0.07 0.00 0.45 0.00 -0.17 0.03 0.30 0.01 -0.19 0.03 0.30 0.01 -0.14 0.02 0.30 0.01 -0.29 0.08 0.10 0.01 -0.44 0.19 0.10 0.02 -0.19 0.04 0.10 0.00 1.00 0.03 1.00 0.06 1.00 0.02 Covriance of Stock A & Stock B Covriance of Stock B & Stock C Covriance of Stock A & Stock C Product of Deviation from Expected Value of Stock A & Stock B Probability of State of Economy Covariance Product of Deviation from Expected Value of Stock B & Stock C Probability of State of Economy Covariance Product of Deviation from Expected Value of Stock A & Stock C Probability of State of Economy Covariance 0.10 0.15 0.01 0.08 0.15 0.01 0.05 0.15 0.01 0.01 0.45 0.00 0.01 0.45 0.00 0.01 0.45 0.00 0.03 0.30 0.01 0.03 0.30 0.01 0.02 0.30 0.01 0.13 0.10 0.01 0.08 0.10 0.01 0.05 0.10 0.01 1.00 0.04 1.00 0.03 1.00 0.02 Variance of the portfolio is w1^2*Var(s1) + w2^2*Var(s2)+ w3^2*Var(s3) + 2*w1*w2*Cov(s1, s2) + 2*w3*w2*Cov(s3, s2) + 2*w1*w3*Cov(s1, s3) = 0.04 Standard Deviation of the Portfolio is square root of variance of the portfolio 0.20

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