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 .64 .10 .18 .36 Bust .36 .10 .04 .07 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 percent rounded to 2 decimal places, e.g., 32.16.) Expected return % b. What is the variance of a portfolio invested 15 percent each in A and B and 70 percent in C? (Do not round intermediate calculations and round your answer to 6 decimal places, e.g., 32.161616.) I need the Variance

Explanation / Answer

Returns State Probability A B C A - Bar B - Bar C - Bar 1 2 3 4 1*2 1*3 1*4 Boom 0.64 0.10 0.18 0.36 0.0640 0.1152 0.2304 Bust 0.36 0.10 0.04 -0.07 0.0360 0.0144 -0.0252 Expected Return 0.1000 0.1296 0.2052 Returns State Probability A B C A - Abar B - Bbar C - Cbar Var A Var B Var C a b c d e = b - 0.10 f = c - 0.1296 g = d - 0.2052 a*e^2 a*f^2 a*g^2 Boom 0.64 0.10 0.18 0.36 0.000 0.0504 0.1548 0.00000000 0.00162570 0.01533635 Bust 0.36 0.10 0.04 -0.07 0.000 -0.0896 -0.2752 0.00000000 0.00289014 0.02726461 Variance 0.00000000 0.00451584 0.04260096 SD = Variance SD - A 0.0000 SD - B 0.0672 SD - C 0.2064 Investment Proportion Expected Return Portfolio Return Variance Proportion Portfolio Variance a b a*b c d d*c A 33% 0.1000 0.0333 0.00000 15% 0.000000 B 33% 0.1296 0.0432 0.00452 15% 0.000677 C 33% 0.2052 0.0684 0.04260 70% 0.029821 0.14493 0.030498 Expected Return = 14.49% Variance = 0.030498 SD = Variance = 0.174637

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