Chapter 11 Homeworks instructions | help Question 3 (of 9) Save & Exit Submit 3.

Question

Chapter 11 Homeworks instructions | help Question 3 (of 9) Save & Exit Submit 3.value: 11.11 points 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 .20 .367 .467 .347 Good .40 .137 .117 .187 Poor .30 .027 .037 .092 Bust .10 .127 .267 .107 Requirement 1: Your portfolio is invested 32 percent each in A and C and 36 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) Expected return of the portfolio 11.83 % Requirement 2: (a) What is the variance of this portfolio? (Do not round intermediate calculations. Round your answer to 5 decimal places (e.g., 32.16161).) Variance of the portfolio (b) What is the standard deviation of this portfolio? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

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 0.20 0.367 0.467 0.347 0.0734 0.0934 0.0694 Good 0.40 0.137 0.117 0.187 0.0548 0.0468 0.0748 Poor 0.30 0.027 0.037 -0.092 0.0081 0.0111 -0.0276 Bust 0.10 -0.127 -0.267 -0.107 -0.0127 -0.0267 -0.0107 Expected Return 0.1236 0.1246 0.1059 Returns State Probability A B C A - Abar B - Bbar C - Cbar Var A Var B Var C a b c d e= b - 0.1236 f = c - 0.1246 g = d - 0.1059 a*e^2 a*f^2 a*g^2 Boom 0.20 0.367 0.467 0.347 0.243 0.3424 0.2411 0.01184871 0.02344755 0.01162584 Good 0.40 0.137 0.117 0.187 0.013 -0.0076 0.0811 0.00007182 0.00002310 0.00263088 Poor 0.30 0.027 0.037 -0.092 -0.097 -0.0876 -0.1979 0.00279947 0.00230213 0.01174932 Bust 0.10 -0.127 -0.267 -0.107 -0.251 -0.3916 -0.2129 0.00628004 0.01533506 0.00453264 Variance 0.02100004 0.04110784 0.03053869 SD = Variance SD - A 0.1449 SD - B 0.2028 SD - C 0.1748 Investment Proportion Expected Return Portfolio Return Variance Proportion Portfolio Variance a b a*b c d d*c A 32% 0.1236 0.039552 0.02100 32% 0.0067200 B 36% 0.1246 0.044856 0.04111 36% 0.0147988 C 32% 0.1059 0.033888 0.03054 32% 0.0097724 0.1183 0.0312912 Expected Return = 11.83% Variance = 0.03129 SD = Variance = 0.176893 = 0.18

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