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 .15 .30 .40 .31 Good .55 .17 .11 .10 Poor .25 .03 .06 .04 Bust .05 .10 .26 .07 a. Your portfolio is invested 26 percent each in A and C, and 48 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculaitons. Enter your answer as a percent rounded 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. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Standard deviation %

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 0.15 0.30 0.40 0.31 0.0450 0.0600 0.0465 Good 0.55 0.17 0.11 0.10 0.0935 0.0605 0.0550 Poor 0.25 -0.03 -0.06 -0.04 -0.0075 -0.0150 -0.0100 Bust 0.05 -0.10 -0.26 -0.07 -0.0050 -0.0130 -0.0035 Expected Return 0.1260 0.0925 0.0880 Returns State Probability A B C A - Abar B - Bbar C - Cbar Var A Var B Var C a b c d e= b - 0.1260 f = c - 0.0925 g = d - 0.0880 a*e^2 a*f^2 a*g^2 Boom 0.15 0.30 0.40 0.31 0.174 0.3075 0.2220 0.00454140 0.01418344 0.00739260 Good 0.55 0.17 0.11 0.10 0.044 0.0175 0.0120 0.00106480 0.00016844 0.00007920 Poor 0.25 -0.03 -0.06 -0.04 -0.156 -0.1525 -0.1280 0.00608400 0.00581406 0.00409600 Bust 0.05 -0.10 -0.26 -0.07 -0.226 -0.3525 -0.1580 0.00255380 0.00621281 0.00124820 Variance 0.01424400 0.02637875 0.01281600 SD = Variance SD - A 0.1193 SD - B 0.1624 SD - C 0.1132 Investment Proportion Expected Return Portfolio Return Variance Proportion Portfolio Variance a b a*b c d d*c A 26% 0.1260 0.03276 0.01424 26% 0.0037034 B 48% 0.0925 0.0444 0.02638 48% 0.0126618 C 26% 0.0880 0.02288 0.01282 26% 0.0033322 0.1000 0.0196974 Expected Return (Portfoilio) = 10% Variance = 0.01970 SD = Variance = 0.140347 = 14.03%

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