Consider the following information: Rate of Return If State Occurs. Probability

Question

Consider the following information: Rate of Return If State Occurs. Probability of state of economy, Boom=.64, Bust= .36 Stock A, Boom=.11 Bust=.18 Stock B, Boom=.20 Bust= .10 Stock C, Boom=.38, Bust=-.04 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 17.58 % B. What is the variance of a portfolio invested 20 percent each in A and B and 60 percent in C? (Do not round intermediate calculations and round your answer to 6 decimal places, e.g., 32.161616.) A is correct I am just not sure how to find the variance in part B.

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 0.11 0.20 0.38 0.0704 0.1280 0.2432 Bust 0.36 0.18 0.10 -0.04 0.0648 0.0360 -0.0144 Expected Return 0.1352 0.1640 0.2288 Returns State Probability A B C A - Abar B - Bbar C - Cbar Var A Var B Var C a b c d e= b - 0.1352 f = c - 0.1640 g = d - 0.2288 a*e^2 a*f^2 a*g^2 Boom 0.64 0.11 0.20 0.38 -0.025 0.0360 0.1512 0.00040643 0.00082944 0.01463132 Bust 0.36 0.18 0.10 -0.04 0.045 -0.0640 -0.2688 0.00072253 0.00147456 0.02601124 Variance 0.00112896 0.00230400 0.04064256 SD = Variance SD - A 0.0336 SD - B 0.0480 SD - C 0.2016 Investment Proportion Expected Return Portfolio Return Variance Proportion Portfolio Variance a b a*b c d d*c A 33% 0.1352 0.045067 0.00113 20% 0.0002258 B 33% 0.1640 0.054667 0.00230 20% 0.0004608 C 33% 0.2288 0.076267 0.04064 60% 0.0243855 0.1760 0.0250721 Expected Return = 17.60% Variance = 0.0250721 SD = Variance = 0.158342

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