Consider the following information: Your portfolio is invested 25 percent each i

Question

Consider the following information:

Your portfolio is invested 25 percent each in A and C, and 50 percent in B. What is the expected return of the portfolio? (Round your answer 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 and round your final answer to 2 decimal places. (e.g., 32.16))

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Rate of Return if State Occurs   State of Probability of   Economy State of Economy Stock A Stock B Stock C   Boom 0.10 0.34 0.44 0.24   Good 0.60 0.19 0.15 0.08   Poor 0.25 ? 0.01 ? 0.09 ? 0.07   Bust 0.05 ? 0.15 ? 0.19 ? 0.11

Explanation / Answer

expected return of the portfolio(r) = .1*.365 + .6*0.1425 + .25*0.065 + .05*(-0.16) = 13.03%

variance = 0.005510756 + 0.000090038 + 0.001064391 + 0.004212253 = 1.08774%

standard deviation = (1.08774%)^.5 = 10.43%

Returns State of Economy Probability(pi) Stock A Stock B Stock C Portfolio Return(R) (R-r)2 pi*(R-r)2 Boom 0.1 0.34 0.44 0.24 0.365 0.055107563 0.005510756 Good 0.6 0.19 0.15 0.08 0.1425 0.000150063    0.000090038 Poor 0.25 0.01 0.09 0.07 0.065 0.004257563 0.001064391 Bust 0.05 -0.15 -0.19 -0.11 -0.16 0.084245063 0.004212253

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