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 0.15 0.350 0.450 0.330 Good 0.45 0.120 0.100 0.170 Poor 0.35 0.010 0.020 −0.050 Bust 0.05 −0.110 −0.250 −0.090 Your portfolio is invested 30 percent each in A and C and 40 percent in B. What is the expected return of the portfolio?


What is the variance of this portfolio?


What is the standard deviation of this portfolio? Consider the following information:

Explanation / Answer

Expected return in boom is 0.35 * 0.3 + 0.45 * 0.4 + 0.33 * 0.3 = 0.384

Expected return in good is 0.12 * 0.3 + 0.1 * 0.4 + 0.17 * 0.3 = 0.127

Expected return in poor is 0.01 * 0.3 + 0.02 * 0.4 - 0.05 * 0.3 = -0.004

Expected return in Bust = -0.11 * 0.3 - 0.25 * 0.4 - 0.09 * 0.3 = -0.16

Expected return is 0.15 * 0.384 + 0.45 * 0.127 - 0.35 * 0.004 -0.05 * 0.16 = 0.10535

Variance is

( 0.15 * ( 0.384 - 0.10535 )^2 + 0.45 * ( 0.127 - 0.10535 )^2 + 0.35 * ( -0.004 - 0.10535 )^2 + 0.05 * ( -0.15 - 0.10535 )^2 )

= 0.0193030775 =~ 0.0193

Standard deviation is sqrt( variance ) = 0.13893551561785777

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