Question

10. Returns and Standard Deviations Consider the following information: Rate of Return if State Occurs Probability of State of Economy State of Economy Stock A Stock B Stock C Boom 1 Good .11 .02 .45 .10 .02 -.25 .33 .17 -05 -.09 Poor Bust a. Your portfolio is invested 25 percent each in A and C and 50 percent in B. What is the expected return of the portfolio? b. What is the variance of this portfolio? The standard deviation?

Answer 1

0.25 0.5 0.25 Weight Rate of Return If State Occurs State of Return weight Probability Economy Boom Good Poor Bust Stock A 0.15 0.33 0.55 0.11 0.21 0.02 0.1 -0.12 Stock B 0.45 0.1 0.02 -0.25 Stock C 0.33 0.17 -0.05 -0.09 A 0.0825 0.0275 0.005 -0.03 0.225 0.05 0.01 -0.125 0.0825 0.0425 -0.0125 -0.0225 Total*probability Total-Expected return d2*probability Expected Portfolio Deviatio TOTAL Return Deviation n^2 VARIANCE 0.39 0.0585) 0.28275 0.079948 0.011992134 0.12 0.066 0.01275 0.000163 8.94094E-05 0.0025 0.0005 -0.10475 0.010973 0.002194513 -0.1775 -0.01775 -0.28475 0.081083 0.008108256 0.10725 0.022384313 10.73% Expected return variance 0.10725 0.02238 14.96%! standard deviation(variance^(1/2)) 0.02238^(1/2)