Question

Consider the following information on Stocks A, B, C and their returns (in decimals) in each state: State Prob. of State A B C Boom 20% 0.26 0.2 0.15 Good 45% 0.15 0.11 0.06 Poor 25% 0.04 0.03 0.02 Bust 10% -0.1 -0.06 -0.02 If your portfolio is invested 25% in A, 40% in B, and 35% in C, what is the standard deviation of the portfolio in percent?

Answer 1

0.25 0.4 0.35 Weight Rate of Return If State Occurs State of Return weight Probability Economy Boom Good Poor Bust Stock A Stock B Stock C 0.21 0.26 0.21 0.15 0.45 0.15 0.11 0.06 0.25 0.04 0.03 0.02 0.11 -0.11 -0.06 -0.02 AB 0.065 0.08 0.0375 0.044 0.01 0.012 -0.025 -0.024 0.0525 0.021 0.007 -0.007 Total*probability Total-Expected return d2*probability Expected Portfolio Deviatio TOTAL Return Deviation n^2 VARIANCE 0.1975 0.0395 0.110225 0.01215 0.00242991 0.1025 0.046125 0.015225 0.000232 0.00010431 0.029 0.00725 -0.058275 0.003396 0.000848994 -0.056 -0.0056 -0.143275 0.020528 0.002052773 0.087275 0.005435987 8.73% Expected return variance standard deviation(variance^(1/2)) 0.087275 0.00544 7.37%! (0.00544)^(1/2)