Question

State of Economy Probability of State of Economy                                      Stock A Stock B Stock C

Boom                            .20                                                                                     38   .48        .28                                                                       

Good                            .50                                                                                     .14    .19        .12

Poor                              .20                                                                                    −.05 −.08     −.06

Bust                             .10                                                                                    −.19 −.23     −.09

Portfolio is invested 22 % each in A AND C and 56% in B.

What is expected return and variance of portfolio?

Answer 1

E(r) = [Pi x Ri]

E(rA) = [0.20 x 0.38] + [0.50 x 0.14] + [0.20 x -0.05] + [0.10 x -0.19]

= 0.076 + 0.07 - 0.01 - 0.019 = 0.117

E(rB) = [0.20 x 0.48] + [0.50 x 0.19] + [0.20 x -0.08] + [0.10 x -0.23]

= 0.096 + 0.095 - 0.016 - 0.023 = 0.152

E(rC) = [0.20 x 0.28] + [0.50 x 0.12] + [0.20 x -0.06] + [0.10 x -0.09]

= 0.056 + 0.06 - 0.012 - 0.009 = 0.095

E(rP) = [0.22 x 0.117] + [0.56 x 0.152] + [0.22 x 0.095] = 0.02574 + 0.08512 + 0.0209 = 0.13176

² = [{Pi x (E(r) - Ri)²}]

= [0.22 x (0.13176 - 0.117)²] + [0.56 x (0.13176 - 0.152)²] + [0.22 x (0.13176 - 0.095)²]

= 0.000047929 + 0.000229408 + 0.000297285 = 0.000574622