Consider the following information: Rate of Return if State Occurs State of Econ

Question

Consider the following information: Rate of Return if State Occurs State of Economy Boom Bust Probability of State of Economy 0.65 0.35 Stock A 0.11 0.12 Stock B 0.19 0.06 Stock C 0.37 0.05 a. What is the expected return on an equally weighted portfolio of these three stocks? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Expected return 16.03 % b. What is the variance of a portfolio invested 16 percent each in A and B and 68 percent in C? (Do not round intermediate calculations and round your answer to 6 decimal places. (e.g., 32.161616)) Variance

Explanation / Answer

a.

We can compute expected return of portfolio in each economic state by adding return of each assets and dividing by three.

Expected return of portfolio in Boom economic state:

RP = (0.11 + 0.19 + 0.37) /3 = 0.67/3 = 0.2233 or 22.33 %

Expected return of portfolio in Bust economic state:

RP = (0.12 + 0.06 - 0.05) /3 = 0.13/3 = 0.0433 or 4.33 %

To get expected return of portfolio we can multiply return in each state of economy with respective probability and then adding both the results.

Expected return of portfolio:

E (RP) = (0.65 x 0.2233) + (0.35 x 0.0433) = 0.145167 + 0.015167 = 0.160333 or 16.03 %

b.

Return of portfolio with unequal weighted assets for each economic state can be computed as:

Boom RP = (0.16 x 0.11) + (0.16 x 0.19) + (0.68 x 0.37) = 0.0176 + 0.0304 + 0.2516 = 0.2996 or 29.96 %

Bust RP = (0.16 x 0.12) + (0.16 x 0.06) + [0.68 x (-0.05)] = 0.0192 + 0.0096 - 0.034 = -0.0052 or – 0.52 %

Expected return of portfolio:

E(RP) = (0.65 x 0.2996) + (0.35 x - 0.0052) = 0.19474 - 0.00182 = 0.19292 or 19.29 %

Variance of portfolio is sum of Multiplication between Probability and squared deviation.

Variance, ? p2 = 0.65 x (0.2996 - 0.1929)2 + 0.35 x (-0.52 – 0.1929)2

                           = 0.65 x (0.10668)2 + 0.35 x (- 0.19812) 2

                           = 0.65 x 0.011381 + 0.35 x 0.039252

                           = 0.007397 + 0.013738 = 0.021135

Variance of portfolio is 0.021135

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