Question

Consider the following information: Rate of Return If State OccursState ofProbability ofEconomyState of EconomyStock AStock BStock C Boom .18 .353 .453 .333 Good .42 .123 .103 .173 Poor .32 .013 .023 −.053 Bust .08 −.113 −.253 −.093 a.Your portfolio is invested 29 percent each in A and C and 42 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)b.What is the variance of this portfolio? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.)c.What is the standard deviation of this portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Expected Return Boom = 0.29(0.353) + 0.42(0.453) + 0.29(0.333)

Expected Return Boom = 0.3892

Expected Return Boom = 38.92%

Expected Return Good= 0.29(0.123) + 0.42(0.103) + 0.29(0.173)

Expected Return Good = 0.1291

Expected Return Good = 12.91%

Expected Return Poor = 0.29(0.013) + 0.42(0.023) + 0.29(-0.053)

Expected Return Poor = - 0.00194

Expected Return Poor = - 0.194%

Expected Return Bust = 0.29(-0.113) + 0.42(-0.253) + 0.29(-0.093)

Expected Return Bust= - 0.166

Expected Return Bust= - 16.6%

a. Expected return portfolio = 0.3892*0.18 + 0.1291*0.42 + 0.32*- 0.00194 + 0.08*- 0.166

Expected return portfolio = 0.1104

Expected return portfolio = 11.04%

b. Variance = 0.18*(0.3892-0.1104)^2 + 0.42*(0.1291-0.1104)^2 + 0.32*(- 0.00194-0.1104)^2 + 0.08*(- 0.166-0.1104)^2

Variance = 0.02429

c. Standard Deviation = (0.02429)^(0.5)

Standard Deviation = 0.1558

Standard Deviation = 15.58%