Consider the following information: Rate of Return If State Occurs State of Prob

Question

Consider the following information: Rate of Return If State Occurs State of Probability of Economy State of Economy Stock A Stock B Stock C Boom .20 .31 .41 .32 Good .50 .18 .12 .11 Poor .25 .04 .07 .05 Bust .05 .15 .27 .08 a.

Your portfolio is invested 28 percent each in A and C, and 44 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculaitons. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return

b-1 What is the variance of this portfolio? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.) Variance=

b-2 What is the standard deviation? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Standard deviation=

Explanation / Answer

Part a)

The expected return on the portfolio can be calculated as follows:

Expected Return of Portfolio = Probability of Boom*Expected Retun under Boom + Probability of Good*Expected Return under Good + Probability of Poor*Expected Return under Poor + Probability of Bust*Expected Return under Bust

Expected Return under Boom = Investment Percentage in Stock A*Return of Stock A under Boom + Investment Percentage in Stock B*Return of Stock B under Boom + Investment Percentage in Stock C*Return of Stock C under Boom

Similarly, we can derive formulas for Expected Return under Good, Poor and Bust

________

Using the values provided in the question, we get,

Expected Return under Boom = 28%*.31 + 44%*.41 + 28%*.32 = 35.68%

Expected Return under Good = 28%*.18 + 44%*.12 + 28%*.11 = 13.40%

Expected Return under Poor = 28%*(-.04) + 44%*(-.07) + 28%*(-.05) = -.5.60%

Expected Return under Bust = = 28%*(-.15) + 44%*(-.27) + 28%*(-.08) = -18.32%

Expected Return of Portfolio = .20*35.68% + .50*13.40% + .25*(-5.60%) + .05*(-18.32%) = 11.52%

____________

Part b-1)

The variance of the portfolio is calculated with the use of following formula:

Variance = Probability of Boom*(Expected Return under Boom - Expected Return of the Portfolio)^2 + Probability of Good*(Expected Return under Good - Expected Return of the Portfolio)^2 +Probability of Poor*(Expected Return under Poor - Expected Return of the Portfolio)^2 + Probability of Bust*(Expected Return under Bust - Expected Return of the Portfolio)^2

Using the values calculated in Part a), we get

Variance = .20*(35.68% - 11.52%)^2 + .50*(13.40% - 11.52%)^2 + .25*(-5.60% - 11.52%)^2 + .05*(-18.32% - 11.52%)^2 = .02363

____________

Part b-2)

The standard deviation can be calculated as follows:

Standard Deviation = (Variance)^(1/2) = (.02363)^(1/2) = 15.37%

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