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# Given the following information, what is the standard deviation of the returns on a portfolio that is invested 40 percent in Stock A, 35 percent in Stock B, and the remainder in Stock C?

Asked 10 months ago
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1
Rate of Return is State Occurs

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

Normal .65 14.3% 16.7% 18.2%
Recession .35 -9.8% 5.4% -26.9%

a. 12.72 percent
b. 14.07 percent
c. 1.41 percent
d. 7.41 percent
e. 11.86 percent

2

e. 11.86 percent

Explanation:

Expected return = Portfolio Invested * Return of stock

Expected return for Normal = [(40%*14.3%) + (35%*16.7%) + (25%*18.2%)] = 0.16115

Expected return for Recession = [(40%*-9,8%) + (35%*5.4%) + (25%*-26.9%)]  = -0.0876

Expected return of Portfolio = [Probability * Expected Return]

Expected return of Portfolio = [(0.65*0.16115) + (0.35*-0.0876)

Expected return of Portfolio = 0.074105

Expected return of Portfolio = 7.41%

Variance = [Probability * (Expected return - Expected re*(Return of Portfolio)^2]

Variance = [0.65*(0.16115-0.074105)^2 + [(0.35*(-0.0876*0.074105)^2]

Variance = 0.0140712

Standard deviation = Standard deviation = Standard deviation = 0.118622089

Standard deviation = 11.86% ##### Joannie Gorczany
15.5k 3 10 26
answered 10 months ago