Question

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?


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

Answer 1

Answer:

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 = $\sqrt{Variance }$

Standard deviation = $\sqrt{0.0140712}$

Standard deviation = 0.118622089

Standard deviation = 11.86%