Given the following information, what is the standard deviation of the returns on a portfolio...
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, andthe remainder in stock C?
State of Economy Prob. of State of Economy Rate of Return is state occurs
Normal .65 Stock A-14.3% Stock B- 16.7% Stock C- 18.2%
Recession .35 -9.8% 5.4% -26.9%
Homework Answers
Portfolio return in normal = 40%*14.3% + 35%*16.7% + 25%*18.2% = 16.115%
Portfolio return in recession = 40%*(-9.8%) + 35%*5.4% + 25%*(-26.9%) = 4.695%
So E[X] = 0.65 * 16.115% + 0.35*4.695% = 12.118%
E[X^2] = 0.65*(16.115%)^2 + 0.35*(4.695%)^2 = 0.1765
Stand Dev =√(E[X^2] -E[X]^2 ) = 5.447%
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