What is the standard deviation of the returns on a portfolio that is invested in stocks A,B,and C? Twenty five percent of the portfolio is invested in stock A and 40 percent is invested in stock C.
A)6.31 percent
B)6.49 percent
C)7.40 percent
D)7.83 percent
E) 8.72 percent

Question

What is the standard deviation of the returns on a portfolio that is invested in stocks A,B,and C? Twenty five percent of the portfolio is invested in stock A and 40 percent is invested in stock C. 
A)6.31 percent 
B)6.49 percent 
C)7.40 percent 
D)7.83 percent 
E) 8.72 percent

Quizplus · Accepted Answer

E(r)_Boom = (0.25 × 0.17) + (0.35 × 0.06) + (0.40 × 0.22) = 0.1515E(r)_Normal = (0.25 × 0.08) + (0.35 × 0.10) + (0.40 × 0.15) = 0.115E(r)_Bust = (0.25 × -0.03) + (0.35 × 0.19) + (0.40 × -0.25) = -0.041E(r)_Portfolio = (0.05 × 0.1515) + (0.55 × 0.115) + (0.40 × -0.041) = 0.054425Var_Portfolio = [0.05 × (0.1515 - 0.054425)²] + [0.55 × (0.115 - 0.054425)²] + [0.40 × (-0.041 - 0.054425)²] = 0.006132Std dev = √.006132 = 7.83 percent

What Is the Standard Deviation of the Returns on a Portfolio