What is the standard deviation of the returns on a $30,000 portfolio which consists of stocks S and T? Stock S is valued at $21,000.
A)2.07 percent
B)2.61 percent
C)3.36 percent
D)3.49 percent
E)3.63 percent

Question

What is the standard deviation of the returns on a $30,000 portfolio which consists of stocks S and T? Stock S is valued at $21,000. 
A)2.07 percent 
B)2.61 percent 
C)3.36 percent 
D)3.49 percent 
E)3.63 percent

Quizplus · Accepted Answer

E(r)_Boom = [$21,000/$30,000] [0.11] + [($30,000 - $21,000)/$30,000] [0.05] = 0.092E(r)_Normal = [$21,000/$30,000] [0.08] + [($30,000 - $21,000)/$30,000] [0.06] = 0.074E(r)_Bust = [$21,000/$30,000] [-0.05] + [($30,000 - $21,000)/$30,000] [0.08] = -0.011E(r)_Portfolio = (0.05 × 0.092) + (0.85 × 0.074) + (0.10 × -0.011) = 0.0664Var_Portfolio = [0.05 × (0.074 - 0.0664)²] + [0.85 × (0.068 - 0.0664)²] + [0.10 × (0.028 - 0.0664)²] = .000680940Std dev = √0.000680940 = 2.61 percent

What Is the Standard Deviation of the Returns on a $30,000