Suppose you plan to create a portfolio with three securities: Dizzy (D),Lazy (L),and Crazy (C).The expected returns for Dizzy,Lazy and Crazy are 6 percent,8 percent,and 10 percent,respectively.The standard deviation is 9 percent for Dizzy,15 percent for Lazy,and 12 percent for Crazy.The correlation coefficients among the returns for the three securities are: CORRDL= 0.6,CORRDC = -0.3,and CORRLC = 0.4.What is the portfolio standard deviation if 30 percent of the portfolio is in Dizzy and 40 percent is in Lazy?
A) 0.34%
B) 0.87%
C) 5.82%
D) 9.33%

Question

Quizplus · Accepted Answer

σ_P = √[(w²_D)(σ²_D)+(w²_L)(σ²_L)+(w²_C)(σ²_C)+2w_Dw_Lσ_Dσ_Lρ_DL+2w_Dw_Cσ_Dσ_Cρ_DC+2w_Lw_Cσ_Lσ_Cρ_LC] =√[0.000729+0.0036+0.001296+0.001944-0.000583+0.001728] = 9.33%

Suppose You Plan to Create a Portfolio with Three Securities