Question

# Eric Poppovich invests money in two stocks for the upcoming year. His investment is shown below:...

Eric Poppovich invests money in two stocks for the upcoming year. His investment is shown below:

STOCK: # of shares Price Per Share Expected Return Standard Deviation
LBJ Corporation (A) 49.00 \$38.51 5.00% 16.00%
Duncan Inc. (B) 29.00 \$52.41 10.00% 20.00%

The correlation between LBJ and Duncan is 0.50.

what is the standard deviation of the portfolio?

Here,

total investment made in portfolio = 49*38.51+29*52.41

= 1886.99+1519.89

= 3406.88

Portfolio Standard Deviation = [(WA*SDA)^2 + (WB*SDB)^2 + (2*WA*WB*SDA*SDB*CorAB)]

where

WA - Weight of stock A =1886.99/3406.88 = 0.55387627389

WB - Weight of stock B =1519.89/3406.88 = 0.4461237261

SDA - Standard Deviation of stock A = 16

SDB - Standard Deviation of stock B = 20

CorAB - Correlation coefficient = .50

Portfolio Standard Deviation = [(0.55387627389*16)^2 + (0.4461237261*20)^2 + (2*0.55387627389*0.4461237261*16*20*.50)]

= (78.5354052552+79.6105515957+79.071151074)

= 237.217107925

= 15.40%