Question

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?

Answer #1

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%**

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