Question

11.) Mr. Jones has a 2-stock portfolio with a total value of $510,000. $175,000 is invested in Stock A and the remainder is invested in Stock B. If standard deviation of Stock A is 16.95%, Stock B is 11.45%, and correlation between Stock A and Stock B is –0.20, what would be the expected risk on Mr. Jones’ portfolio (standard deviation of the portfolio return)?

Answer 1

Standard deviation of the portfolio return

8.54%

Working:

Step-1:Calculation of weight of each Stock

Total Investment

5,10,000

Less investment in Stock A

1,75,000

Investment in Stock B

3,35,000

Weight of Investment in:

Stock A

1,75,000

/

5,10,000

=

0.34

Stock B

3,35,000

/

5,10,000

=

0.66

Total

1.00

Step-2:Calculation of Standard deviation of return of portfolio

Standard deviation of return of portfolio

=

((WA^2)*(SdA^2)+(WB^2)*(SdB^2)+2*WA*WB*SdA*SdB*cAB)^(1/2)

Where,

=

((0.34^2)*(0.1695^2)+(0.66^2)*(0.1145^2)+2*0.34*0.66*0.1695*0.1145*-0.20)^(1/2)

WA

Weight fo A

0.34

=

0.0854

WB

Weight of B

0.66

SdA

Standard deviation of A

0.1695

Thus, Standard deviation of return of portfolio is 8.54%

SdB

Standard deviation of B

0.1145

cAB

correlation between Stock A and Stock B

-0.20