Question

a. You have constructed a portfolio consisting of 40 percent Stock A and 60 percent Stock B. Stock A has expected return of 15 percent and standard deviation of 20 percent. Stock B has expected return of 7 percent and standard deviation of 10 percent. The correlation between the returns of these stocks is 0.5. Compute the expected return and standard deviation of your portfolio returns. (10 pts)

Answer 1

Expected Return for Stock A (E_RA) = 15%
Weight of Stock A in portfolio (W_A) = 40%
Standard Deviation of Stock A (SD_A) = 20%

Expected Return for Stock B (E_RB) = 7%
Weight of Stock A in portfolio (W_B) = 60%
Standard Deviation of Stock B (SD_B) = 10%

Correlation between Stock A and B (r_AB) = 0.5

a.

Expected Return of the portfolio:

= (W_A x E_RA) + (W_B x E_RB)
= (0.40 x 0.15) + (0.60 x 0.07)
= 0.06 + 0.042
= 0.102
= 10.2% (Answer)

Standard Deviation of the portfolio returns:

=

(W2 x SD)(W x SD)2WA x Wg x SDA x SDB X TAB

=

(0.60 | (0.402 х0.202) + х 0.102) + 2 х 0.60х0.40 x 0.20 х0.10 х0.5

=

0.00640.00360.0048

=

0.0148

= 0.121655

= 12.1655% = 12.17% (Answer)