Stock A has an expected return of 10% and a standard deviation of 10%.Stock B has an expected return of 15% and a standard deviation of 20%.The two stocks are perfectly negatively correlated ( = -1).What set of weights yields a portfolio with a zero variance?
A) 2/3 in Stock A; 1/3 in Stock B
B) 2/3 in Stock B; 1/3 in Stock A
C) 2 in Stock A; -1 in Stock B
D) 2 in Stock B; -1 in Stock A
E) None of the above.

Question

Stock A has an expected return of 10% and a standard deviation of 10%.Stock B has an expected return of 15% and a standard deviation of 20%.The two stocks are perfectly negatively correlated (  = -1).What set of weights yields a portfolio with a zero variance?
A) 2/3 in Stock A; 1/3 in Stock B 
B) 2/3 in Stock B; 1/3 in Stock A 
C) 2 in Stock A; -1 in Stock B 
D) 2 in Stock B; -1 in Stock A 
E) None of the above.

Quizplus · Accepted Answer

From the text we know the equation for the standard deviation of a 2 asset portfolio is: 11ea7fdb_fc04_ce11_a768_77cc8244d77e_TB2902_11 = 11ea7fdb_fc04_ce12_a768_a3cd239eddcc_TB2902_11 After substituting the correlation of -1, setting the variance to zero, and squaring both sides we have:
0 = 11ea7fdb_fc04_ce13_a768_27ec6cc53bf9_TB2902_11 11ea7fdb_fc04_ce14_a768_cde709ef1d0b_TB2902_11 + 11ea7fdb_fc04_ce15_a768_25debfffc47c_TB2902_11 11ea7fdb_fc04_ce16_a768_03d73f25af70_TB2902_11 + 2w(1 - w)(-1)(0.1)(0.2)
0 = 11ea7fdb_fc04_f527_a768_4733681419d1_TB2902_11 [ 11ea7fdb_fc04_f528_a768_ff7e0d529101_TB2902_11 + 11ea7fdb_fc04_f529_a768_e3393b5394cb_TB2902_11 + 0.04] - w [2 11ea7fdb_fc04_f52a_a768_65c31d80acac_TB2902_11 + 0.04] + 11ea7fdb_fc04_f52b_a768_a3ce10473d94_TB2902_11 0 = 0.09 11ea7fdb_fc04_f52c_a768_77d401fa7cac_TB2902_11 - 0.12w + 0.04
After multiplying both sides of the equation by 100 we get:
0 = 9 11ea7fdb_fc04_f52d_a768_c93e52d37936_TB2902_11 - 12w + 4
By factoring the quadratic equation we get:
0 = (3w - 2)(3w - 2)
0 = 3w - 2
w = 2/3

Stock a Has an Expected Return of 10% and a Standard