Question

Question 1

Consider two risky assets A and B with E(rA)= 15%, Sigma_A= 32%, E(rB)= 0.09, Sigma_B= 23%, corrA,B= 0.2. The risk free rate is 5%. The optimal risky portfolio of comprised of the two risky assets is to allocate 64% to A and the rest to B. What is the standard deviation of the optimal risky portfolio ?

Select one:

a. 20.75%

b. 23.61%

c. 22.86%

d. 23.00%

Question 2

Continued with previous question. What is the Sharpe ratio of the optimal risky portfolio?

Select one:

a. 0.33

b. 0.35

c. 0.31

d. 0.29

Answer 1

1). Standard Deviation = [{wA * S.D.(A)}² + {wB * S.D.(B)}² + {2 * wA * wB * S.D.(A) * S.D.(B) * Corr(A,B)}]^1/2

= [(0.64 * 32%)² + (0.36 * 23%)² + (2 * 0.64 * 0.36 * 32% * 23% * 0.2)]^1/2

= [419.4304%² + 68.5584%² + 67.82976%²]^1/2

= [555.81856%²]^1/2 = 23.61%

Option "b" is correct.

2). E(r) = [wA * E(rA)] * [wB * E(rB)]

= [0.64 * 15%] + [0.36 * 9%] = 9.6% + 3.24% = 12.84%

Sharpe Ratio = [E(r) - rF] / S.D.

= [12.84% - 5%] / 23.61% = 7.84% / 23.61% = 0.33

Option "a" is correct.