Question

The following data are available for two securities:

	Asset A	Asset B
Expected Return	10%	10%
Standard Deviation	3%	3%

An an investor forms a portfolio of 50% in Asset A and 50% in Asset B. If the correlation between the two assets is 1.0, the coefficient of variation for the portfolio is closest to:

Multiple Choice

• 0.30.

• 0.03.

• 0.0009.

• 3.33.

• 0.10.

Answer 1

Expected Return of portfolio =

(Return of stock A* weight of stock A) + (Return of stock B* weight of stock B)

=

(10%*0.50)+(10%*0.50)

=

10%

Standard Deviation of Portfolio=

[{(weight of A)^2 * (sigma of A)^2} + {(weight of B)^2 + (sigma of B)^2} + {2*(weight of A)*(weight of B)*(Correlation of A&B * sigma of A* sigma of B}]^(1/2)

=

((0.50)^2*(3)^2 + (0.50)^2*(3)^2 + (2*0.5*0.5*1*3*3))^(1/2)

=

3.0

Coefficient of variation=

(Standard Deviation/Mean)*100

0.3

(3/10)

The correct answer is option1 i.e 0.30