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.
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 |
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