Suppose the characteristics of security A and B are given as follow:
Expected return Standard deviation Stock A 12% 8% Stock B 18% 15%
Correlation coefficient between return of stock A and B is 0.5.
What is the expected value and standard deviation of return of minimum variance portfolio constructed from stock A and B?
Expected value of portfolio constructed from stock A and stock B will be calculated as follows:
E(R)= weightage of stock A× return of stock A+ weightage of stock B× return of stock B.
In the present case weightage is not given, so we assume it to be 0.5 for stock A and 0.5 for stock B.
So, expected return= 0.5× 0.12+0.5×0.18= 0.15 or 15%
Now, variance of return of portfolio = weight of A)2.standard deviation of A)2. Return on A+ weightage of stock B)2.(standard deviation of stock B)2. Return of stock B+ 2. weightage of stock A. weightage of stock B. Correlation coefficient of stock A and B.
= 0.5)(0.5)(0.08)(0.08)(0.12)+(0.5)(0.5)(0.15)(0.15)(0.18)+ 2(0.5)(0.5)(0.5)
That gives standard deviation of portfolio is square root of variance that is 27.02% . So standard deviation is approximately 5.2% .
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