Question

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?

Answer #1

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)

= 27.02%

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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