Question

What is the standard deviation for the following portfolio? The portfolio has weights of 0.25 and 0.75 on stocks A and B, respectively. The correlation between stock A and B is 0.4. The variance for each stock was computed by using rates of returns and not percentages. (Round your answer to two decimal digits)

Stocks	Expected return	Variance
A	17%	0.0169
B	13%	0.0361

Answer 1

Solution :-

Variance of Stock A = 0.0169 = 1.69%

Standard Deviation of Stock A ( SDa ) = ( 1.69 % )^1/2 = 13.00% = 0.13

Variance of Stock B = 0.0361 = 3.61%

Standard Deviation of Stock B ( SDb) = ( 3.61% )^1/2 = 19.00% = 0.19

Now Weight of Stock A = 0.25

Weight of Stock B = 0.75

Correlation between stock A and B ( r ) = 0.4

= Variance of Portfolio = ( Wa * SDa )² + ( Wb * SDb )² + ( 2 * SDa * SDb * Wa * Wb * r )

= ( 0.25 * 0.13 )² + ( 0.75 * 0.19 )² + ( 2 * 0.13 * 0.19 * 0.25 * 0.75 * 0.40 )

= 0.00105625 + 0.02030625 + 0.003705

= 0.0250675

= 2.507%

Now Standard Deviation of Portfolio = ( 2.507% )^1/2

= 15.83%

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