Question

Consider two perfectly positively correlated risky securities, A and B. Security A has an expected rate of return of 16% and a standard deviation of return of 20%. B has an expected rate of return of 10% and a standard deviation of return of 30%. Solve for the minimum variance portfolio (i.e., what are the weights in A and B of the minimum variance portfolio). What is the variance of this portfolio?

Answer 1

EXPECTED RETURN A	16%
EXPECTED RETURN B	10%
SD OF STOCK A	20%
SD OF STOCK B	30%
CORELATION	1
VARIANCE OF STOCK A (SDa^2)	0.04
VARIANCE OF STOCK B (SDb^2)	0.09
COVARIANCE A&B (COVab)	-0.060
OPTIMAL RISKY PORTFOLIO	((SDb^2)-COV(ab))/((SDa^2)+(SDb^2)-2xCOV(ab))
(PORTFOLIO INVESTED IN A)
PORTFOLIO INVESTED IN A	0.6
PORTFOLIO INVESTED IN B	0.4

PORTFOLIO VARIANCE	(SDa^2 x Wa^2) + (SDb^2 x Wb^2) + 2 x SDa x SDb x Wa x Wb x corelation
	0.0576
	5.76%