Question

An investor can design a risky portfolio based on two stocks, 1 and 2. Stock 1 has an expected return of 15% and a standard deviation of return of 25%. Stock 2 has an expected return of 12% and a standard deviation of return of 20%. The correlation coefficient between the returns of 1 and 2 is 0.2. The risk-free rate of return is 1.5%.

Approximately what is the proportion of the optimal risky portfolio that should be invested in Stock 2?

Answer 1

WEIGHT OF STOCK 2 = 0.55

EXPECTED RETURN A	15%
EXPECTED RETURN B	12%
SD OF STOCK A	25%
SD OF STOCK B	20%
CORELATION	0.2
VARIANCE OF STOCK A (SDa^2)	0.06
VARIANCE OF STOCK B (SDb^2)	0.04
COVARIANCE A&B (COVab)	-0.050
OPTIMAL RISKY PORTFOLIO	((SDb^2)-COV(ab))/((SDa^2)+(SDb^2)-2xCOV(ab))
PORTFOLIO INVESTED IN A (Wa)	0.45
PORTFOLIO INVESTED IN B (Wb)	0.55

NOTE -COVARIANCE A&B IS NEGATIVE TO AN OPPOSITE EFFECT TO STANDARD DEVIATION