Question

An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 24% and a standard deviation of return of 35%. Stock B has an expected return of 13% and a standard deviation of return of 20%. The correlation coefficient between the returns of A and B is .5. The risk-free rate of return is 6%. The proportion of the optimal risky portfolio that should be invested in stock B is approximately _________.

		35.17%
		32.38%
		50.80%
		27.66%

Answer 1

Weight in Stock B = ((Expected return on Stock B - Risk free rate)  * (Standard Deviation of Stock A)² - ((Expected return on Stock A - Risk free rate) * Standard Deviation of Stock A * Standard Deviation of Stock B * Correlation between Stock A & Stock B))) / ((Expected return on Stock A - Risk free rate) * (Standard Deviation of Stock B)² + (Expected return on Stock B - Risk free rate)  * (Standard Deviation of Stock A)²  - ((Expected return on Stock A - Risk free rate + Expected return on Stock B - Risk free rate) * Standard Deviation of Stock A * Standard Deviation of Stock B * Correlation between Stock A & Stock B))

Weight in Stock B = ((13% - 6%) * (35%)² - ((24% - 6%) * 35% * 20% * 0.5)) / ((24% - 6%) * (20%)² + (13% - 6%) * (35%)² - ((24% - 6% + 13% - 6%) * 35% * 20% * 0.5))

Weight in Stock B = 32.38%