Question

Assume Stocks A and B have the following characteristics:

  

Stock	Expected Return	Standard Deviation
A	9.2%	33.2%
B	15.2%	62.2%

  

The covariance between the returns on the two stocks is .0012.

a.	Suppose an investor holds a portfolio consisting of only Stock A and Stock B. Find the portfolio weights, XA and XB, such that the variance of her portfolio is minimized. (Hint: Remember that the sum of the two weights must equal 1.) (Do not round intermediate calculations and round your answers to 4 decimal places, e.g., 32.1616.)
b.	What is the expected return on the minimum variance portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
c.	If the covariance between the returns on the two stocks is −.05, what are the minimum variance weights? (Do not round intermediate calculations and round your answers to 4 decimal places, e.g., .1616.)
d.	What is the variance of the portfolio in part (c)? (Do not round intermediate calculations and round your answer to 4 decimal places, e.g., .1616.)

	a. Stock A weight Stock B weight b. Expected return % c. Stock A weight Stock B weight d. Portfolio variance

Answer 1

a. Stock A Weight = (Variance B - Covariance) / (Variance A + variance B - 2 * Co Variance)

Stock A Weight = (0.622^2 - 0.0012) / (0.332^2 + 0.622^2 - 2 * 0.0012)

Stock A Weight = 0.385684 / 0.494708

Stock A Weight = 0.7796

Stock B Weight = 1 - 0.7796 = 0.2204

b. Expected Return = 0.7796 * 0.092 + 0.2204 * 0.152

Expected Return = 10.52%

c. Stock A Weight = (Variance B - Covariance) / (Variance A + variance B - 2 * Co Variance)

Stock A Weight = (0.622^2 + 0.05) / (0.332^2 + 0.622^2 + 2 * 0.05)

Stock A Weight = 0.4368 / 0.5971

Stock A Weight = 0.7317

Stock B Weight = 1 - 0.7317 = 0.2683

d. Variance = Weight A^2 * SD A^2 + Weight B^2 * SD B^2 + 2 * WA * WB * SDA * SDB

Variance = 0.7317^2 * 0.332^2 + 0.2683^2 * 0.622^2 + 2 * 0.7317 * 0.2683 * 0.332 * 0.622

Variance = 0.1679