Question

The following information pertains to Question 6 to Question 8 A fund manager has created a 2-stock portfolio. They shorted \$7 million worth of Stock A and has purchased $17 million of Stock B. The correlation between Stock A's and Stock B's returns is 0.45 The expected returns and standard deviations of the two stocks are:

Stock A ER=10% SD=40%
Stock B ER=14.5% SD=45%

What is the standard deviation for this portfolio?

A. 43.0%
B. 34.5%
C. 38.6%
D. 68.6%

Answer 1

To calculate the standard deviation of a portfolio, we need to take into account the weights and correlations of the individual stocks. In this case, Stock A has a weight of -0.29 and Stock B has a weight of 0.71.

Step-by-step explanation:

To calculate the standard deviation of a portfolio, we need to take into account the weights and correlations of the individual stocks. In this case, Stock A weighs -7 million / (-7 million + 17 million) = -0.29, and Stock B weighs 17 million / (-7 million + 17 million) = 0.71.

The standard deviation of the portfolio can be calculated using the formula:

Standard Deviation = sqrt((weight A)^2 * (SD A)^2 + (weight B)^2 * (SD B)^2 + 2 * weight A * weight B * (correlation * SD A * SD B))

Plugging in the values, we get:
Standard Deviation = sqrt((-0.29)^2 * (0.4)^2 + (0.71)^2 * (0.45)^2 + 2 * -0.29 * 0.71 * (0.45 * 0.4)) = 0.386, or 38.6%