Use the table for the question(s)below.
Consider the following expected returns,volatilities,and correlations:
-The volatility of a portfolio that consists of a long position of $10,000 in Wal-Mart and a short position of $2000 in Microsoft is closest to:
A)9%.
B)14%.
C)11%.
D)12%.

Question

Use the table for the question(s)below.
Consider the following expected returns,volatilities,and correlations: 
-The volatility of a portfolio that consists of a long position of $10,000 in Wal-Mart and a short position of $2000 in Microsoft is closest to:
A)9%. 
B)14%. 
C)11%. 
D)12%.

Quizplus · Accepted Answer

To calculate the volatility of the portfolio, we need to use the following formula:
Portfolio Volatility = sqrt[(w1^2 x StdDev1^2)+(w2^2 x StdDev2^2)+(2 x w1 x w2 x Covariance)]
Where:
w1 is the weight of Wal-Mart in the portfolio, which is 10,000/(10,000-2,000) = 0.833
w2 is the weight of Microsoft in the portfolio, which is -2,000/(10,000-2,000) = -0.167 (note the negative sign due to short position)
StdDev1 is the standard deviation of Wal-Mart, which is 14%
StdDev2 is the standard deviation of Microsoft, which is 22%
Covariance is the covariance between Wal-Mart and Microsoft, which is -0.2
Plugging in these values, we get:
Portfolio Volatility = sqrt[(0.833^2 x 0.14^2) + (-0.167^2 x 0.22^2) + (2 x 0.833 x -0.167 x -0.2)] = 0.139 or 13.9%
Therefore, the closest option is B)14%.

Use the Table for the Question(s)below