Homework 5

Due 2/27

1. (30 points) Your security analyst says that the expected return and standard deviation for Federal Express (ticker symbol FDX) are 20% and 40%, respectively. For Duke Power (ticker symbol DUK), the expected return is 12%, with a standard deviation of 15%. The correlation between DUK's return and FDX's return is 0.30.

   1. What is the covariance of FDX's return with DUK's?

      
      
      

   2. Compute the means and standard deviations of portfolios of FDX and DUK with the following percentages in FDX, and the complement in DUK: (i) 100%, (ii) 60%, (iii) 30%, and (iv) 0%.

      

      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      

   3. Plot the points in (b) and smooth a curve of potential means and standard deviations that could be achieved with portfolios of FDX and DUK.

      
      
      
      
      

2. (30 points) Consider 2 portfolios of 3 risky assets that have the following covariance matrix and mean vector:

   :

   

   

   

   E=

   .20 .18 .12

   Portfolio A has weights (0.5 0.5 0), and portfolio B has weights (0 0.5 0.5).

   1. What is the standard deviation of each individual asset? What are the variances?

      
      
      
      
      

   2. What are the correlations of each asset with each other asset? Covariances?
      
      

   3. What are the standard deviations of portfolios A and B? What is their covariance? What is their correlation? What are the portfolios' means?

      
      
      
      
      

      
      
      Note