Homework 6

Due 2/27

1. (40 points) You are considering investing in 3 risky assets and a riskless asset with expected returns, E covariance matrix V and covariance matrix inverse V as given below:

   E=

   IBM .12

   Polaroid .15

   Gold .08

   Riskless .06

   V=

   .0625 .05 .0037

   .05 .16 .006

   .0037 .006 .0225

   V=

   21.3 -6.6 -1.7

   -6.6 8.34 -1.14

   -1.7 -1.14 44.9

   1. What are the proportions in the optimal portfolio of risky assets (for IBM, Polaroid, and Gold)? Show some of your calculations.

   2. If you decided that you wish to have a portfolio standard deviation of 30%, what is the maximum expected return that you can achieve? (Hint: compute the capital market line first.)

   3. What portfolio would you hold to achieve your goal in (b)?

   4. If someone else looked at these same assets and agreed with you on the covariance, but thought that the mean returns could be (.20 .15 .06 .06), respectively, what optimal mix of risky assets should she hold? Compare this portfolio to that in (a). Is it different in sensible ways?