Investments-Optimal Portfolio

Optimal Portfolio

George Markov eagerly awaited his first day at his new job with Athena Asset Management in a major metropolitan area in the northeastern United States. His future boss had given him a list of questions that would prepare him well for the job. According to the boss: If you can master these questions, you'll be well on your way to becoming a portfolio manager! Before attempting those questions, be sure to read carefully Chapter 7 of Bodie, Kane, and Marcus's Investments book.

Exhibit 1 contains data on several stocks, including returns, standard deviations and correlations. Markov's starting date of September 1 was approaching fast; it was, in fact, only a week away. He was determined to finish the practice questions that day.

1. Pick up three stocks, GE, GM and MRK, risk free rate is 7%. Construct the optimal risky portfolio. How should your client allocate his money between risk free asset and optimal risky portfolio if he wants to achieve 15% expected return. How should your client allocate his money among the three stocks if there is no risk free asset and he still wants to achieve 15% return.

2. Suppose that GM has decided to become a diversified conglomerate, much like GE, so that its correlation with GE will be 0.80 instead of 0.26. Rerun your calculation, what happens to the weights and to the overall portfolio Sharpe ratio?

Why?

3. Now suppose that GM has decided to focus on automobiles and move away from

anything that GE is doing (both with respect to businesses and markets), so that the correlation between GE and GM is expected to be as low as -0.80. Rerun your calculation, what happens to the weights and to the overall portfolio Sharpe

ratio? Why?

4. How does the optimal-portfolio Sharpe ratio change, if shorting is not allowed

and no asset can be allotted more than 50% of the total portfolio?

5. How does your portfolio change if the risk-free rate goes down to 5% from the current7%?

6. Replace GE with Intel in your...