1.When the CAPM correctly prices risk, the market portfolio is an efficient portfolio. Explain why.
2.A big pharmaceutical company, DRIg, has just announced a potential cure for cancer. The stock price increased from $5 to $100 in one day. A friend calls to tell you that he owns DRIg. You proudly reply that you do too. Since you have been friends for some time, you know that he holds the market, as do you, and so you both are invested in this stock. Both of you care only about expected return and volatility. The risk-free rate is 3%, quoted as an APR based on a 365-day year. DRIg made up 0.2% of the market portfolio before the news announcement.
a. On the announcement your overall wealth went up by 1% (assume all other price changes canceled out so that without DRIg, the market return would have been zero). How is your wealth invested?
b. Your friend’s wealth went up by 2%. How is he invested?
3.Your investment portfolio consists of $15,000 invested in only one stock—Microsoft. Suppose the risk-free rate is 5%, Microsoft stock has an expected return of 12% and a volatility of 40%, and the market portfolio has an expected return of 10% and a volatility of 18%. Under the CAPM assumptions,
a. What alternative investment has the lowest possible volatility while having the same expected return as Microsoft? What is the volatility of this investment?
b. What investment has the highest possible expected return while having the same volatility as Microsoft? What is the expected return of this investment?