Stock F (friends) has an expected return of 10% and volatility 15%. Stock U (you) has an expected return of 5% and volatility 10%. Stock N (anywhere) has an expected return of 20% and volatility 50%. The correlation between F and U is -0.5, between F and N is 0.3, and between U and N is 0.7. Suppose you are required to have 20% of your money invested in stock N at all times.
(a) Give an example of an efficient portfolio under this setting, with justification.
(b) What is the expected return and volatility of a portfolio with equal investments in F and U?
(c) What is the minimum variance portfolio, assuming we are not shorting any stocks?