You were allowed to invest in two stocks (A and B) for your portfolio. The expected returns of A and B are 10% and 20%, respectively, and the risks of A and B are 18% and 35%, respectively. You know the correlation coefficient between the two stocks is -0.3, and the risk-free rate is 2%. What would be your allocations (i.e., weights) in the two stocks if you want to put together a portfolio that:

(i) Provides you the lowest possible level of risk? Show your work.

(ii) Provides you with the best risk and return tradeoff? Show your work.

Suppose your investor's coefficient of risk aversion is 5. What would be your allocations (i.e., weights) in the risk-free asset and the two stocks if you want to put together a portfolio that:

(iii) Provides you the highest level of satisfaction? Show your work.