Suppose an investor holds a portfolio consisting of 10 of firm X and 10 of firm Y. Securities X and Y are traded at 10 each, and their prices are negatively correlated, with a correlation coefficient equal to 0.5. The annual expected return equals = 10% and = 5%, while the standard deviation of returns equals = 20% and = 15%, respectively.

1. Assuming that transaction costs are zero, how this portfolio should be rebalanced (self-financing strategy, i.e. increase/decrease the number of securities X and Y accordingly without changing the total market value of the portfolio) in order to minimize the portfolio risk?

2. Evaluate your findings and comment on the risk-return profile of the rebalanced portfolio