Question

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

Answer 1

There should be an equal allocation between portfolio X and Y in order to minimize the portfolio risk.

If we increase /decrease the allocation then it will end up increase the portfolio risk (10.9) rather than to minimize it.