Exact solution for the portfolio diversification problem based on maximizing the risk adjusted return

The potential benefits of portfolio diversification have been known to investors for a long time. Markowitz (1952) suggested the seminal approach for optimizing the portfolio problem based on finding the weights as budget shares that minimize the variance of the underlying portfolio. Hatemi-J and El-Khatib (2015) suggested finding the weights that will result in maximizing the risk adjusted return of the portfolio. This approach seems to be preferred by the rational investors since it combines risk and return when the optimal budget shares are sought for. The current paper provides a general solution for this risk adjusted return problem that can be utilized for any potential number of assets that are included in the portfolio. An application is also provided in order to investigate the potential portfolio diversification benefits between the three largest financial markets in the world.