# Exact Solution for the Portfolio Diversification Problem Based on Maximizing the Risk Adjusted Return

## TL;DR

This paper presents an exact solution for optimizing portfolio weights to maximize risk-adjusted return, extending previous methods to portfolios with any number of assets.

## Contribution

It provides a general, exact solution for the portfolio diversification problem focused on maximizing risk-adjusted return, applicable to portfolios of any size.

## Key findings

- Derived a closed-form solution for the risk-adjusted return maximization problem.
- Applicable to portfolios with any number of assets.
- Enhances portfolio optimization techniques by providing an exact analytical method.

## Abstract

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.