Background: Optimization and the Axioma Portfolio Advantage
In the 1950s, Dr. Harry M. Markowitz pioneered a mathematical approach to asset allocation. The technique is known as mean-variance optimization. Markowitz was awarded the Nobel Memorial Prize for Economics for his work. Over the years, the original approach has been improved upon, but the fundamental concepts, such as diversification (selecting assets that complement one another in order to mitigate risk), remain at the heart of asset management. Mean-variance optimization characterizes each asset in terms of its expected return and volatility. The interaction between each pair of assets is characterized by the correlation between their respective returns. Based on these characterizations, an optimal asset allocation that simultaneously maximizes expected return and minimizes risk can be generated.
The underlying mathematical model of the basic portfolio construction problem is a quadratic optimization problem, i.e., a mathematical program with a quadratic objective function and linear constraints. However, adding features such as risk targets (global or per sector), limited diversification, market impact, and minimum and maximum number of holdings, changes this underlying structure and greatly complicates the search for a solution.
From an optimization perspective, most of these features significantly increase the complexity of the underlying asset allocation problem. Consequently, with most portfolio optimization software, the portfolio manager must choose between solving the real problem inaccurately and solving a crude approximation of the problem accurately. The advanced science built into Axioma Portfolio addresses these issues properly, removing the need to choose between two bad alternatives, and delivers accuracy, speed, and exceptional versatility.
