Investors typically measure an asset’s potential to diversify a portfolio by its correlations with the portfolio’s other assets, but correlation is useful only if it provides a good estimate of how an asset’s returns co-occur cumulatively with the other asset returns over the investor’s...

Proceeding to portfolio allocation in the framework of Markowitz, a numerical inconsistency may occur when the sample covariance matrix of assets returns has to be inverted. This is mainly caused by the magnitude of its lowest eigenvalues. In this paper, we tackle the Markowitz problem as an...

Portfolio implementation is an essential part of active investment strategies. The trading horizon-the length of time allocated for trade implementation, is an important consideration in portfolio trading. Previous research on optimal trading limits the trading horizon as a fixed value. In this...

The purpose of these notes is to provide a systematic quantitative framework - in what is intended to be a "pedagogical" fashion - for discussing mean-reversion and optimization. We start with pair trading and add complexity by following the sequence "mean-reversion via demeaning → regression...

In these notes we discuss investment allocation to multiple alpha streams traded on the same execution platform, including when trades are crossed internally resulting in turnover reduction. We discuss approaches to alpha weight optimization where one maximizes P&L subject to bounds on...

We will in this paper discuss portfolio theory and portfolio optimization. Traditionally Quadratic Programming (QP) has been used to solve portfolio optimization problems. However, when an investor is faced with a large universe of securities the performance of QP will decrease. This paper shows...

The C-Sharpe ratio is defined as the amount of expected excess return per unit of risk, where the risk is given by the CVaR dispersion measure (not to be confused with the CVaR risk measure). Then, C-Sharpe optimal portfolio is the portfolio with the largest C-Sharpe ratio. It can be identified...

This article exclusively formulates and presents three innovative hypotheses related to the execution of share buybacks, employing Genetic Algorithms (GAs) and mathematical optimization techniques. Drawing on the foundational contributions of scholars such as Osterrieder, Seigne, Masters, and...

It is evident that linear programming model remains the most potent mathematical tool for the efficient allocation of scarce operational resources of an organization. Whilst projecting the graphical method as the easiest solution approach to linear programming where only two constraining factors...