Discrete portfolio optimisation for large scale systematic trading applications

Markowitz´s mean-variance portfolio optimisation is not suitable for a large number of assets due to the unacceptably slow quadratic optimisation procedure involved. This is particularly important in systematic/algorithmic/automated trading applications where instead of assets, automated trading systems are used. We propose a much faster heuristic approach that scales linearly rather than the quadratic scaling in the Markowitz method. Moreover, our proposed approach, Comgen, is on average better than the Markowitz approach when applied to unseen data. Additionally, Comgen always finds a solution, whereas the Markowitz procedure occasionally fails as the covariance matrix is not always positive-semidefinite. In an empirical study of a ~2000 day history, we demonstrate the benefits of this novel approach by using ~3200 time series produced by automatic trading systems. We perform a 3 year walk-forward analysis and show that in most of the 12́3=36 months out of the sample periods, this novel approach produces a better Sharpe ratio than the Markowitz approach, at the same time being a thousand times faster (and 2400 times faster if number of assets is 4000).