A Fast Successive QP Algorithm for General Mean-Variance Portfolio Optimization

The mean and variance of portfolio returns are the standard quantities to measure the expected return and risk of a portfolio. Efficient portfolios that provide optimal trade-offs between mean and variance warrant consideration. To express a preference among these efficient portfolios, investors have put forward many mean-variance portfolio (MVP) formulations which date back to the classical Markowitz portfolio. However, most existing algorithms are highly specialized to particular formulations and cannot be generalized for broader applications. Therefore, a fast and unified algorithm would be extremely beneficial. In this paper, we first introduce a general MVP problem formulation that can fit most existing cases by exploring their commonalities. Then, we propose a widely applicable and provably convergent successive quadratic programming algorithm (SCQP) for the general formulation. The proposed algorithm can be implemented based on only the QP solvers and thus is computationally efficient. In addition, a fast implementation is considered to accelerate the algorithm. The numerical results show that our proposed algorithm significantly outperforms the state-of-the-art ones in terms of convergence speed and scalability.