General sparse risk parity portfolio design via successive convex optimization

Abstract Since the 2008 financial crisis, risk management has become more important and portfolio approaches, such as the minimum-variance and equally weighted portfolios, have gained popularity. However, such portfolios still do not diversify the risk in the true sense. Recently, risk parity portfolios has been receiving significant interest from both the theoretical and practical perspectives due to its advantages in the diversification of (ex-ante) risk contributions among assets. However, this portfolio type usually results in nonzero weights in all the assets, which implies high transaction cost in practice. In addition, focusing only on the risk aspect can make this type of portfolio unsatisfactory if other performance factors, e.g., annual yield, are considered. In this paper, we jointly consider asset selection and risk diversification via imposing sparsity and risk parity regularization in the portfolio problem formulation, which turns out to be a general and flexible portfolio framework. Then we propose an efficient sequential algorithm based on the successive convex optimization framework. The numerical results on historical data show that our portfolio approach, compared with benchmark portfolios, can achieve a good balance among asset selection, risk diversification and other evaluation criteria, and achieves the best performance on profit and loss (P&L) and/or drawdown.