Wealth Flow Model: Online Portfolio Selection Based on Learning Wealth Flow Matrices

This article proposes a deep learning solution to the online portfolio selection problem based on learning a latent structure directly from a price time series. It introduces a novel wealth flow matrix for representing a latent structure that has special regular conditions to encode the knowledge about the relative strengths of assets in portfolios. Therefore, a wealth flow model (WFM) is proposed to learn wealth flow matrices and maximize portfolio wealth simultaneously. Compared with existing approaches, our work has several distinctive benefits: (1) the learning of wealth flow matrices makes our model more generalizable than models that only predict wealth proportion vectors, and (2) the exploitation of wealth flow matrices and the exploration of wealth growth are integrated into our deep reinforcement algorithm for the WFM. These benefits, in combination, lead to a highly-effective approach for generating reasonable investment behavior, including short-term trend following, the following of a few losers, no self-investment, and sparse portfolios. Extensive experiments on five benchmark datasets from real-world stock markets confirm the theoretical advantage of the WFM, which achieves the Pareto improvements in terms of multiple performance indicators and the steady growth of wealth over the state-of-the-art algorithms.

A Scalable Algorithm for Sparse Portfolio Selection

The sparse portfolio selection problem is one of the most famous and frequently studied problems in the optimization and financial economics literatures. In a universe of risky assets, the goal is to construct a portfolio with maximal expected return and minimum variance, subject to an upper bound on the number of positions, linear inequalities, and minimum investment constraints. Existing certifiably optimal approaches to this problem have not been shown to converge within a practical amount of time at real-world problem sizes with more than 400 securities. In this paper, we propose a more scalable approach. By imposing a ridge regularization term, we reformulate the problem as a convex binary optimization problem, which is solvable via an efficient outer-approximation procedure. We propose various techniques for improving the performance of the procedure, including a heuristic that supplies high-quality warm-starts, and a second heuristic for generating additional cuts that strengthens the root relaxation. We also study the problem’s continuous relaxation, establish that it is second-order cone representable, and supply a sufficient condition for its tightness. In numerical experiments, we establish that a conjunction of the imposition of ridge regularization and the use of the outer-approximation procedure gives rise to dramatic speedups for sparse portfolio selection problems.

Systemic Risk-Driven Portfolio Selection

How can we construct portfolios that perform well in the face of systemic events? The global financial crisis of 2007–2008 and the coronavirus disease 2019 pandemic have highlighted the importance of accounting for extreme form of risks. In “Systemic Risk-Driven Portfolio Selection,” Capponi and Rubtsov investigate the design of portfolios that trade off tail risk and expected growth of the investment. The authors show how two well-known risk measures, the value-at-risk and the conditional value-at-risk, can be used to construct portfolios that perform well in the face of systemic events. The paper uses U.S. stock data from the S&P500 Financials Index and Canadian stock data from the S&P/TSX Capped Financial Index, and it demonstrates that portfolios accounting for systemic risk attain higher risk-adjusted expected returns, compared with well-known benchmark portfolio criteria, during times of market downturn.