Optimizing Sparse Mean-Reverting Portfolio

ArXiv ID: 2406.17155 “View on arXiv”

Authors: Unknown

Abstract

Mean-reverting behavior of individuals assets is widely known in financial markets. In fact, we can construct a portfolio that has mean-reverting behavior and use it in trading strategies to extract profits. In this paper, we show that we are able to find the optimal weights of stocks to construct portfolio that has the fastest mean-reverting behavior. We further add minimum variance and sparsity constraints to the optimization problem and transform into Semidefinite Programming (SDP) problem to find the optimal weights. Using the optimal weights, we empirically compare the performance of contrarian strategies between non-sparse mean-reverting portfolio and sparse mean-reverting portfolio to argue that the latter provides higher returns when we take into account of transaction costs.

Keywords: Mean-Reverting Portfolio, Semidefinite Programming (SDP), Contrarian Strategies, Sparsity Constraints

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail
  • Why: The paper employs advanced mathematical techniques like semidefinite programming (SDP) and eigenvalue problems, resulting in a high math complexity score. It also includes empirical backtesting on S&P 500 data with transaction cost considerations, leading to a strong empirical rigor score.
  flowchart TD
    A["Research Goal:<br>Find optimal sparse<br>mean-reverting portfolio<br>for trading strategies"] --> B["Key Methodology:<br>Formulate optimization problem<br>with fastest mean-reversion,<br>minimum variance, and sparsity constraints"]
    B --> C["Computational Process:<br>Transform problem into<br>Semidefinite Programming (SDP)<br>for optimal weight calculation"]
    C --> D["Data/Inputs:<br>Historical stock prices<br>to compute covariance matrix<br>and mean-reversion parameters"]
    D --> E["Outcomes & Findings:<br>Sparse portfolios yield<br>higher returns vs. non-sparse<br>when accounting for transaction costs<br>in contrarian strategies"]