Paper: arXiv 2303.13282

Authors: Álvaro Rubio-García, Samuel Fernández-Lorenzo, Juan José García-Ripoll, Diego Porras

Abstract

An actively managed portfolio almost never beats the market in the long term. Thus, many investors often resort to passively managed portfolios whose aim is to follow a certain financial index. The task of building such passive portfolios aiming also to minimize the transaction costs is called Index Tracking (IT), where the goal is to track the index by holding only a small subset of assets in the index. As such, it is an NP-hard problem and becomes unfeasible to solve exactly for indices with more than 100 assets. In this work, we present a novel hybrid simulated annealing method that can efficiently solve the IT problem for large indices and is flexible enough to adapt to financially relevant constraints. By tracking the S&P-500 index between the years 2011 and 2018 we show that our algorithm is capable of finding optimal solutions in the in-sample period of past returns and can be tuned to provide optimal returns in the out-of-sample period of future returns. Finally, we focus on the task of holding an IT portfolio during one year and rebalancing the portfolio every month. Here, our hybrid simulated annealing algorithm is capable of producing financially optimal portfolios already for small subsets of assets and using reasonable computational resources, making it an appropriate tool for financial managers.

Complexity vs Empirical Score

  • Math Complexity: 5.5/10
  • Empirical Rigor: 6.0/10 (capped from 7.0: transaction costs not modelled; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a solid hybrid simulated annealing approach to solve the NP-hard Index Tracking problem under practical constraints. It demonstrates strong empirical utility by testing on S&P 500 data from 2011 to 2018 with realistic monthly rebalancing, though reproducibility depends on exact parameter tuning details.

Research Flowchart

  flowchart TD
    A[Research Goal: Solve Index Tracking NP-hard problem & minimize transaction costs] --> B[Input Data: S&P-500 equity returns 2011-2018]
    B --> C[Method: Hybrid Simulated Annealing Algorithm]
    C --> D[Computational Optimization: Select asset subset & perform monthly portfolio rebalancing]
    D --> E[In-Sample Testing: Find optimal tracking solutions on past returns]
    D --> F[Out-of-Sample Testing: Tune for optimal future returns]
    E & F --> G[Key Outcome: Financially optimal portfolios with small asset subsets & efficient resource use]