Correlation-diversified portfolio construction by finding maximum independent set in large-scale market graph

TL;DR

This work tackles correlation-driven diversification by casting portfolio selection as a maximum independent set (MIS) problem on a market graph where edges encode stock correlations. It implements a quantum-inspired simulated bifurcation (SB) solver on an FPGA accelerator (SBM) to solve large MIS instances up to 2,048 spins and evaluates performance via long-run backcasts using a TOPIX-based universe (>1,700 stocks). The best MIS-based strategy (threshold around $\theta\approx0.23$ with inverse-volatility weighting) achieves an annualized return of about $16.3\%$ with $14.0\%$ risk and a Sharpe ratio of roughly $1.16$ from 2013–2023, outperforming major indices such as TOPIX and MSCI Japan Min Vol. The results demonstrate that MIS-based diversification, especially involving smaller-cap stocks with low correlations, can yield superior risk-adjusted performance, and the SBM accelerator provides scalable, practical computation for large-scale market graphs.

Abstract

Correlation-diversified portfolios can be constructed by finding the maximum independent sets (MISs) in market graphs with edges corresponding to correlations between two stocks. The computational complexity to find the MIS increases exponentially as the size of the market graph increases, making the MIS selection in a large-scale market graph difficult. Here we construct a diversified portfolio by solving the MIS problem for a large-scale market graph with a combinatorial optimization solver (an Ising machine) based on a quantum-inspired algorithm called simulated bifurcation (SB) and investigate the investment performance of the constructed portfolio using long-term historical market data. Comparisons using stock universes of various sizes [TOPIX 100, Nikkei 225, TOPIX 1000, and TOPIX (including approximately 2,000 constituents)] show that the SB-based solver outperforms conventional MIS solvers in terms of computation-time and solution-accuracy. By using the SB-based solver, we optimized the parameters of a MIS portfolio strategy through iteration of the backcast simulation that calculates the performance of the MIS portfolio strategy based on a large-scale universe covering more than 1,700 Japanese stocks for a long period of 10 years. It has been found that the best MIS portfolio strategy (Sharpe ratio = 1.16, annualized return/risk = 16.3%/14.0%) outperforms the major indices such as TOPIX (0.66, 10.0%/15.2%) and MSCI Japan Minimum Volatility Index (0.64, 7.7%/12.1%) for the period from 2013 to 2023.

Figures (13)

• Figure 1: Market graph for an $N$-stock universe ($N = 6$). Red nodes are the maximum independent set (MIS).
• Figure 2: Flowchart for simulation of MIS portfolio strategy.
• Figure 3: System architecture of the MIS portfolio simulator.
• Figure 4: Core circuit architecture of the bSB accelerator.
• Figure 5: Performance comparison of the three MIS solvers, SBM (heuristic), NetworkX (heuristic), and OR-tools (exact-solution), in terms of (a) computation-time and (b) relative solution-accuracy (the size of the independent set found). The computation-time (the shorter, the better) and the size of the independent set found (the larger, the better) when solving the MIS problem for each of 10 market graphs having the same size but different edges were measured and averaged over the 10 market graphs. Each value in (b) is the ratio to the largest one of the (averaged) sizes of independent sets found by the three solvers.