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.

翻译：相关性分散投资组合可通过在市场图中寻找最大独立集（MIS）来构建，其中市场图的边对应两只股票之间的相关性。寻找MIS的计算复杂度随市场图规模呈指数增长，这使得在大规模市场图中选择MIS变得困难。本文通过使用基于量子启发式算法——模拟分岔（SB）的组合优化求解器（伊辛机），解决大规模市场图的MIS问题来构建分散投资组合，并利用长期历史市场数据研究所构建投资组合的投资绩效。对多种规模股票池（TOPIX 100、日经225、TOPIX 1000以及包含约2000只成分股的TOPIX）的比较表明，基于SB的求解器在计算时间和解精度方面均优于传统MIS求解器。通过使用基于SB的求解器，我们迭代回测仿真（该仿真基于覆盖超过1700只日本股票的大规模股票池，计算10年长期区间内MIS投资组合策略的绩效）优化了MIS投资组合策略的参数。研究发现，在2013年至2023年期间，最优MIS投资组合策略（夏普比率=1.16，年化收益/风险=16.3%/14.0%）优于主要指数，如TOPIX（0.66，10.0%/15.2%）和MSCI日本最小波动率指数（0.64，7.7%/12.1%）。