How to do big portfolio selection is very important but challenging for both researchers and practitioners. In this paper, we propose a new graph-based conditional moments (GRACE) method to do portfolio selection based on thousands of stocks or more. The GRACE method first learns the conditional quantiles and mean of stock returns via a factor-augmented temporal graph convolutional network, which guides the learning procedure through a factor-hypergraph built by the set of stock-to-stock relations from the domain knowledge as well as the set of factor-to-stock relations from the asset pricing knowledge. Next, the GRACE method learns the conditional variance, skewness, and kurtosis of stock returns from the learned conditional quantiles by using the quantiled conditional moment (QCM) method. The QCM method is a supervised learning procedure to learn these conditional higher-order moments, so it largely overcomes the computational difficulty from the classical high-dimensional GARCH-type methods. Moreover, the QCM method allows the mis-specification in modeling conditional quantiles to some extent, due to its regression-based nature. Finally, the GRACE method uses the learned conditional mean, variance, skewness, and kurtosis to construct several performance measures, which are criteria to sort the stocks to proceed the portfolio selection in the well-known 10-decile framework. An application to NASDAQ and NYSE stock markets shows that the GRACE method performs much better than its competitors, particularly when the performance measures are comprised of conditional variance, skewness, and kurtosis.

翻译：如何进行大规模投资组合选择对研究者与实践者至关重要且充满挑战。本文提出一种新的基于图的条件矩（GRACE）方法，可基于数千只甚至更多股票实现投资组合选择。GRACE方法首先通过因子增强的时间图卷积网络学习股票收益的条件分位数与条件均值——该网络借助领域知识构建的股票间关系超图与资产定价知识构建的因子-股票关系超图来引导学习过程；继而利用分位数条件矩（QCM）方法从已学习的条件分位数中推导股票收益的条件方差、偏度与峰度。QCM方法作为监督学习框架，能够学习这些条件高阶矩，从而大幅克服经典高维GARCH类方法的计算困难。此外，基于回归特性的QCM方法可允许条件分位数建模存在一定程度的误设定。最后，GRACE方法利用已学习的条件均值、方差、偏度与峰度构建多种绩效度量指标，这些指标在著名的十分位框架中作为股票排序标准用于投资组合选择。对纳斯达克与纽约证券交易所股票市场的实证研究表明，当绩效度量指标包含条件方差、偏度与峰度时，GRACE方法的业绩显著优于其竞争对手。