Estimating the covariance of asset returns, i.e., the risk model, is a key component of financial portfolio construction and evaluation. Most risk modeling approaches produce a factor model that decomposes the asset variability into two components: the first attributed to a small number of factors that are common among the assets and the second attributed to the idiosyncratic behavior of each asset. Third-party providers typically provide risk models to investors, and while these models are typically of high quality, they may fail to capture important information, e.g., changing market regimes and transient factors. To overcome these limitations, we propose a systematic method based on maximum likelihood estimation to enhance an existing factor model by both refining the given model and adding new statistical factors. Our approach relies only on the observed sequence of realized returns and on the choice of two hyperparameters: the number of additional factors and the half-life parameter that determines the weights assigned to returns in the log-likelihood objective. Importantly, our methodology applies to the situation where asset returns may be missing, making it suitable for typical equity datasets. We demonstrate our approach on the Barra short-term US risk model, a high-quality risk model used in practice, for a universe of US high-capitalization equities. We show that the proposed extension captures structure in the returns that is missed by the original model.

翻译：估计资产收益的协方差（即风险模型）是金融投资组合构建与评估的关键环节。大多数风险建模方法生成因子模型，将资产波动性分解为两部分：第一部分归因于少数在资产间具有共性的共同因子，第二部分归因于各资产的特异性行为。第三方服务商通常向投资者提供风险模型，尽管这些模型通常质量较高，但可能无法捕捉重要信息（如市场机制变化和瞬态因子）。为克服这些局限，我们提出一种基于最大似然估计的系统化方法，通过改进现有模型并添加新统计因子来增强其性能。该方法仅依赖已实现的收益序列观测值，以及两个超参数的选择：额外因子数量和确定对数似然目标中收益权重的半衰期参数。值得注意的是，本方法可处理资产收益存在缺失的情况，因而适用于典型股票数据集。我们在实际使用的高质量风险模型——Barra美国短期风险模型上，以美国高市值股票为样本空间进行了实证。结果表明，所提出的扩展方法能够捕捉原模型遗漏的收益结构特征。