We assess the advantage of combining univariate and multivariate portfolio risk forecasts with the aid of forecast reconciliation techniques. In our analyzes, we assume knowledge of portfolio weights, a standard for portfolio risk management applications. With an extensive simulation experiment, we show that, if the true covariance is known, forecast reconciliation improves over a standard multivariate approach, in particular when the adopted multivariate model is misspecified. However, if noisy proxies are used, correctly specified models and the misspecified ones (for instance, neglecting spillovers) turn out to be, in several cases, indistinguishable, with forecast reconciliation still providing improvements. The noise in the covariance proxy plays a crucial role in determining the improvement of both the forecast reconciliation and the correct model specification. An empirical analysis shows how forecast reconciliation can be adopted with real data to improve traditional GARCH-based portfolio variance forecasts.

翻译：我们评估了借助预测调和技术结合单变量与多变量投资组合风险预测的优势。在分析中，我们假设已知投资组合权重——这是投资组合风险管理应用的标准设定。通过大规模模拟实验，我们证明：若真实协方差已知，预测调和相较于标准多变量方法能带来改进，尤其是在所采用的多变量模型被误设时。然而，若使用含噪声的代理变量，正确设定的模型与误设模型（例如忽略溢出效应）在多类情形下表现为难以区分，此时预测调和仍能提供改进。协方差代理变量的噪声在决定预测调和及正确模型规范改进程度中起关键作用。实证分析表明，预测调和可应用于实际数据，以改进基于传统GARCH的投资组合方差预测。