高频和低频数据的合理使用一直是投资组合领域的重要问题之一. 文章将混频的思想引入投资组合策略中, 首先利用包含长期信息的低频数据构建CVaR约束, 并将其引入基于高频已实现协方差估计量的全局方差最小(GMV)策略中. 在协波动率的估计量和预测方法上, 文章将一种最优滚动窗宽选择方法与常用的HAR 预测模型相结合, 对具有降噪纠偏特性的预平均波动率估计量(PRVM) 进行了样本外预测. 基于A股2011年--2018年的1分钟高频交易数据, 实证结果表明, 与等权重以及GMV 策略相比, 文章提出的混频策略在降低日最大损失和标准差方面明显具有更优的表现. 其在实现短期风险分散化的同时, 显著降低了投资组合在更长时期内的损失, 特别是显著改善了投资组合在2015年``615''股灾期间的资产权重分配情况. 此外, 改进后的协波动率预测模型效果在预测步长为周和旬时, 比使用默认窗宽的基础模型更优.

In the domain of portfolio optimization, the proper use of high-frequency and low-frequency strategies is one of the most important questions. This paper aims to bring the notion of mixed-frequency into portfolio optimization. Firstly, we use low-frequency data that contains long-term information to construct CVaR constaints, and then bring it into the global minimum variance (GMV) high-frequency portfolio strategy. In terms of co-volatility estimator and forecasting method, this paper combines an optimal window selection method with the popular HAR model, and uses it to perform out-of-sample prediction upon the pre-averaging volatility matrix (PRVM), which is capable of dealing with the microstructure noise. Utilizing the 1-minute high-frequency data of all stocks in A-share market spanning from 2011 to 2018, the empirical results show that, compared to equally-weighted and GMV startegy, the mixed-frequency GMV-CVaR strategy performs better in terms of lowering the daily maximum losses and standard deviation. The GMV-CVaR can diversify short-term risk while significantly lowering loss in the longer horizon. Especially when coming across the ``615'' stock crash in 2015, the allocation of portfolio weight is improved using GMV-CVaR. Moreover, the modified HAR model performs better than basic model on weekly and biweekly predictions.