The Covariance Structure between Liquid and Illiquid Assets
针对非流动性资产（如私募股权、贷款、房地产）因缺乏报价而难以估计风险的问题，提出一种横截面方法，利用资产间的价格离散度估计方差和协方差，构建的协方差矩阵与基于时间序列的流动性资产矩阵一致，为包含两类资产的投资组合提供了统一的风险评估框架。
The traditional methods of estimating investment risk based on the observed variation of asset prices falter on sparsely traded assets owing to the lack of price quotes. The price variance of illiquid assets such as private equity, loans, or real estate is, if calculable at all, not meaningful. Nor does the observed covariance between illiquid assets indicate a degree of proximity in the price behavior. The author proposes a cross-sectional approach instead, taking the price dispersion across assets as an estimate of variance and using the so-called cross dispersion of covariance. The covariance matrix computed in this way over traded and nontraded assets seems coherent with the (sub)matrix computed over time on traded assets. The cross-sectional matrix sets a universal framework for managing portfolios invested in traded and nontraded assets, making all-encompassing risk assessments possible.