Estimating Conditional Variances and Covariances: Measurement Accuracy and Implications for Asset Pricing and Portfolio Choice

大多数资产定价理论都将资产的预期回报与其条件方差和协方差联系起来。大量的经验金融学文献证明，这些条件时刻会随着时间的推移而改变。1929年和1987年股市崩盘的实践经验印证了这一结论。不幸的是，条件协方差不能直接观察到。在资产定价理论的检验中，研究人员必须使用条件二阶矩的估计。同样，市场参与者在套期保值、期权定价以及投资组合选择的许多其他方面都使用条件方差和协方差的估计。这个项目解决了以下重要问题：估计的方差和协方差有多准确？如何才能更准确地估计它们呢？不可避免的衡量误差对投资组合选择和资产定价理论测试的影响有多大？在金融领域从事实证工作的研究人员采用了许多策略来适应条件方差和协方差的变化。在流行的策略中有：(1)将可用数据切成短的时间块并假设块内的同方差，(B)单边滚动回归，其中仅使用例如前五年期间的数据来估计给定日期的回报的条件协方差，(C)双边滚动回归，其中使用例如五年滞后和五年领先来估计每个日期的协方差，以及(D)自回归条件异方差(ARCH)模型。这些方法之间的选择传统上是临时的，因为还没有理论来比较它们在环境中的相对效率。本项目解决这个问题的方法是，在使用方法(A)到(D)时，对测量误差建立连续记录的渐近近似。

Most asset pricing theories relate expected returns on assets to their conditional variances and covariances. An enormous literature in empirical finance has documented that these conditional moments change over time. Practical experience as in the 1929 and 1987 stock market crashes reinforces this conclusion. Unfortunately, conditional covariances are not directly observable. In tests of asset pricing theories, researchers must use estimates of conditional second moments. Similarly, market participants use estimates of conditional variances and covariances in hedging, option pricing, and in many other aspects of portfolio selection. This projects addresses the following important questions: How accurate are the estimated variances and covariances? How can they be estimated more accurately? How severely do the inevitable measurement errors affect portfolio selection and tests of asset pricing theories? Researchers doing empirical work in finance have adopted many strategies for accommodating changes in conditional variances and covariances. Among the popular strategies are: (1) chopping the available data into short blocks of time and assuming homoskedasticity within the blocks, (b) one-sided rolling regressions, in which only data from, say, the preceding five year period is used to estimate the conditional covariance of returns at a given date, (c) two-sided rolling regressions, in which covariances are estimated for each date using, say, five years of lags and five years of leads, and (d) Autoregressive Conditional Heteroscedatic (ARCH) models. The choice between these methods has traditionally been ad hoc, since no theory has been available to compare their relative efficiency in settings. This project addresses this problem by developing continuous record asymptotic approximations for the measurement errors when methods (a) through (d) are used.