In evaluating tail risks for returns of stock portfolios, it is important yet difficult to deliver a statistically sound solution when the return horizon is long. Traditional parametric methods which rely on strong model assumptions or simulating samples suffer various drawbacks. The present paper investigates the problem by focusing on an important risk measure, the conditional tail expectation (CTE), under a general multivariate stochastic volatility model. To overcome the estimation difficulties caused by the long duration, we adopt a new approach in which an asymptotic formula for approximating the CTE is derived. Based on the formula, a simple non-parametric estimate of the unconditional CTE is proposed and shown to be consistent and asymptotically normal. We further forecast the CTE by using a predictor which is modified from the non-parametric estimator. Treating Statistica Sinica: Newly accepted Paper (accepted author-version subject to English editing)

中文翻译：

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长期回报的条件尾部预期的估计和预测

在评估股票投资组合回报的尾部风险时，当回报期很长时，提供一个统计上合理的解决方案很重要但也很困难。依赖强模型假设或模拟样本的传统​​参数方法存在各种缺陷。本论文通过在一般多元随机波动率模型下关注重要的风险度量条件尾期望 (CTE) 来研究该问题。为了克服持续时间长造成的估计困难，我们采用了一种新方法，其中推导了近似 CTE 的渐近公式。基于该公式，提出了一个简单的无条件 CTE 的非参数估计，并证明是一致的和渐近正态的。我们通过使用从非参数估计器修改而来的预测器进一步预测 CTE。Treating Statistica Sinica：新接受的论文（接受的作者版本需英文编辑）