LAUSR

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)