Academia Sinica * Institute of Statistical Science
Abstract:
When evaluating the tail risk of stock portfolio returns, providing statistically sound solutions for long return horizons is important, but difficult. Furthermore, there are drawbacks to using traditional parametric methods that rely on
strong model assumptions or simulations. This study 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 period, we derive an asymptotic formula to approximate the CTE. Based on this formula, we propose a simple nonparametric estimate
of the unconditional CTE, and show that it is both consistent and asymptotically
normal. Next, we forecast the CTE using a modified form of the nonparametric
estimator. With the help of the asymptotic formula, we evaluate the accuracy of
the CTE predictor by treating it as an interval forecast for furure returns. Simulation studies demonstrate the applicability of our approach. Lastly, we apply the
proposed estimation and predictor to daily S&P 500 index returns.
