LCARE - Localizing Conditional Autoregressive Expectiles

Abstract

We account for time-varying parameters in the conditional expectile based value at risk (EVaR) model. EVaR appears more sensitive to the magnitude of portfolio losses compared to the quantile-based Value at Risk (QVaR), nevertheless, by fitting the models over relatively long ad-hoc fixed time intervals, research ignores the potential time-varying parameter properties. Our work focuses on this issue by exploiting the local parametric approach in quantifying tail risk dynamics. By achieving a balance between parameter variability and modelling bias, one can safely fit a parametric expectile model over a stable interval of homogeneity. Empirical evidence at three stock markets from [2005][2006][2007][2008][2009][2010][2011][2012][2013][2014] shows that the parameter homogeneity interval lengths account for approximately 1-6 months of daily observations. Our method outperforms models with one-year fixed intervals, as well as quantile based candidates while employing a time invariant portfolio protection (TIPP) strategy for the DAX portfolio. The tail risk measure implied by our model finally provides valuable insights for asset allocation and portfolio insurance.JEL classification: C32, C51, G17

Econometric modeling of risk measures: A selective review of the recent literature

“…As noted by Kuan et al (2009), this paper is concerned mainly with the determination of quantile-based VaR based on expectiles; thus, their models are the same as the CAViaR models of Engle and Manganelli (2004). More recently, Xu et al (2018) considered the potential time-varying parameter property and employed an adaptive method to fit a parametric expectile model for quantifying tail risk dynamics.…”

How Sensitive are Tail-Related Risk Measures in a Contamination Neighbourhood?

“…where I{•} stands for the indicator function. It is well-known that the expectile is the only coherent risk measure possessing elicitability, a desirable property for model selection, generalized regression, forecast ranking and comparative backtesting, Nolde et al (2017); Xu et al (2018). Further, the expectile is the so-called index of prudentiality in financial set-up, i.e., the amount of money added to a position with a pre-specified, sufficiently high gain-loss ratio, Bellini and Di Bernardino (2017); Daouia et al (2017).…”