lCARE – localizing Conditional AutoRegressive Expectiles

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- 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.