Investment Risk Measurement Based on Quantiles and Expectiles

Abstract

In the presented research, we attempt to examine special investment risk measurement. We use quantile regression as a model by describing more general properties of the response distribution. In quantile regression, we assume regression effects on the conditional quantile function of the response. In regression modelling, the focus is on extending linear regression (OLS), and in this paper we seek to apply expectile regression. The purpose of using both approaches is investment risk measurement. Both regression models are a version of least weighted squares model. The families of risk measures most commonly used in practice are the Value‑at‑Risk (VaR) and the Conditional Value‑at‑Risk (CVaR), which can be estimated by quantiles or expectiles in the tail of the response distribution.

Keywords

• quantile
• expectile
• VaR
• CVaR
• least asymmetrically weighted squares