Statistics and Its Interface

Volume 8 (2015)

Number 3

A regression analysis of expected shortfall

Pages: 295 – 303

DOI: http://dx.doi.org/10.4310/SII.2015.v8.n3.a4

Authors

Zongwu Cai (Department of Economics, University of Kansas, Lawrence, Ks., U.S.A.; and the Wang Yanan Institute for Studies in Economics, MOE Key Laboratory of Econometrics, and Fujian Key Laboratory of Statistical Sciences, Xiamen University, Xiamen, Fujian, China)

Jia Su (Institute for Quantitative Economics, Huaqiao University, Xiamen, Fujian, China)

Sufianti (Wang Yanan Institute for Studies in Economics, MOE Key Laboratory of Econometrics, and Fujian Key Laboratory of Statistical Sciences, Xiamen University, Xiamen, Fujian, China)

Abstract

To estimate the expected shortfall, a coherent risk measure, this paper proposes an easily implemented regression technique based on a proportional mean residual life regression model with explanatory (lagged) variables. The parameters are estimated by using a quasi-likelihood method and the asymptotic normality of the proposed estimator is derived under an α-mixing process assumption. Based on a simulation study, the proposed estimator performs fairly well. In the empirical study, the backtesting procedure is conducted based on the daily and weekly return of S&P 500 Index using the 95% confidence level. The performance of the model is evaluated by its ability to accurately estimate ES compared with two more alternative models. The results generally favor the proposed model over the alternative models.

Keywords

backtesting method, coherent risk, expected shortfall, proportional mean residual life function, quasi-likelihood estimation, risk management, semiparametric modeling

2010 Mathematics Subject Classification

Primary 91B30. Secondary 37M10.

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Published 17 April 2015