A1500
Title: A bootstrap equality test to compare portfolio value at risk and expected shortfall
Authors: Mario Maggi - University of Pavia (Italy) [presenting]
Pierpaolo Uberti - University of Milano-Bicocca (Italy)
Abstract: In financial risk management, assessing the risk of an investment is fundamental, both from an absolute perspective and relative to some given benchmark. In practice, it often happens that an authority prescribes the risk measure to be used by the investors. For example, the international regulatory framework for banks Basel III imposes the expected shortfall at a given significance level in substitution to the value at risk. The aim is to propose a statistical test to measure if two investments are statistically significantly different in terms of value at risk and/or expected shortfall. The test is defined in non-parametric general settings. This permits comparing the risk of different investments without assuming a theoretical distribution of the returns. A method is also provided to build confidence intervals around the risk indicator of a given portfolio or asset. The only necessary assumption behind the methodology is that the risk measure verifies the translation invariance property. Although the focus is on the value at risk and the expected shortfall, the present approach is very general and can potentially be applied to a large class of risk measures. To support the proposal, some applications on real financial data are provided, and the results are discussed.
