Title: Controlling tail risk measures with estimation error
Authors: Tetsuya Kaji - University of Chicago (United States) [presenting]
Hyungjune Kang - Two Sigma (United States)
Abstract: Assessment of risk and its control play an important role in investment decision making, financial regulations, actuary science, and operations research. In practice, accuracy of estimated risk is subject to estimation error. While the estimation error can be estimated in many cases, it remains a question as to how the error thus estimated can be incorporated into actual control of the true but unobservable risk. We propose the class of risk measures, called the tail risk measures, that give the upper bounds below which the quantities of interest fall with probability at least as much as a pre-specified confidence level. We show that a simple rule based on the Bonferroni inequality can control a tail risk measure at a desired level, even when the true risk is unknown and needs to be estimated. Most popular risk measures such as Value-at-Risk and expected shortfall are interpreted as tail risk measures. For coherent tail risk measures, the true risk of any combination of assets can be controlled by knowledge of estimated risk and estimated error of individual assets. Empirical applications illustrate how the proposed concept can be applied to practical risk control problems.