Tail Risks in Corporate Finance: Simulation-Based Analyses of Extreme Values

Abstract

Recently, simulation-based methods for assessing company-specific risks have become increasingly popular in corporate finance. This is because modern capital market theory, with its assumptions of perfect and complete capital markets, cannot satisfactorily explain the risk situation in companies and its effects on entrepreneurial success. Through simulation, the individual risks of a company can be aggregated, and the risk effect on a target variable can be shown. The aim of this article is to investigate which statistical methods can best assess tail risks in the overall distribution of the target variables. By doing so, the article investigates whether extreme value theory is suitable to model tail risks in a business plan independent of company-specific data. For this purpose, the simulated cash flows of a medium-sized company are analyzed. Different statistical ratios, statistical tests, calibrations, and extreme value theory are applied. The findings indicate that the overall distribution of the simulated cash flows can be multimodal. In the example studied, the potential loss side of the cash flow exhibits a superimposed, well-delimitable second distribution. This tail distribution is extensively analyzed through calibration and the application of extreme value theory. Using the example studied, it is shown that similar tail risk distributions can be modeled both by calibrating the simulation data in the tail and by using extreme value theory to describe it. This creates the possibility of working with tail risks even if only a few planning data are available. Thus, this approach contributes to systematically combining risk management and corporate finance and significantly improving corporate risk management. Based on these findings, further analyses can be performed in terms of risk coverage potential and rating to improve the risk situation in a company.