Risk Analysis through the Half-Normal Distribution

Maria-Teresa Bosch-Badia, Joan Montllor-Serrats and Maria-Antonia Tarrazon-Rodon
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Maria-Teresa Bosch-Badia: Deparment of Busines, Campus de Montilivi, Universitat de Girona, 17071 Girona, Spain
Joan Montllor-Serrats: Department of Business, Universitat Autonoma de Barcelona, 08193 Cerdanyola del Valles, Spain
Maria-Antonia Tarrazon-Rodon: Department of Business, Universitat Autonoma de Barcelona, 08193 Cerdanyola del Valles, Spain

Mathematics, 2020, vol. 8, issue 11, 1-27

Abstract: We study the applicability of the half-normal distribution to the probability–severity risk analysis traditionally performed through risk matrices and continuous probability–consequence diagrams (CPCDs). To this end, we develop a model that adapts the financial risk measures Value-at-Risk (VaR) and Conditional Value at Risk (CVaR) to risky scenarios that face only negative impacts. This model leads to three risk indicators: The Hazards Index-at-Risk (HIaR), the Expected Hazards Damage (EHD), and the Conditional HIaR (CHIaR). HIaR measures the expected highest hazards impact under a certain probability, while EHD consists of the expected impact that stems from truncating the half-normal distribution at the HIaR point. CHIaR, in turn, measures the expected damage in the case it exceeds the HIaR. Therefore, the Truncated Risk Model that we develop generates a measure for hazards expectations (EHD) and another measure for hazards surprises (CHIaR). Our analysis includes deduction of the mathematical functions that relate HIaR, EHD, and CHIaR to one another as well as the expected loss estimated by risk matrices. By extending the model to the generalised half-normal distribution, we incorporate a shape parameter into the model that can be interpreted as a hazard aversion coefficient.

Keywords: half-normal distribution; generalised half-normal distribution; risk matrices; continuous probability–consequence diagrams (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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