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Risk Analysis through the Half-Normal Distribution

Author

Listed:
  • 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)

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.

Suggested Citation

  • Maria-Teresa Bosch-Badia & Joan Montllor-Serrats & Maria-Antonia Tarrazon-Rodon, 2020. "Risk Analysis through the Half-Normal Distribution," Mathematics, MDPI, vol. 8(11), pages 1-27, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2080-:d:448978
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    References listed on IDEAS

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