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Multiperiod Maximum Loss is time unit invariant.

Raimund M Kovacevic1, Thomas Breuer2

  • 1Vienna University of Technology, Wiedner Hauptstraße 8/E105-4, 1040 Vienna, Austria.

Springerplus
|August 27, 2016
PubMed
Summary
This summary is machine-generated.

Time unit invariance is a new requirement for multiperiod risk measures. Only multiperiod Maximum Loss and entropic risk measures satisfy this property, unlike Value at Risk and Expected Shortfall.

Keywords:
Ambiguity aversionMultiperiod risk measuresRelative entropy

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Area of Science:

  • Quantitative Finance
  • Risk Management
  • Financial Mathematics

Background:

  • Multiperiod risk measures are crucial for financial decision-making over extended horizons.
  • Assessing the consistency of risk measures across different time scales is essential.
  • Existing risk measures may not adequately capture time-dependent risk dynamics.

Purpose of the Study:

  • Introduce and define time unit invariance for multiperiod risk measures.
  • Investigate which common risk measures satisfy this new invariance property.
  • Provide a theoretical foundation for developing time-consistent risk management tools.

Main Methods:

  • Formal definition of time unit invariance for risk measures.
  • Analysis of multiperiod Maximum Loss over Kullback-Leibler balls.
  • Evaluation of the entropic risk measure under time unit invariance.
  • Examination of multiperiod Value at Risk and Expected Shortfall.

Main Results:

  • Time unit invariance requires multiperiod risk to equal one-period aggregated risk for constant portfolios and i.i.d. risk factors.
  • Multiperiod Maximum Loss and the entropic risk measure are demonstrated to be time unit invariant.
  • Multiperiod Value at Risk and multiperiod Expected Shortfall are shown to lack time unit invariance.

Conclusions:

  • Time unit invariance is a critical property for robust multiperiod risk assessment.
  • The entropic risk measure and Maximum Loss offer superior time consistency compared to Value at Risk and Expected Shortfall.
  • Findings guide the selection and development of more reliable financial risk management instruments.