Shortfall Deviation Risk: An alternative to risk measurement

TL;DR

The paper introduces Shortfall Deviation Risk (SDR), a new coherent risk measure combining expected shortfall and deviation, providing better protection during turbulent, high-risk scenarios.

Contribution

It proposes SDR and Shortfall Deviation (SD), establishing their theoretical properties and demonstrating SDR's advantages over VaR and ES in risk measurement.

Findings

SDR is a coherent risk measure with dual representation.

SDR offers greater protection in turbulent risk scenarios.

SDR outperforms VaR and ES in real and simulated data.

Abstract

We present the Shortfall Deviation Risk (SDR), a risk measure that represents the expected loss that occurs with certain probability penalized by the dispersion of results that are worse than such an expectation. SDR combines Expected Shortfall (ES) and Shortfall Deviation (SD), which we also introduce, contemplating two fundamental pillars of the risk concept, the probability of adverse events and the variability of an expectation, and considers extreme results. We demonstrate that SD is a generalized deviation measure, whereas SDR is a coherent risk measure. We achieve the dual representation of SDR, and we discuss issues such as its representation by a weighted ES, acceptance sets, convexity, continuity and the relationship with stochastic dominance. Illustrations with real and simulated data allow us to conclude that SDR offers greater protection in risk measurement compared with VaR and ES, especially in times of significant turbulence in riskier scenarios.