Shortfall Deviation Risk: An alternative to risk measurement

We present the Shortfall Deviation Risk (SDR), a risk measure that represents the expected loss that occur with certain probability penalized by the dispersion of results worse than such expectation. The SDR combines the Expected Shortfall (ES) and the Shortfall Deviation (SD), which we also introduce, contemplating the two fundamental pillars of the risk concept, the probability of adverse events (ES) and the variability of an expectation (SD), and considers extreme results. We demonstrate that the SD is a generalized deviation measure, whereas the SDR is a coherent risk measure. We achieve the dual representation of the SDR, and we discuss issues such as its representation by a weighted ES, acceptance sets, convexity, continuity and the relationship with stochastic dominance. Illustrations using Monte Carlo simulation and real data indicate that the SDR offers greater protection to measure risk than other measures, especially in turbulent times.