Journal of Risk

Shortfall deviation risk: an alternative for risk measurement

Marcelo Brutti Righi and Paulo Sergio Ceretta

  • SDR contemplates the probability of adverse events and the variability of an expectation.
  • We demonstrate that SDR is a coherent risk measure. 
  • SDR offers greater protection in risk measurement compared with VaR and ES.


We present the shortfall deviation risk (SDR): a risk measure that represents the expected loss that occurs with a 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 considering 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. Examples using real and simulated data allow us to conclude that SDR offers greater protection in risk measurement than value-at-risk and ES, especially in times of significant turbulence in riskier scenarios.

Sorry, our subscription options are not loading right now

Please try again later. Get in touch with our customer services team if this issue persists.

New to View our subscription options

You need to sign in to use this feature. If you don’t have a account, please register for a trial.

Sign in
You are currently on corporate access.

To use this feature you will need an individual account. If you have one already please sign in.

Sign in.

Alternatively you can request an individual account here