Folio Lab/Documentation

Minimum EVaR

Minimise Entropic Value-at-Risk — the tightest convex upper bound on CVaR derived from the moment-generating function. EVaR is coherent and consistently more conservative than CVaR.

Overview

Entropic Value-at-Risk (EVaR), introduced by Ahmadi-Javid (2012), is a coherent risk measure that bounds VaR and CVaR from above. It comes from a Chernoff-style argument applied to the loss distribution and inherits very strong properties: it is convex, monotonic, translation invariant, and positively homogeneous.

For tail-risk-sensitive portfolios — where you care about the probability and the magnitude of large losses — EVaR is a useful stricter alternative to CVaR.

Mathematical Formulation

For a loss random variable with moment-generating function , EVaR at confidence level is:

The portfolio problem is:

Folio Lab uses skfolio's MeanRisk with RiskMeasure.EVAR at by default. The problem is exponential-cone representable and is solved with CLARABEL with SCS as a fallback.

EVaR vs CVaR

For any confidence level, the inequality holds. EVaR is therefore always more conservative — useful when the tail is fat or when CVaR estimation noise is high.

Advantages & Limitations

Advantages

  • Coherent risk measure: Subadditive, monotonic, positively homogeneous.
  • Tighter upper bound: Stricter than CVaR; protective in fat-tail regimes.
  • Convex problem: Tractable via exponential-cone solvers.
  • Differentiable in : Smooth optimisation surface.

Limitations

  • Conservative: Can give up upside relative to CVaR.
  • Solver requirements: Needs an exponential-cone capable solver.
  • Less intuitive: Harder to communicate to non-technical stakeholders than VaR/CVaR.
  • Sample-size sensitive: Tail estimation requires data.

References

  • Ahmadi-Javid, A. (2012). "Entropic value-at-risk: A new coherent risk measure." Journal of Optimization Theory and Applications, 155(3), 1105-1123.
  • Ahmadi-Javid, A., & Fallah-Tafti, M. (2019). "Portfolio optimization with entropic value-at-risk." European Journal of Operational Research, 279(1), 225-241.
  • skfolio documentation — skfolio.RiskMeasure.EVAR.