  The entropic value-at-risk (EVaR) is a new coherent risk measure, which is an
upper bound for both the value-at-risk (VaR) and conditional value-at-risk
(CVaR). As important properties, the EVaR is strongly monotone over its domain
and strictly monotone over a broad sub-domain including all continuous
distributions, while well-known monotone risk measures, such as VaR and CVaR
lack these properties. A key feature for a risk measure, besides its financial
properties, is its applicability in large-scale sample-based portfolio
optimization. If the negative return of an investment portfolio is a
differentiable convex function, the portfolio optimization with the EVaR
results in a differentiable convex program whose number of variables and
constraints is independent of the sample size, which is not the case for the
VaR and CVaR. This enables us to design an efficient algorithm using
differentiable convex optimization. Our extensive numerical study shows the
high efficiency of the algorithm in large scales, compared to the existing
convex optimization software packages. The computational efficiency of the EVaR
portfolio optimization approach is also compared with that of CVaR-based
portfolio optimization. This comparison shows that the EVaR approach generally
performs similarly, and it outperforms as the sample size increases. Moreover,
the comparison of the portfolios obtained for a real case by the EVaR and CVaR
approaches shows that the EVaR approach can find portfolios with better
expectations and VaR values at high confidence levels.
