What is the Rockafellar-Uryasev CVaR formulation?

CVaR_alpha = min_{eta} { eta + (1/(1-alpha)) * E[max(-r*w - eta, 0)] }. This converts CVaR minimization into a linear program with auxiliary variables z_s = max(-r_s*w - eta, 0) for each scenario s.

Why is CVaR preferred to VaR for optimization?

CVaR is a coherent risk measure (sub-additive), so the optimizer exploits diversification. VaR can increase with diversification and leads to non-convex optimization problems.

CVaR Conditional Value-at-Risk Portfolio Optimization

Optimize portfolio to minimize CVaR (Expected Shortfall) at a given confidence level. Formulated as a linear program using Rockafellar-Uryasev representation over scenario returns.

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Frequently Asked Questions

What is the Rockafellar-Uryasev CVaR formulation?

Why is CVaR preferred to VaR for optimization?