Hedging Conditional Value at Risk with options

•We derive an analytic formula for CVaR of stock hedged with put options.•The CVaR of such position can be optimised using linear programming.•The work is a generalisation of Ahn et al. (1999), where VaR was used instead of CVaR.

We present a method of hedging Conditional Value at Risk of a position in stock using put options. The result leads to a linear programming problem that can be solved to optimise risk hedging.