RORAC

As $V$ is a constant, the partial derivatives (21) of the ES-RORAC under the portfolio constraint (16) are similar to those of RORC (24):

$$\frac{\partial \psi_{\alpha}'}{\partial u_i} = - \mathbf{E}[X]\cdot \frac{\mathbf{E}[X_i \vert X \leq - \text{Va... ...{(V+\text{ES}_{\alpha}(X))^2} + \frac{\mathbf{E}[X_i]}{V+\text{ES}_{\alpha}(X)}$$ (25)

$$- \frac{V_i}{V_n} \left( - \mathbf{E}[X]\cdot \frac{\mathbf{E}[X_... ...ES}_{\alpha}(X))^2} + \frac{\mathbf{E}[X_n]}{V+\text{ES}_{\alpha}(X)} \right) .$$