**Optimization Problem 2**

Code in PSG Text format:

```
minimize
cvar2_dev(0.75,matrix_s)
value:
cvar_risk(0.75,matrix_s)
```
*JRFM* **2019**, *12*, 107

The code includes two parts. The first part begins with the keyword "minimize" indicating that the objective function is minimized. It implements Step 1 of the Optimization Problem 2, which minimizes deviation from the CVaR quadrangle (for determining the optimal vector *C*<sup>∗</sup> of regression coefficients without an intercept). The PSG function cvar2\_dev(0.75,matrix\_s) calculates deviation Dα(*<sup>Z</sup>*0(*C*)) with α = 0.75. The matrix\_s contains scenarios of the residual of the regression without an intercept *<sup>Z</sup>*0(*C*) = *V* − *CTY*.

The second part of the code begins with the keyword "value." This part implements Step 2 of the Optimization Problem 2 for calculating the optimal value of intercept *<sup>C</sup>*<sup>∗</sup>0. The PSG function cvar\_risk(0.75,matrix\_s) calculates *CVaR*α(*<sup>Z</sup>*0(*C*<sup>∗</sup>)) with α = 0.75 at the optimal point *C*<sup>∗</sup>.
