# Case Study: CVaR Norm Regression

Instructions for optimization with PSG Run-File, PSG MATLAB Toolbox, PSG MATLAB Subroutines and PSG R.

PROBLEM1: problem_CVaR_Risk_Abs_Style_Classification_Fidelity_Magellan

minimizing cvar_risk (using absolute value of loss)
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Dataset 4 1,264 0.01491 <0.01 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) Environments Run-File Problem Statement Data Solution Matlab Toolbox Data Matlab Subroutines Matlab Code Data R R Code Data

PROBLEM2: problem_CVaR_Risk_Abs_Style_Classification_Fidelity_Magellan

minimizing cvar_risk (with doubled set of scenarios)
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Dataset 4 1,264 0.01491 0.02 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) Environments Run-File Problem Statement Data Solution Matlab Toolbox Data Matlab Subroutines Matlab Code Data R R Code Data

PROBLEM3: problem_CVaR_Max_Style_Classification_Fidelity_Magellan

minimizing cvar_max_risk
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cvar_max_risk = cvar maximum risk function
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Dataset 4 1,264 0.01491 0.01 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) Environments Run-File Problem Statement Data Solution Matlab Toolbox Data Matlab Subroutines Matlab Code Data R R Code Data
CASE STUDY SUMMARY

This case study conducts Linear Regression using CVaR Norm Error function, see .
We consider three alternative implementations for the same Linear Regression problem:
1. The CVaR Norm calculated as the superposition of the CVaR Risk and the absolute value of regression residuals (i.e., absolute value of the standard PSG linear losses).
2. The CVaR Norm is calculated using the standard CVaR Risk function with doubled design matrix (the designed matrix is formed by doubling the number of observations and changing the confidence level, see, Proposition 4 in ).
3. The CVaR Norm is calculated with PSG CVaR Max Risk function, which is CVaR of the maximum of several loss functions on every scenario.
We used the dataset from the case study “Case Study: Style Classification with Quantile Regression”.
The data contains returns of the Fidelity Magellan Fund as a dependent variable. Russell Value Index (RUJ), Russell 1000 Value Index (RLV), Russell 2000 Growth Index (RUO), and Russell 1000 Growth Index (RLG) are taken as independent variables. Data include 1,264 observations.

References

1. Mafusalov, A. and S. Uryasev. Conditional Value-at-Risk (CVaR) Norm: Stochastic Case. Research Report 2013-5, ISE Dept., University of Florida, 2013.