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** Case study background and formulation of problems**

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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# of Variables |
# of Scenarios |
Objective Value |
Solving Time, PC 3.14GHz (sec) |
||||

Dataset | 4 | 1,264 | 0.01491 | <0.01 | |||
---|---|---|---|---|---|---|---|

Environments |
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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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# of Variables |
# of Scenarios |
Objective Value |
Solving Time, PC 3.14GHz (sec) |
||||

Dataset | 4 | 1,264 | 0.01491 | 0.02 | |||
---|---|---|---|---|---|---|---|

Environments |
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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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# of Variables |
# of Scenarios |
Objective Value |
Solving Time, PC 3.14GHz (sec) |
||||

Dataset | 4 | 1,264 | 0.01491 | 0.01 | |||
---|---|---|---|---|---|---|---|

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 [1].

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 [1]).

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.