Background

Problem 1. Minimizing Rockafellar Error

Simplified Problem Statement

Mathematical Problem Statement

Problem dimension and solving time

Solution in Run-File Environment

Problem 2. Minimizing Partial Moment Penalty

Simplified Problem Statement

Mathematical Problem Statement

Problem dimension and solving time

Solution in Run-File Environment

Solution in MATLAB Environment

 

 

Background

This case study applies Mixed Percentile Regression for the estimation of Conditional Value-at-Risk (CVaR) of return distribution of a mutual fund.

The approach is similar to the percentile regression used by Bassett and Chen (2001) for the estimation of the tail percentile of the return distribution of the mutual fund. Bassett and Chen (2001) regresses the percentile of the fund return by several indices. The estimated coefficients represent the fund’s style with respect to each of the indices, and therefore the procedure is called “style classification.”

We regresses CVaR of the return distribution of the Fidelity Magellan Fund on the Russell Value Index (RUJ), RUSSELL 1000 VALUE INDEX (RLV), Russell 2000 Growth Index (RUO) and Russell 1000 Growth Index (RLG). We want to calculate coefficients for the explanatory variables of the tail of the distribution of residuals (these coefficients may differ from the regression coefficients for the mean and the median of the distribution). 0.9-CVaR with confidence level 0.9 is approximated by the weighted average of four Value-at-Risks (VaRs) with confidence levels 0.92, 0.94, 0.96, 0.98 .

 

Problem 1

 

Simplified Problem Statement

 

Minimize Rockafellar Error Function (ro_err)

 

where

 

ro_err = Rockafellar Error Function

 

Mathematical Problem Statement

 

 

Problem dimension and solving time

 

 

Solution in Run-File Environment

 

 

Input Files to run CS:

 

Output Files:

 

Problem 2

 

Simplified Problem Statement

 

Minimize alpha*Pm_pen + (1-alpha)*Pm_pen_g

 

where

 

Pm_pen = Partial Moment Penalty for Loss

Pm_pen_g = Partial Moment Penalty for Gain

 

 

Mathematical Problem Statement

 

 

Problem dimension and solving time

 

 

Solution in Run-File Environment

 

 

Input Files to run CS:

 

Output Files:

 

Solution in MATLAB Environment

 

Solved with riskprog PSG subroutine (General (Text) Format of PSG in MATLAB):

 

Input Files to run CS: