Case Study: Calibrating Risk Preferences

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Case study background and problem formulations

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

PROBLEM:
Minimize Meanabs_pen (minimizing objective function)
subject to
Linear = 1 (sum of lambdas)
Box constraints (lower bounds on positions)
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Meanabs_pen = Mean Absolute Penalty
Box constraints = constraints on individual decision variables
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Data and solution in Run-File Environment
Problem Datasets # of Variables # of Scenarios Objective Value Solving Time, PC 2.66GHz (sec)
Dataset1 Problem Statement Data Solution 5 30 0.000833137 <0.01

Data and solution in MATLAB Environment
Problem Datasets # of Variables # of Scenarios Objective Value Solving Time, PC 2.66GHz (sec)
Dataset1 Matlab code Data Solution 5 30 0.000833137 <0.01

CASE STUDY SUMMARY
This case study extracts risk preferences of investors by solving a linear regression model with linear constraints on coefficients. “Risk preferences” are expressed by a risk functional (a deviation measure), which is used by an investor for measuring risk and solving portfolio optimization problems. Contrary to the classical Markowitz portfolio theory, where investors measure risk by standard deviation, this case study assumes that the unknown deviation measure belongs to a class of Mixed CVaR Deviations. In particular, we consider the case when the Mixed CVaR Deviation is a weighted average of the following five CVaR Deviation terms with confidence levels 50%, 75%, 85%, 95%, and 99% (theory and description of this case are available in Kalinchenko et al (2012)). The Mixed CVaR Deviation has five weighting parameters (lambdas), which are nonnegative and sum up to 1. These lambda coefficients are estimated by matching the market option prices with prices expressed via generalized CAPM pricing relations. Matching is done by minimizing a L1 (the error term is sum of absolute values of the differences between market and calculated prices).

This webpage contains files for one instance of the regression problem, which is solved in PSG Run-File Text Environment.
To run this Case Study in the PSG MATLAB Environment:
1) Click on the link files for running CS_Calibrating_Risk_Preferences in PSG MATLAB Environment and extract two M-files and file OptionPrices.csv;
2) Create sub-folder CS_Calibrating_Risk_Preferences in folder …PSGMATLAB and place two M-files to this sub-folder;
3) Create sub-folder CS_Calibrating_Risk_PreferencesData in folder …PSGMATLAB and place file IndexReturns.mat to this sub-folder;
4) Run files CalibratingRiskPreferences_ExtractData_POSTING_VERSION.m and then run file CS_CalibratingRiskPreferences_POSTING_VERSION.m

References
• Kalinchenko, K., Uryasev, S. and R.T. Rockafellar (2012). Calibrating risk preferences with generalized CAPM based on mixed CVaR deviation. Journal of Risk, 15(1), pp. 1–26.