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2012•Systems Engineering ProcediaOpen access

Coherent Distortion Risk Measures in Portfolio Selection

Ming Bin Feng, Ken Seng Tan

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Abstract

The theme of this paper relates to solving portfolio selection problems using linear programming. We extend the well-known linear optimization framework for Conditional Value-at-Risk (CVaR)-based portfolio selection problems [1], [2] to optimization over a more general class of risk measure known as the class of Coherent Distortion Risk Measure (CDRM). CDRM encompasses many well-known risk measures including CVaR, Wang Transform measure, Proportional Hazard measure, and lookback measure. A case study is conducted to illustrate the flexibility of the linear optimization scheme, explore the efficiency of the 1/n-portfolio strategy, as well as compare and contrast optimal portfolios with respect to different CDRMs.

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What this paper is about

The theme of this paper relates to solving portfolio selection problems using linear programming. We extend the well-known linear optimization framework for Conditional Value-at-Risk (CVaR)-based portfolio selection problems [1], [2] to optimization over a more general class of risk measure known as the class of Coherent Distortion Risk Measure (CDRM). CDRM encompasses many well-known risk measures including CVaR, Wang Transform measure, Proportional Hazard measure, and lookback measure. A case study is conducted to illustrate the flexibility of the linear optimization scheme, explore the efficiency of the 1/n-portfolio strategy, as well as compare and contrast optimal portfolios with respect to different CDRMs.

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Available abstract

The theme of this paper relates to solving portfolio selection problems using linear programming. We extend the well-known linear optimization framework for Conditional Value-at-Risk (CVaR)-based portfolio selection problems [1], [2] to optimization over a more general class of risk measure known as the class of Coherent Distortion Risk Measure (CDRM). CDRM encompasses many well-known risk measures including CVaR, Wang Transform measure, Proportional Hazard measure, and lookback measure. A case study is conducted to illustrate the flexibility of the linear optimization scheme, explore the efficiency of the 1/n-portfolio strategy, as well as compare and contrast optimal portfolios with respect to different CDRMs.

Key concepts: CVAR, Portfolio optimization, Risk measure, Portfolio, Expected shortfall, Mathematical optimization, Coherent risk measure, Spectral risk measure

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