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Risk measure index tracking model

Author

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  • Sant’Anna, Leonardo Riegel
  • Righi, Marcelo Brutti
  • Müller, Fernanda Maria
  • Guedes, Pablo Cristini

Abstract

We take a standard index tracking (IT) optimization model and include seven risk measures as constraints, as we seek to estimate portfolios that not only aim at tracking the market benchmark but also have their risk constrained by the market risk. We consider seven risk measures: Expected Loss (EL), Semi-deviation (SD−), Expected Loss Deviation (ELD), Expected Shortfall (ESα), Shortfall Deviation (SDα), Shortfall Deviation Risk (SDRα), and Maximum Loss (ML), so that we have measures that assess the loss, deviation, and both risk concepts simultaneously. We use the S&P 500 and a sample of 501 stocks with daily returns from 2006 to 2019. Our findings show that some risk measures result in portfolios with tighter risk (mainly ESα and SDRα) than others (mainly EL, ELD, SDα and SD−), and that such risk reduction is followed systematically by larger tracking error. Then, we propose two performance metrics to consolidate both tracking error and risk in one single result. This analysis show that SD−, SDα, and ESα stand out as the most prominent risk measures to be used as constraints in the optimization, as they combined low tracking error and risk.

Suggested Citation

  • Sant’Anna, Leonardo Riegel & Righi, Marcelo Brutti & Müller, Fernanda Maria & Guedes, Pablo Cristini, 2022. "Risk measure index tracking model," International Review of Economics & Finance, Elsevier, vol. 80(C), pages 361-383.
    • Handle: RePEc:eee:reveco:v:80:y:2022:i:c:p:361-383
    DOI: 10.1016/j.iref.2022.02.032
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    More about this item

    Keywords

    Risk; Index tracking; Portfolio optimization;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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