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Exhibiting Abnormal Returns Under a Risk Averse Strategy

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Abstract

This paper is devoted to the investment strategies that combine asset pricing models and coherent risk measures. In particular, we utilize the theoretical framework of Balbas et al. (J Risk 18(4):25–52, 2016), which suggests that simply by managing a portfolio of assets, an investor can achieve risk that converges to − and returns that converge to + . We contribute on that framework by providing evidence that arise from the CAPM model, in regard to the efficient market hypothesis. In addition, our results suggest that an investor can exhibit returns that outperform the market index by managing a portfolio less volatile than the market.

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References

  • Acerbi C (2002) Spectral measures of risk: a coherent representation of subjective risk aversion. J Bank Finance 26(7):1505–1518

    Article  Google Scholar 

  • Acerbi C, Tasche D (2002) On the coherence of expected shortfall. J Bank Finance 26(7):1487–1503

    Article  Google Scholar 

  • Alexander G, Baptista A (2002) Economic implications of using a Mean-Var model for portfolio selection: a comparison with mean variance analysis. J Econ Dyn Control 26:1159–1193

    Article  MathSciNet  MATH  Google Scholar 

  • Artzner P, Delbaen F, Eber JM, Heath D (1999) Coherent measures of risk. Math Financ 9(3):203–228

    Article  MathSciNet  MATH  Google Scholar 

  • Balbas A, Balbas B, Balbas R (2016) Outperforming benchmarks with their derivatives: theory and empirical evidence. J Risk 18(4):25–52

    Article  MATH  Google Scholar 

  • Balbas A, Balbas B, Balbas R (2010a) CAPM and APT-like models with risk measures. J Bank Finance 34:1166–1174

    Article  MATH  Google Scholar 

  • Balbas A, Balbas B, Balbas R (2010b) Minimizing measures of risk by saddle point conditions. J Comput Appl Math 234:2924–2931

    Article  MathSciNet  MATH  Google Scholar 

  • Balbas A, Balbas B, Balbas R (2013) Good deals in markets with friction. Quant Finance 13:827–836

    Article  MathSciNet  MATH  Google Scholar 

  • Barrieu P, El Karoui N (2005) Inf-convolution of risk measures and optimal risk transfer. Finance Stochast 9(2):269–298

    Article  MathSciNet  MATH  Google Scholar 

  • Bertsimas D, Lauprete GJ, Samarov A (2004) Shortfall as risk measure: properties, optimization and applications. J Econ Dyn Control 28:1353–1381

    Article  MathSciNet  MATH  Google Scholar 

  • BCBS (2012) Consultative Document May 2012. Fundamental review of the trading book: Basel committee on banking supervision. Bank for International Settlements, Basel

    Google Scholar 

  • Cai J, Liu H, Wang R (2018) Asymptotic equivalence of risk measures under dependence uncertainty. Math Financ 28(1):29–49

    Article  MathSciNet  MATH  Google Scholar 

  • Carhart MM (1997) On persistence in mutual fund performance. J Finance 52 (1):57–81

    Article  Google Scholar 

  • Cochrane JH (2000) Asset Pricing. Princeton University Press, Princeton

    Google Scholar 

  • Cremers M, Petajisto A (2009) How active is your fund manager? A new measure that predicts performance. Rev Financ Stud 22(9):3329–3365

    Article  Google Scholar 

  • Cuthbertson K, Nitzsche D, O’Sullivan N (2008) UK Mutual fund performance: skill or luck?. J Empirical Finance 15:613–634

    Article  Google Scholar 

  • Dhaene J, Denuit MJ, Goovaerts R, Kaas R, Vyncke D (2002) The concept of comonotonicity in actuarial science and finance: Theory. Insurance: Math Econ 31 (1):3–33

    MathSciNet  MATH  Google Scholar 

  • Dhaene J, Laeven RJA, Vanduffel S, Darkiewicz G, Goovaerts MJ (2008) Can a coherent risk measure be too subadditive?. J Risk Insurance 15(2):365–386

    Article  Google Scholar 

  • Elton JE, Gruber JM, Blake RC (1996) Survivor bias and mutual fund performance. Rev Financ Stud 9(4):1097–1120

    Article  Google Scholar 

  • Embrechts P, Puccetti G, Ruschendorf L, Wang R, Beleraz A (2014) An academic response to basel 3.5. Risks 2:25–48. https://doi.org/10.3390/risks2010025

    Article  Google Scholar 

  • Evans R (2007) The incubation bias, Darden Graduate School of Business, University of Virginia

  • Fama E, French K (2010) Luck versus skill in the cross section of mutual fund returns. J Finance 65(5):1915–1947

    Article  Google Scholar 

  • Fama E, French K (1993) Common risk factors in the returns on stocks and bonds. J Financ Econ 33(1):3–56

    Article  MATH  Google Scholar 

  • Fama E (1970) Efficient capital markets: a review of theory and empirical work. J Financ 26(2):383–417

    Article  Google Scholar 

  • Follmer H, Shied A (2004) Stochastic finance: an introduction in discrete time., Series: Walter de Gruyter No. 2

  • Follmer H, Shied A (2002) Convex measures of risk and trading constraints. Financ Stochastics 6(4):429– 447

    Article  MathSciNet  MATH  Google Scholar 

  • Follmer H, Shied A (2008) Convex and coherent measures of risk. Hamboldt University, 1–12

  • Gaivoronski A, Pflug G (2005) Value-at-risk in portfolio optimization: properties and computational approach. J Risk 7(2):1–31

    Article  Google Scholar 

  • Jensen CM (1967) The performance of mutual funds in the period 1945-1964. J Finance 23:389–416

    Article  Google Scholar 

  • Kosowski R, Timmerman A, Wermers R, White H (2006) Can mutual fund stars really pick stocks? new evidence from a bootstrap analysis. J Finance 61 (6):2551–2595

    Article  Google Scholar 

  • Leopold M (2015) Value-at-risk and other risk measures, University of Zurich and the Swiss Finance Institute, Investment Risk Management, First Edition. Oxford University Press, New York

    Google Scholar 

  • Lintner J (1965) The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Rev Econ Stat 47(1):13–37

    Article  Google Scholar 

  • Luenberger DG (1969) Optimization by vector space methods. Wiley, New York

    MATH  Google Scholar 

  • Markowitz H (1952) Portfolio selection. J Finance 7(1):77–91

    Google Scholar 

  • Pflug G, Römisch W (2007) Modeling measuring and managing risk. World Scientific, Singapore

    Book  MATH  Google Scholar 

  • Rockafellar RT, Uryasev SP (2000) Optimization of conditional value-at-risk. J Risk 2(3):21–42

    Article  Google Scholar 

  • Rockafellar RT, Uryasev SP, Zabarankin M (2006) Generalized deviations in risk analysis. Finance Stochast 10:51–74

    Article  MathSciNet  MATH  Google Scholar 

  • Sharpe FW (1994) The sharpe ratio. J Portfolio Manag 21(1):49–58

    Article  Google Scholar 

  • Sharpe FW (1991) The arithmetic of active management. Financ Anal J 47 (1):7–9

    Article  Google Scholar 

  • Sharpe FW (1964) Capital asset prices: a theory of market equilibrium under conditions of risk. J Financ 19(3):425–442

    Google Scholar 

  • Szego G (2004) Risk measures for the 21st Century. Wiley, New York

    Google Scholar 

  • Wang SS (2000) A class of distortion operators for financial and insurance risks. J Risk Insurance 67(1):15–36

    Article  Google Scholar 

  • Zachos GC (2015) Accuracy of the risk estimators. Stochastic Modeling, Data Analysis and Statistical Applications, book devoted to the 3rd Stochastic Modeling Techniques and Data Analysis (SMTDA 2014), ISBN (print):978-618-5180-08-9, ISBN (e-book):978-618-5180-11-9, ISAST, 393–407

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Acknowledgements

The authors express their gratitude to the editor and the anonymous referees for their significant comments.

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Correspondence to Dimitrios G. Konstantinides.

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Konstantinides, D.G., Zachos, G.C. Exhibiting Abnormal Returns Under a Risk Averse Strategy. Methodol Comput Appl Probab 21, 551–566 (2019). https://doi.org/10.1007/s11009-018-9673-9

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  • DOI: https://doi.org/10.1007/s11009-018-9673-9

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