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Alpha as Ambiguity: Robust Mean-Variance Portfolio Analysis

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  • Fabio Maccheroni
  • Massimo Marinacci
  • Doriana Ruffino

Abstract

We derive the analogue of the classic Arrow-Pratt approximation of the certainty equivalent under model uncertainty as defined by the smooth model of decision making under ambiguity of Klibanoff, Marinacci and Mukerji (2005). We study its scope via a portfolio allocation exercise that delivers a tractable mean-variance model adjusted for model uncertainty. In a problem with a risk-free asset, a risky asset, and an ambiguous asset, we find that portfolio rebalancing in response to higher model uncertainty only depends on the ambiguous asset's alpha, setting the performance of the risky asset as benchmark. In addition, the portfolios recommended by our model are not systematically conservative on the share held in the ambiguous asset: indeed, in general, it is not true that greater ambiguity reduces the optimal demand for the ambiguous asset. The analytical tractability of the enhanced Arrow-Pratt approximation renders our model especially well suited for calibration exercises aimed at exploring the consequences of ambiguity aversion on equilibrium asset prices.

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Bibliographic Info

Paper provided by IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University in its series Working Papers with number 373.

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Date of creation: 2010
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Handle: RePEc:igi:igierp:373

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  1. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2002. "A smooth model of decision making under ambiguity," ICER Working Papers - Applied Mathematics Series 11-2003, ICER - International Centre for Economic Research, revised Apr 2003.
  2. Nengjiu Ju & Jianjun Miao, 2010. "Ambiguity, Learning, and Asset Returns," CEMA Working Papers 438, China Economics and Management Academy, Central University of Finance and Economics.
  3. Massimo Marinacci & Fabio Maccheroni & Aldo Rustichini & Marco Taboga, 2005. "Portfolio Selection with Monotone Mean-Variance Preferences," Finance 0502014, EconWPA.
  4. Sujoy Mukerji & Kevin Sheppard & Fabrice Collard and Jean-Marc Tallon, 2011. "Ambiguity and the historical equity premium," Economics Series Working Papers 550, University of Oxford, Department of Economics.
  5. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2008. "Uncertainty Averse Preferences," Carlo Alberto Notebooks 77, Collegio Carlo Alberto.
  6. Larry G. Epstein & JianJun Miao, 2001. "A Two-Person Dynamic Equilibrium under Ambiguity," RCER Working Papers 478, University of Rochester - Center for Economic Research (RCER).
  7. Huberman, Gur, 2001. "Familiarity Breeds Investment," Review of Financial Studies, Society for Financial Studies, vol. 14(3), pages 659-80.
  8. Judson A. Caskey, 2009. "Information in Equity Markets with Ambiguity-Averse Investors," Review of Financial Studies, Society for Financial Studies, vol. 22(9), pages 3595-3627, September.
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Cited by:
  1. Sujoy Mukerji & Kevin Sheppard & Fabrice Collard and Jean-Marc Tallon, 2011. "Ambiguity and the historical equity premium," Economics Series Working Papers 550, University of Oxford, Department of Economics.
  2. Oliver Walker & Simon Dietz, 2012. "Ambiguity and insurance: robust capital requirements and premiums," Grantham Research Institute on Climate Change and the Environment Working Papers 97, Grantham Research Institute on Climate Change and the Environment.
  3. Eric André, 2013. "Optimal Portfolio with Vector Expected Utility," AMSE Working Papers 1308, Aix-Marseille School of Economics, Marseille, France, revised 11 Feb 2013.
  4. Eric André, 2013. "Optimal Portfolio with Vector Expected Utility," Working Papers halshs-00796482, HAL.
  5. Elabed, Ghada & Carter, Michael R., 2013. "Basis Risk and Compound-Risk Aversion: Evidence from a WTP Experiment in Mali," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 150353, Agricultural and Applied Economics Association.

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