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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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References

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  1. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2008. "Uncertainty Averse Preferences," Carlo Alberto Notebooks 77, Collegio Carlo Alberto.
  2. Epstein, Larry G. & Miao, Jianjun, 2003. "A two-person dynamic equilibrium under ambiguity," Journal of Economic Dynamics and Control, Elsevier, vol. 27(7), pages 1253-1288, May.
  3. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini & Marco Taboga, 2008. "Portfolio Selection with Monotone Mean-Variance Preferences," Temi di discussione (Economic working papers) 664, Bank of Italy, Economic Research and International Relations Area.
  4. Nengjiu Ju & Jianjun Miao, 2012. "Ambiguity, Learning, and Asset Returns," Econometrica, Econometric Society, vol. 80(2), pages 559-591, 03.
  5. Fabrice Collard & Sujoy Mukerji & Kevin Sheppard & Jean-Marc Tallon, 2011. "Ambiguity and the historical equity premium," Documents de travail du Centre d'Economie de la Sorbonne 11032r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Aug 2012.
  6. Huberman, Gur, 2001. "Familiarity Breeds Investment," Review of Financial Studies, Society for Financial Studies, vol. 14(3), pages 659-80.
  7. 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.
  8. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
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Cited by:
  1. Massimo Guidolin & Francesca Rinaldi, 2010. "Ambiguity in asset pricing and portfolio choice: a review of the literature," Working Papers 2010-028, Federal Reserve Bank of St. Louis.
  2. 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.
  3. 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.
  4. Dennis Dlugosch & Kristian Horn & Mei Wang, 2014. "Behavioral determinants of home bias - theory and experiment," Working Papers 2014-11, Faculty of Economics and Statistics, University of Innsbruck.
  5. Fabrice Collard & Sujoy Mukerji & Kevin Sheppard & Jean-Marc Tallon, 2011. "Ambiguity and the historical equity premium," Documents de travail du Centre d'Economie de la Sorbonne 11032, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  6. Eric André, 2013. "Optimal Portfolio with Vector Expected Utility," Working Papers halshs-00796482, HAL.
  7. Giuseppe Attanasi & Aldo Montesano, 2012. "The price for information about probabilities and its relation with risk and ambiguity," Theory and Decision, Springer, vol. 73(1), pages 125-160, July.

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