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Alpha as Ambiguity: Robust Mean‐Variance Portfolio Analysis

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Author Info

  • 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

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 81 (2013)
Issue (Month): 3 (05)
Pages: 1075-1113

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Handle: RePEc:ecm:emetrp:v:81:y:2013:i:3:p:1075-1113

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References

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  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. Fabrice Collard & Sujoy Mukerji & Kevin Sheppard & Jean-Marc Tallon, 2011. "Ambiguity and the historical equity premium," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00594096, HAL.
  6. Jianjun Miao & NENGJIU JU, 2010. "Ambiguity, Learning, And Asset Returns," Boston University - Department of Economics - Working Papers Series WP2010-031, Boston University - Department of Economics.
  7. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2008. "Uncertainty Averse Preferences," Carlo Alberto Notebooks 77, Collegio Carlo Alberto.
  8. Huberman, Gur, 2001. "Familiarity Breeds Investment," Review of Financial Studies, Society for Financial Studies, vol. 14(3), pages 659-80.
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Citations

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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. 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.
  3. 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.
  4. 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.
  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.
  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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