Alpha As Ambiguity: Robust Mean-Variance Portfolio Analysis

32 Pages Posted: 11 Jan 2012

See all articles by Fabio Maccheroni

Fabio Maccheroni

Bocconi University - Department of Decision Sciences

Massimo Marinacci

University of Turin - Department of Statistics and Applied Mathematics

Doriana Ruffino

Board of Governors of the Federal Reserve System

Date Written: October 29, 2010

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.

Keywords: Smooth preferences, Ambiguity aversion, Risk aversion, Mean-variance portfolio choices, Alpha

JEL Classification: D80, D81, G11

Suggested Citation

Maccheroni, Fabio and Marinacci, Massimo and Ruffino, Doriana, Alpha As Ambiguity: Robust Mean-Variance Portfolio Analysis (October 29, 2010). Midwest Finance Association 2012 Annual Meetings Paper. Available at SSRN: https://ssrn.com/abstract=1571620 or http://dx.doi.org/10.2139/ssrn.1571620

Fabio Maccheroni

Bocconi University - Department of Decision Sciences ( email )

Via Roentgen 1
Milan, 20136
Italy

Massimo Marinacci

University of Turin - Department of Statistics and Applied Mathematics ( email )

Piazza Arbarello 8
Turin, I-10122
Italy

HOME PAGE: http://web.econ.unito.it/gma/massimo.htm

Doriana Ruffino (Contact Author)

Board of Governors of the Federal Reserve System ( email )

20th and C Streets, NW
Washington, DC 20551
United States

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