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Keynes Meets Markowitz: The Trade-off Between Familiarity and Diversification

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  • Boyle, Phelim
  • Garlappi, Lorenzo
  • Uppal, Raman
  • Wang, Tan

Abstract

We develop a model of portfolio choice to nest the views of Keynes - who advocates concentration in a few familiar assets - and Markowitz - who advocates diversification across assets. We rely on the concepts of ambiguity and ambiguity aversion to formalize the idea of an investor’s "familiarity" toward assets. The model shows that when an investor is equally ambiguous about all assets, then the optimal portfolio corresponds to Markowitz’s fully diversified portfolio. In contrast, when an investor exhibits different degrees of familiarity across assets, the optimal portfolio depends on (i) the relative degree of ambiguity across assets, and (ii) the standard deviation of the estimate of expected return on each asset. If the standard deviation of the expected return estimate and the difference between the ambiguity about familiar and unfamiliar assets are low, then the optimal portfolio is composed of a mix of both familiar and unfamiliar assets; moreover, an increase in correlation between assets causes an investor to increase concentration in the assets with which they are familiar (flight to familiarity). Alternatively, if the standard deviation of the expected return estimate and the difference between the ambiguity of familiar and unfamiliar assets are high, then the optimal portfolio contains only the familiar asset(s) as Keynes would have advocated. In the extreme case in which the ambiguity about all assets and the standard deviation of the estimated mean are high, then no risky asset is held (non-participation). The model also has empirically testable implications for trading behavior: in response to a change in idiosyncratic volatility, the Keynesian portfolio always exhibits more trading than the Markowitz portfolio, while the opposite is true for a change in systematic volatility. In the equilibrium version of the model with heterogeneous investors who are familiar with different assets, we find that the risk premium of stocks depends on both systematic and idiosyncratic volatility, and that the equity risk premium is significantly higher than in the standard model without ambiguity.

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Bibliographic Info

Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 7687.

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Date of creation: Feb 2010
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Handle: RePEc:cpr:ceprdp:7687

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Keywords: ambiguity; diversification; investment; portfolio choice; robust control;

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References

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  1. Kelly, Morgan, 1995. "All their eggs in one basket: Portfolio diversification of US households," Journal of Economic Behavior & Organization, Elsevier, vol. 27(1), pages 87-96, June.
  2. Calvet, Laurent & Campbell, John Y. & Sodini, Paolo, 2006. "Down or out: assessing the welfare costs of household investment mistakes," Les Cahiers de Recherche 832, HEC Paris.
  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. Massa, Massimo & Simonov, Andrei, 2004. "Hedging, Familiarity and Portfolio Choice," CEPR Discussion Papers 4789, C.E.P.R. Discussion Papers.
  5. John Y. Campbell, 2006. "Household Finance," NBER Working Papers 12149, National Bureau of Economic Research, Inc.
  6. Bryan R. Routledge & Stanley E. Zin, 2001. "Model Uncertainty and Liquidity," NBER Working Papers 8683, National Bureau of Economic Research, Inc.
  7. Valery Polkovnichenko, 2005. "Household Portfolio Diversification: A Case for Rank-Dependent Preferences," Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1467-1502.
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Cited by:
  1. Xie, Jun & Yang, Chunpeng, 2013. "Shouldn't all eggs be putted in one basket? A portfolio model based on investor sentiment and inertial thinking," Economic Modelling, Elsevier, vol. 35(C), pages 682-688.
  2. Hui Chen & Nengjiu Ju & Jianjun Miao, . "Dynamic Asset Allocation with Ambiguous Return Predictability," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics.
  3. Guiso, Luigi & Sodini, Paolo, 2012. "Household Finance: An Emerging Field," CEPR Discussion Papers 8934, C.E.P.R. Discussion Papers.
  4. David Chambers & Elroy Dimson, 2013. "Retrospectives: John Maynard Keynes, Investment Innovator," Journal of Economic Perspectives, American Economic Association, vol. 27(3), pages 213-28, Summer.
  5. Marcello Basili & Luca Pratelli, 2013. "Aggregation of not necessarily independent opinions," Department of Economics University of Siena 677, Department of Economics, University of Siena.

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