Keynes Meets Markowitz: The Trade-Off between Familiarity and Diversification

45 Pages Posted: 1 Mar 2010

See all articles by Phelim P. Boyle

Phelim P. Boyle

Wilfrid Laurier University - School of Business & Economics; University of Waterloo

Lorenzo Garlappi

University of British Columbia (UBC) - Sauder School of Business

Raman Uppal

EDHEC Business School; Centre for Economic Policy Research (CEPR)

Tan Wang

University of British Columbia (UBC) - Division of Finance; China Academy of Financial Research (CAFR)

Multiple version iconThere are 3 versions of this paper

Date Written: February 2010

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 investorÂ’s "familiarity" toward assets. The model shows that when an investor is equally ambiguous about all assets, then the optimal portfolio corresponds to MarkowitzÂ’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.

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

JEL Classification: D81, G11, G12, G23

Suggested Citation

Boyle, Phelim P. and Garlappi, Lorenzo and Uppal, Raman and Wang, Tan, Keynes Meets Markowitz: The Trade-Off between Familiarity and Diversification (February 2010). CEPR Discussion Paper No. DP7687. Available at SSRN: https://ssrn.com/abstract=1559643

Phelim P. Boyle (Contact Author)

Wilfrid Laurier University - School of Business & Economics ( email )

Waterloo, Ontario N2L 3C5
Canada
519 884 1970 (Phone)
519 888 1015 (Fax)

University of Waterloo

Waterloo, Ontario N2L 3G1
Canada

Lorenzo Garlappi

University of British Columbia (UBC) - Sauder School of Business ( email )

2053 Main Mall
Vancouver, BC V6T 1Z2
Canada

Raman Uppal

EDHEC Business School ( email )

58 rue du Port
Lille, 59046
France

Centre for Economic Policy Research (CEPR)

90-98 Goswell Road
London, EC1V 7RR
United Kingdom

Tan Wang

University of British Columbia (UBC) - Division of Finance ( email )

2053 Main Mall
Vancouver, BC V6T 1Z2
Canada
604-822-9414 (Phone)
604-822-8521 (Fax)

China Academy of Financial Research (CAFR)

1954 Huashan Road
Shanghai P.R.China, 200030
China

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