Keynes Meets Markowitz: The Tradeoff Between Familiarity and Diversification

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 investor's ``familiarity" towards assets. The model shows that when investors are equally ambiguous about all assets, then the optimal portfolio corresponds to Markowitz's fully-diversified portfolio. In contrast, when investors exhibit 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 is low and the difference between the ambiguity about the familiar and unfamiliar assets is small, then the optimal portfolio is composed of a mix of both familiar and unfamiliar assets; moreover, an increase in correlation between assets causes investors to increase concentration in the assets with which they are familiar (flight to familiarity). Alternatively, if the standard deviation of the expected-return estimate is high and the difference between the ambiguity of familiar and unfamiliar assets is large, 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 risk 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 agents 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: Investment, portfolio choice, ambiguity, robust control

JEL Classification: G11, G12, G23, D81