# Working papers

Working papers serie, SCOR-PSE Chair on Macroeconomic Risk

## WP n°2019-01 - Trading ambiguity: a tale of two heterogeneities

By **Sujoy Mukerji** (Queen Mary University of London), **Han N. Ozsoylev** (Koç University) and **Jean-Marc Tallon** (Paris School of Economics, CNRS)

- Download this working paper in pdf, that includes a dedicated Executive summary (see below)

*Executive Summary*

The financial literature largely assumes that investors know the distribution of asset returns. In most real-world situations, however, decision makers are uncertain about the data-generating process underlying asset returns. This has important implications for portfolio choice, because investors may prefer portfolio allocations that are robust across the set of return distributions believed to be possible. Novel to the literature, the paper shows that such ambiguity potentially explains several puzzling cross-sectional regularities.

Two heterogeneities are key: First, the heterogeneity in the uncertainty about the mean of an asset’s return distribution. This uncertainty parameter encapsulates the ambiguity of assets. It is high, for example, for stock returns of new-technology companies whose risks have not yet been fully learned. Second, investors differ, additionally to their risk aversion, in their tolerance for ambiguity. Together, these heterogeneities give rise to a parsimonious extension of the standard mean-variance framework (referred to as robust mean-variance) in which investors face a three-way trade-off between expected return, variance, and ambiguity. The paper considers, in turn, the implications for portfolio choice, equilibrium prices and returns, and trade upon the arrival of public information.

More ambiguity-averse investors are shown to hold less of the more ambiguous assets. This finding not only confirms the failure of the classical mutual funds theorem (Tobin, 1958) in the presence of heterogeneous ambiguity-aversion, but the direction of departure is also empirically compelling. Indeed, conservative investors are commonly encouraged to hold more bonds, relative to stocks. Such financial planning advice is inconsistent with standard mean-variance investors (asset allocation puzzle), but can be accommodated in this framework.

Turning to equilibrium prices, the authors show that despite the failure of the mutual funds theorem, a single-factor pricing formula emerges. As in the standard consumption asset pricing model (CAPM), the single factor is the excess return of the market portfolio. However, the CAPM beta is adjusted by the extent to which the ambiguity of the asset return is correlated with the ambiguity of the market portfolio. Two uncertainty premia explain the cross-section of expected returns: a risk premium and an ambiguity premium. The latter has the potential to explain the size and value premia documented by Fama and French (1992, 1993). High book-to-market firms, which tend to be in financial distress, and small-cap firms, due to their over-reliance on external financing, likely carry a high ambiguity premium.

In the dynamic extensions of the model implications of public signals for trading volumes are analysed. Earning announcements or aggregate uncertainty shocks are shown to induce trading if and only if agents are heterogeneously ambiguity averse. Such trade occurs because public signals change the return-risk-ambiguity trade-off, making investors seek a different allocation across ambiguous assets depending on their different ambiguity tolerances. Trade results from uncertainty sharing considerations and leads to no or very small price movements, which is consistent with the empirical literature.

The paper concludes by proposing strategies to estimate the ambiguity of individual assets returns. Since ambiguity about the return distribution is taken to be the uncertainty about the mean of the return distribution, a measure can be obtained from a Bayesian estimate of this parameter.