Learning under Ambiguous Reversion

While “it is now widely accepted that excess returns are predictable” (Lettau and Ludvigson, 2001, Journal of Finance), there also are authors finding otherwise, claiming that the predictive models are unstable or even spurious. This paper proposes a model of learning through which we can study the behavior of an investor under such ambiguous circumstances. The proposed model describes how observations are translated into a set of probability measures that represents the investor’s view of the immediate future; and I explicitly characterize the set’s evolution up to a system of differential equations that generalizes the Kalman-Bucy filter in the presence of ambiguity. The model of learning is then applied to the portfolio choice problem of a log investor; and learning under ambiguity is seen to have a significant effect on hedging demand: under a reasonable calibration, the optimal demand for the risky asset at zero instantaneous equity premium decreases, as the investor loses confidence, by half of wealth.