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"It is now widely accepted that excess returns are predictable" (Lettau and Lud- vigson, 2001). However, there also have been authors nding otherwise, claiming that most of the predictive models are \unstable or even spurious" (Welch and Goyal, 2008). This paper proposes a model of learning through which we can investigate the behav- ior 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 dierential equations that generalizes the Kalman-Bucy lter 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 signicant eect on hedging demand|under a reasonable calibration, the optimal demand for the risky asset at zero instantaneous equity premium decreases, as the investor loses condence, by half of wealth.