Higher order expectations, learning, and sentiment pricing dynamics

We present a dynamic asset pricing model combining individual investor sentiment, higher order expectations with learning. In the basic model, the forward-looking expectation of individual investors is distorted by individual sentiment and higher order expectations, so prices react more sluggishly to changes in fundamentals of the asset. We find that investor sentiment plays a significant role in the effect of higher order expectations on asset pricing. Investor sentiment not only makes the price tightly anchor to the initial price, but also increases the sentiment drift of the price. Higher order expectations exhibit inertia, therefore aggravating the anchor to the initial price. With the increase of the order, more and more investor sentiment is integrated into the prices, amplifying the bias of pubic signal relative to fundamentals. When individual sentiment investors learn valuable public information through price system in the long term, the information component of the equilibrium price increases, thus drawing the asset price back toward the rational expected value. The model could offer a partial explanation to the inertia and drift in the price path.