Abstract: We present and estimate an asset pricing model based on an intertemporal asset allocation problem with n available assets, in which agents have heterogeneous expectations about the future. We, thus, want to bridge the literatures on intertemporal asset allocation and on heterogeneous beliefs. In our model, the interaction between two switching types of agents, e.g. fundamentalists and chartists, is responsible for endogenously generating the observed price trends. We assume that agents have a long horizon objective, based on a stream of consumption, maximizing a recursive utility function. Agents in our model may try to make profits using strategies that are not driven by fundamentals, not necessarily meaning that they behave irrationally. Among the new features in our model, we can mention that the usual representative agent approach for long term investors is no longer valid. Besides, assuming that investors have a long term investment horizon changes the resulting optimum asset allocations and, thus, relative asset prices when compared to short term models. This last feature is even more important since we consider more than one risky asset. We estimate the model considering an investor from USA who can trade four major stock indices: Dow Jones, FTSE, Nikkei and Hang Seng. This lets us check wether or not price movements are driven by fundamentals, helping predicting the creation of bubbles.