Abstract
I present a model of consumption and portfolio choice with imperfect information. I solve analytically the consumption and portfolio choice problem for an investor learning about the current value of time-varying expected returns. When prices are the only observables, the investor optimally estimates the current expected returns using the realized returns. Because of this, the market is observationally complete for an imperfectly informed investor. The observational completeness of the market allows me to find analytical, closed-form solutions to the investor's consumption and portfolio choice problem. I show how learning affects both the covariance and the consumption smoothing component of the hedging portfolio. Applying the model to monthly return data, I show a significant reduction in hedging demands due to imperfect information. In contrast to portfolio choice assuming expected returns are observed, in some cases the reduction implies the agent will optimally hold a negative hedging portfolio. I solve in closed-form for the model implied R2 for the return forecast regression, in other words the predictable fraction of return variance, and discuss the relationship between the reduction in hedging demands and the reduction in the model implied R2 for the return forecast regression.
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