Hedging Demands under Incomplete Information

I present a model of consumption and portfolio choice under market incompleteness and imperfect information regarding the investment opportunity set. I solve analytically the consumption and portfolio choice problem for an investor learning about the true state of the economy. When prices are the only observations, the previously unspanned state variables are spanned by the market securities under the optimal inference/learning process. The market is observationally complete for the imperfectly informed investor. I show how learning affects both the covariance and the duration component of the hedging portfolio. I apply the model to the case where the Sharpe ratio is mean reverting. For the parameters presented in Wachter (2002), I show a reduction in hedging demands due to imperfect information. I solve in closed-form for the model implied R for the return forecast regression. I discuss the relationship between the reduction in hedging demands and the reduction in the model implied R for the return forecast regression. ∗Ph.D. Candidate, Sloan School of Management, Massachusetts Institute of Technology. Corresponding Address: MIT Sloan School of Management; 50 Memorial Drive, E52-458; Cambridge, MA 02142. E-mail: [email protected]. I thank my advisors Jonathan Lewellen and Steve Ross for their guidance. This paper benefitted from suggestions by John Campbell, George Chacko, Robin Greenwood, Jonathan Lewellen, Leonid Kogan, Stavros Panageas, Anna Pavlova, Steve Ross, Dimitri Vayanos, Luis Viceira, and Joshua White. I gratefully acknowledge the financial support of the General Electric Faculty for the Future Fellowship. All errors are mine. Updated versions of the paper are available in my website: www.mit.edu/~jfr/researchS02.