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Francisco Vazquez-Grande vazquez-grande@chicagobooth.edu
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This paper documents a significant increase of risk-prices in the presence of learning. We solve a model with long-run risk, where both, the level and persistence of expected consumption growth are unobserved. We introduce a new methodology to quantify the effects of learning about parameter uncertainty and latent variables. The representative consumer chooses state variables that are sufficient statistics of the learning problems and, conditional on her information set, forms posterior distributions of the states and future consumption growth. We present a novel numerical approach that approximates the agent's continuation-value by nesting the solutions of problems with different information sets. This reduces the complexity of the optimization and ensures consistency across information structures. Keeping preference parameters constant, maximum Sharpe ratios increase from .07 in the benchmark case without learning to .45 in the learning economy.
Lars P. Hansen (co-chair) Ruey S. Tsay (co-chair) Homer J. Livingston Distinguished Service Professor H.G.B. Alexander Professor of Econometrics & Statistics Department of Economics, University of Chicago Booth School of Business, University of Chicago lhansen@uchicago.edu Ruey.Tsay@chicagobooth.edu +1 (773) 702-8170 +1 (773) 702-6750 Pietro Veronesi Kenneth L. Judd Roman Family Professor of Finance Paul H. Bauer Senior Fellow Booth School of Business, University of Chicago Hoover Institution, Stanford University pietro.veronesi@chicagobooth.edu judd@hoover.stanford.edu +1 (773) 702-6348 +1 (650) 723-5866
November 23rd, 2009