Jensen's Inequality, Parameter Uncertainty, and Multi-Period Investment
University of California, Los Angeles (UCLA) - Finance Area; Yale University - International Center for Finance; National Bureau of Economic Research (NBER)
Juhani T. Linnainmaa
University of Chicago - Booth School of Business; National Bureau of Economic Research (NBER)
October 30, 2010
Chicago Booth Research Paper No. 10-22
CRSP Working Paper
Classical approaches to estimation and decisions requiring estimation often are at odds. When values critical to the decision are convex or concave functions of unknown parameters, the statistician’s estimation error adjustments are the opposite of what is appropriate for the decision. We illustrate the conflict by studying multi-period investment problems. The proper application of Jensen’s inequality to the decision turns finance intuition on its head. For example, multi-period investments with negative risk premia can be profitable, there can be infinite demand for risky securities by risk averse investors, settings exist where risk averse investors should not diversify, and demand for mutual funds with negative alphas may be rational.
Number of Pages in PDF File: 48
Keywords: Bayesian, Multi-period Investment, Nonlinear Estimation
JEL Classification: C11, G11
Date posted: June 23, 2010 ; Last revised: November 2, 2010
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