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Jensen's Inequality, Parameter Uncertainty, and Multi-Period Investment

48 Pages Posted: 23 Jun 2010 Last revised: 2 Nov 2010

Mark Grinblatt

University of California, Los Angeles (UCLA) - Finance Area; Yale University - International Center for Finance; National Bureau of Economic Research (NBER)

Juhani T. Linnainmaa

USC Marshall School of Business; National Bureau of Economic Research (NBER)

Date Written: October 30, 2010

Abstract

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.

Keywords: Bayesian, Multi-period Investment, Nonlinear Estimation

JEL Classification: C11, G11

Suggested Citation

Grinblatt, Mark and Linnainmaa, Juhani T., Jensen's Inequality, Parameter Uncertainty, and Multi-Period Investment (October 30, 2010). Chicago Booth Research Paper No. 10-22; CRSP Working Paper. Available at SSRN: https://ssrn.com/abstract=1629189 or http://dx.doi.org/10.2139/ssrn.1629189

Mark Grinblatt

University of California, Los Angeles (UCLA) - Finance Area ( email )

Los Angeles, CA 90095-1481
United States
310-825-1098 (Phone)
310-206-5455 (Fax)

Yale University - International Center for Finance

Box 208200
New Haven, CT 06520-8200
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Juhani Linnainmaa (Contact Author)

USC Marshall School of Business ( email )

Marshall School of Business
Los Angeles, CA 90089
United States

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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