Dynamic Mean-Variance Asset Allocation
London Business School; Centre for Economic Policy Research (CEPR)
London School of Economics and Political Science
CEPR Discussion Paper No. DP7256
Mean-variance criteria remain prevalent in multi-period problems, and yet not much is known about their dynamically optimal policies. We provide a fully analytical characterization of the optimal dynamic mean-variance portfolios within a general incomplete-market economy, and recover a simple structure that also inherits several conventional properties of static models. We also identify a probability measure that incorporates intertemporal hedging demands and facilitates much tractability in the explicit computation of portfolios. We solve the problem by explicitly recognizing the time-inconsistency of the mean-variance criterion and deriving a recursive representation for it, which makes dynamic programming applicable. We further show that our time-consistent solution is generically different from the pre-commitment solutions in the extant literature, which maximize the mean-variance criterion at an initial date and which the investor commits to follow despite incentives to deviate. We illustrate the usefulness of our analysis by explicitly computing dynamic mean-variance portfolios under various stochastic investment opportunities in a straightforward way, which does not involve solving a Hamilton-Jacobi-Bellman differential equation. A calibration exercise shows that the mean-variance hedging demands may comprise a significant fraction of the investor's total risky asset demand.
Number of Pages in PDF File: 48
Keywords: Dynamic Programming, Incomplete Markets, Mean-Variance Analysis, Multi-Period Portfolio Choice, Stochastic Investment Opportunities, Time-Consistency
JEL Classification: C61, D81, G11working papers series
Date posted: May 19, 2009
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