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Dynamic Mean-Variance Asset Allocation

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  • Basak, Suleyman
  • Chabakauri, Georgy

Abstract

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.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 7256.

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Date of creation: Apr 2009
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Handle: RePEc:cpr:ceprdp:7256

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Keywords: Dynamic Programming; Incomplete Markets; Mean-Variance Analysis; Multi-Period Portfolio Choice; Stochastic Investment Opportunities; Time-Consistency;

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