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Dynamic Mean-Variance Asset Allocation

46 Pages Posted: 27 Feb 2007 Last revised: 9 Apr 2009

Suleyman Basak

London Business School; Centre for Economic Policy Research (CEPR)

Georgy Chabakauri

London School of Economics and Political Science

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Date Written: April 9, 2009


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.

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

JEL Classification: G11, D81, C61

Suggested Citation

Basak, Suleyman and Chabakauri, Georgy, Dynamic Mean-Variance Asset Allocation (April 9, 2009). EFA 2007 Ljubljana Meetings; AFA 2009 San Francisco Meetings Paper. Available at SSRN: or

Suleyman Basak (Contact Author)

London Business School ( email )

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Centre for Economic Policy Research (CEPR)

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Georgy Chabakauri

London School of Economics and Political Science ( email )

Houghton Street
London, WC2A 2AE
United Kingdom


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