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Title: Dynamic Mean-Variance Asset Allocation

Author(s): Suleyman Basak and Georgy Chabakauri

Publication Date: April 2009

Keyword(s): Dynamic Programming, Incomplete Markets, Mean-Variance Analysis, Multi-Period Portfolio Choice, Stochastic Investment Opportunities and Time-Consistency

Programme Area(s): Financial Economics

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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Bibliographic Reference

Basak, S and Chabakauri, G. 2009. 'Dynamic Mean-Variance Asset Allocation'. London, Centre for Economic Policy Research. https://cepr.org/active/publications/discussion_papers/dp.php?dpno=7256