Dynamic Mean-Variance Asset Allocation

Suleyman Basak and Georgy Chabakauri

No 7256, CEPR Discussion Papers from C.E.P.R. Discussion Papers

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.

Keywords: Dynamic programming; Incomplete markets; Mean-variance analysis; Multi-period portfolio choice; Stochastic investment opportunities; Time-consistency (search for similar items in EconPapers)
JEL-codes: C61 D81 G11 (search for similar items in EconPapers)
Date: 2009-04
New Economics Papers: this item is included in nep-dge
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Journal Article: Dynamic Mean-Variance Asset Allocation (2010)
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