DP7256 Dynamic Mean-Variance Asset Allocation

Author(s): Suleyman Basak, Georgy Chabakauri
Publication Date: April 2009
Keyword(s): Dynamic Programming, Incomplete Markets, Mean-Variance Analysis, Multi-Period Portfolio Choice, Stochastic Investment Opportunities, Time-Consistency
JEL(s): C61, D81, G11
Programme Areas: Financial Economics
Link to this Page: cepr.org/active/publications/discussion_papers/dp.php?dpno=7256

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.