Working Paper: CEPR ID: DP7256
Authors: Suleyman Basak; Georgy Chabakauri
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
JEL Codes: C61; D81; G11
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| optimal investment policy (G11) | influenced by myopic and intertemporal hedging demands (G40) |
| intertemporal hedging demand (D15) | driven by expected total gains or losses from stock investments (G11) |
| expected total gains or losses from stock investments (G11) | influences investment decisions (G11) |
| negative correlation of stock returns with anticipated portfolio gains (G12) | positive hedging demand (G13) |
| lower variability of wealth (D31) | higher attractiveness of the stock (G17) |
| time inconsistency (D15) | deviations from initial investment policies (G11) |
| analytical solutions (C29) | straightforward computation of optimal portfolios (G11) |