Time-consistent mean-variance portfolio selection with only risky assets

Chi Seng Pun

Economic Modelling, 2018, vol. 75, issue C, 281-292

Abstract: Time consistency and optimal diversification criteria are popular in the dynamic portfolio construction in practice. This paper is devoted to the exact analytical solution of the time-consistent mean-variance portfolio selection with assets that can be all risky in a continuous-time economy, of which the time-consistent global minimum-variance portfolio selection is a special case. Our solution generalizes the studies with a risk-free asset in the sense that one of the risky assets can be set as risk-free. By applying the extended dynamic programming, we manage to derive the exact analytical solution of the time-consistent mean-variance strategy with risky assets via the solution of an Abel differential equation. To stabilize the solution, we derive an analytical expansion for the Abel differential equation with any desired accuracy. In addition, we derive the statistical properties of the optimal strategy and prove a separation theorem. Moreover, we establish the links of time-consistent strategy with pre-commitment and myopic strategies and investigate the curse of dimensionality on the time-consistent strategies. We show that under the low-dimensional setting, the intertemporal hedging demands are significant; however, under the high-dimensional setting, the time-consistent strategies are approximately equivalent to myopic strategies, in the presence of estimation risk. Empirical studies are conducted to illustrate and verify our results.

Keywords: Time-consistent strategy; Dynamic global minimum-variance strategy; Extended dynamic programming; Abel's differential equation; Curse of dimensionality (search for similar items in EconPapers)
JEL-codes: C61 C68 C72 D92 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecmode:v:75:y:2018:i:c:p:281-292

DOI: 10.1016/j.econmod.2018.07.002

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