Time-Consistent Mean-Variance Portfolio Selection with Only Risky Assets

30 Pages Posted: 9 May 2017 Last revised: 16 Dec 2018

See all articles by Chi Seng Pun

Chi Seng Pun

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences

Date Written: May 8, 2017

Abstract

Time-consistency and optimal diversification (minimum-variance) criteria are popular in the dynamic portfolio construction in practice. This paper is devoted to the exact analytic 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 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 analytic solution of the time-consistent mean-variance strategy with risky assets via the solution of the 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

JEL Classification: C61, C68, C72, D92

Suggested Citation

Pun, Chi Seng, Time-Consistent Mean-Variance Portfolio Selection with Only Risky Assets (May 8, 2017). Economic Modelling, Vol. 75, 2018, Available at SSRN: https://ssrn.com/abstract=2964718 or http://dx.doi.org/10.2139/ssrn.2964718

Chi Seng Pun (Contact Author)

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences ( email )

SPMS-MAS-05-22
21 Nanyang Link
Singapore, 637371
Singapore
(+65) 6513 7468 (Phone)

HOME PAGE: http://personal.ntu.edu.sg/cspun/

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