Time-consistent mean-variance portfolio selection with only risky assets
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 whic...
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| Format: | Journal Article |
| Language: | English |
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2018
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| Online Access: | https://hdl.handle.net/10356/85117 http://hdl.handle.net/10220/46283 |
| _version_ | 1826120191926337536 |
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| author | Pun, Chi Seng |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Pun, Chi Seng |
| author_sort | Pun, Chi Seng |
| collection | NTU |
| description | 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. |
| first_indexed | 2024-10-01T05:12:30Z |
| format | Journal Article |
| id | ntu-10356/85117 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T05:12:30Z |
| publishDate | 2018 |
| record_format | dspace |
| spelling | ntu-10356/851172023-02-28T19:31:32Z Time-consistent mean-variance portfolio selection with only risky assets Pun, Chi Seng School of Physical and Mathematical Sciences Dynamic Global Minimum-Variance Strategy DRNTU::Science::Mathematics Time-consistent Strategy 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. Accepted version 2018-10-11T05:28:09Z 2019-12-06T15:57:24Z 2018-10-11T05:28:09Z 2019-12-06T15:57:24Z 2018 2018 Journal Article Pun, C. S. (2018). Time-consistent mean-variance portfolio selection with only risky assets. Economic Modelling. In Press. 0264-9993 https://hdl.handle.net/10356/85117 http://hdl.handle.net/10220/46283 10.1016/j.econmod.2018.07.002 208515 en Economic Modelling © 2018 Elsevier. This is the author created version of a work that has been peer reviewed and accepted for publication by Economic Modelling, Elsevier. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://doi.org/10.1016/j.econmod.2018.07.002]. 30 p. application/pdf |
| spellingShingle | Dynamic Global Minimum-Variance Strategy DRNTU::Science::Mathematics Time-consistent Strategy Pun, Chi Seng Time-consistent mean-variance portfolio selection with only risky assets |
| title | Time-consistent mean-variance portfolio selection with only risky assets |
| title_full | Time-consistent mean-variance portfolio selection with only risky assets |
| title_fullStr | Time-consistent mean-variance portfolio selection with only risky assets |
| title_full_unstemmed | Time-consistent mean-variance portfolio selection with only risky assets |
| title_short | Time-consistent mean-variance portfolio selection with only risky assets |
| title_sort | time consistent mean variance portfolio selection with only risky assets |
| topic | Dynamic Global Minimum-Variance Strategy DRNTU::Science::Mathematics Time-consistent Strategy |
| url | https://hdl.handle.net/10356/85117 http://hdl.handle.net/10220/46283 |
| work_keys_str_mv | AT punchiseng timeconsistentmeanvarianceportfolioselectionwithonlyriskyassets |