Optimal intertemporal liquidation of institutional investors with cash requirements and viable loans

Abstract

This study examines the optimal intertemporal liquidation strategies to meet the cash requirements of large institutional investors in the presence of permanent and temporary price impacts. We construct a two-period optimal liquidation problem tailored to investors with intertemporal cash requirements, such as pension funds that need to meet periodic payment obligations. We impose viable government loans that can be deployed by state-owned investors, thereby extending the existing literature, which has focused largely on the private sector. The optimal liquidation strategies from a broader perspective can be sorted into three types: preemptive, conventional, and deferred liquidation. The use of viable large-scale loans can be attractive as a buffer in intertemporal decisions. Proper consideration of the timing and amount for liquidation of institutional investors is necessary. This study has important implications for policy makers and can inform the design of strategies for managing the liquidity needs of large institutional investors.

KEYWORDS:

• Optimal liquidation
• institutional investor
• price impact
• cash requirements
• government loans

JEL CLASSIFICATIONS:

• G11
• G23
• G33

Acknowledgements

We are grateful to the two anonymous referees for their valuable comments and suggestions on this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Several studies assume that the LOB converges exponentially to a steady state after trade execution (Obizhaeva and Wang 2013; Lin and Fahim 2017).

2 We say that the LICQ holds when the active constraint gradients for a given point are linearly independent. The LICQ is a widely used first-order constraint qualification. It guarantees that the optimal solution and Lagrange multipliers of the convex problem satisfy the KKT (Karush-Kuhn-Tucker) conditions.

3 Through LMI relaxations, the nonconvex feasible set can be approximated by successive relaxations, resulting in a convex set inscribed in the previous set. The global optimum is detected by performing a rank test. For a rigorous mathematical treatment of this method, refer to Henrion and Lasserre (2004), and Henrion and Lasserre (2006).

4 If there exists a strictly feasible point, Slater’s condition holds. This is also one of the constraint qualifications.

Additional information

Funding

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (Ministry of Science and ICT, South Korea). (No. RS-2023-00208980).

Notes on contributors

Dongyeol Lee

Dongyeol Lee is a Ph.D. Candidate in Department of Industrial and Systems Engineering at Korea Advanced Institute of Science and Technology (KAIST).

Woo Chang Kim

Woo Chang Kim is a Professor in Department of Industrial and Systems Engineering, and also a PI in Graduate School of Data Science at Korea Advanced Institute of Science and Technology (KAIST).