Illiquidity, Position Limits, and Optimal Investment

45 Pages Posted: 17 Mar 2009

See all articles by Min Dai

Min Dai

National University of Singapore (NUS) - Department of Mathematics

Hanqing Jin

Mathematical Institute; Oxford-Nie Financial Big Data Laboratory; St. Peter's College

Hong Liu

Washington University in St. Louis - Olin Business School; Fudan University - China Institute of Economics and Finance

Date Written: March 15, 2009

Abstract

Mutual funds are often restricted to allocate certain percentages of fund assets to certain securities that have different degrees of illiquidity. However, the existing literature on how mutual funds should trade has largely ignored the coexistence of position limits and differential illiquidity and thus the optimal trading strategy for a typical mutual fund is largely unknown. In this paper, we use a novel approach to study the optimal trading strategy of mutual funds who face both position limits and differential illiquidity. We show the existence, uniqueness, smoothness, and characterization of the optimal trading strategy. We provide extensive analytical comparative statics for the optimal trading strategy and an efficient numerical method for solving a class of similar problems. We find that the presence of position limits can significantly increase liquidity premium and surprisingly, liquidity premium can be higher when the limits are less stringent. We find that myopically choosing the "optimal'' strategy is costly. We also examine the optimal choice of position limits and empirical implications on performance evaluation.

Keywords: Illiquidity, Portfolio Constraints, Liquidity Premium, Transaction Costs

JEL Classification: D11, D91, G11, C61

Suggested Citation

Dai, Min and Jin, Hanqing and Liu, Hong, Illiquidity, Position Limits, and Optimal Investment (March 15, 2009). Available at SSRN: https://ssrn.com/abstract=1360423 or http://dx.doi.org/10.2139/ssrn.1360423

Min Dai

National University of Singapore (NUS) - Department of Mathematics ( email )

Singapore

Hanqing Jin

Mathematical Institute ( email )

Andrew Wiles Building
Radicliff Observatory Quarter, Woodstock Road
Oxford, oxfordshire OX2 6GG
United Kingdom

HOME PAGE: http://www.maths.ox.ac.uk

Oxford-Nie Financial Big Data Laboratory ( email )

Andrew Wiles Building
Woodstock Road
Oxford, Oxfordshire OX2 6GG
United Kingdom

St. Peter's College ( email )

New Inn Hall Street
Oxford, Oxfordshire OX1 2DL
United Kingdom

HOME PAGE: http://www.spc.ox.ac.uk

Hong Liu (Contact Author)

Washington University in St. Louis - Olin Business School ( email )

One Brookings Drive
Campus Box 1133
St. Louis, MO 63130-4899
United States
314-935-5883 (Phone)

Fudan University - China Institute of Economics and Finance ( email )

China

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