Illiquidity, Position Limits, and Optimal Investment

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.