Illiquidity, Portfolio Constraints, and Diversification

44 Pages Posted: 21 Mar 2008

See all articles by Hong Liu

Hong Liu

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

Min Dai

National University of Singapore (NUS) - Department of Mathematics

Hanqing Jin

National University of Singapore (NUS)

Date Written: January 7, 2008

Abstract

Mutual funds are often restricted to allocate certain percentages of fund assets to certain securities that have different degrees of illiquidity. The coexistence of these restrictions and asset illiquidity and the interactions among them are important for the optimal trading strategy of a mutual fund. However, the existing literature ignores this coexistence and the interactions.

In this paper, we consider a fund that can trade a liquid stock and an illiquid stock that is subject to proportional transaction costs. The percentage of capital allocated to the illiquid stock is restricted to remain between a lower bound and an upper bound. We use a novel approach to characterize the value function and to provide analytical comparative statics on the optimal trading strategy. The optimal trading strategy for the illiquid stock is determined by the optimal buy boundary and the optimal sell boundary between which no transaction occurs. We show the existence and uniqueness of the optimal trading strategy. In addition, both the buy boundary and the sell boundary are monotonically decreasing in the portfolio bounds.

We also conduct an extensive numerical analysis on trading strategies, liquidity premium, and diversification. Constantinides (1986) concludes that transaction costs only have a second-order effect on liquidity premia. We find that the presence of portfolio constraints can significantly magnify the effect of transaction costs on liquidity premium and can make it more than a first-order effect. In addition, somewhat surprisingly, the liquidity premium can increase when constraints are less stringent. We show that even for log preferences, the optimal trading strategy is nonmyopic with respect to portfolio constraints, in the sense that a constraint can affect current trading strategy even when it is not binding now. Correlation coefficient between the two stocks affects the efficiency of diversification and thus can significantly alter the optimal trading strategy in both stocks. We also examine the endogenous choice of the portfolio bounds. Our analysis shows that the optimal upper (lower) bound is increasing (decreasing) in transaction costs.

Keywords: Illiquidity, Portfolio Constraints, Portfolio Selection, Transaction Costs

JEL Classification: D11, D91, G11, C61

Suggested Citation

Liu, Hong and Dai, Min and Jin, Hanqing, Illiquidity, Portfolio Constraints, and Diversification (January 7, 2008). Available at SSRN: https://ssrn.com/abstract=1081482 or http://dx.doi.org/10.2139/ssrn.1081482

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

Min Dai

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

Singapore

Hanqing Jin

National University of Singapore (NUS) ( email )

Bukit Timah Road 469 G
Singapore, 117591
Singapore

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
310
Abstract Views
1,640
rank
102,662
PlumX Metrics