Illiquidity, Portfolio Constraints, and Diversification

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.