Liquidity Risk and Optimal Redemption Policies for Illiquid Investments

Abstract

We consider a risk-averse investor whose investable assets are held in a perfectly liquid asset (a portfolio of cash and liquid assets or a mutual fund) and another investment that has liquidity restrictions. The illiquidity could be due to restrictions on the investments (such as hedge funds) or due to nature of the asset held (such as real estate). The investor’s objective is to maximize the utility he derives from his terminal wealth at a future end date of his investment horizon. Furthermore the investor wants to hold his liquid wealth above a certain subsistence level, below which he incurs hefty borrowing costs or shortfall penalty. We consider the optimal conditions under which the investor must liquidate his illiquid assets. The redemption notification problem for hedge fund investors has certain affinity with the optimal control methods used in widely studied inventory management problems. We find that the optimal policy has a monotone structure similar in nature to inventory management problems.