Optimal Portfolios of Illiquid Assets

Abstract: This paper investigates the investment behaviour of a large unregulated financial institution (FI) with CARA risk preferences. It shows how the FI optimizes its trading to account for market illiquidity using an extension of the Almgren-Chriss market impact model of multiple risky assets. This expected utility optimization problem over the set of adapted strategies turns out to have the same solutions as a mean-variance optimization over deterministic trading strategies. That means the optimal adapted trading strategy is both deterministic and time-consistent. It is also found to have an explicit closed form that clearly displays interesting properties. For example, the classic constant Merton portfolio strategy, a particular solution of the frictionless limit of the problem, behaves like an attractor in the space of more general solutions. The main effect of temporary market impact is to slow down the speed of convergence to this constant Merton portfolio. The effect of permanent market impact is to incentivize the FI to buy additional risky assets near the end of the period. This property, that we name the Ponzi property, is related to the creation and bursting of bubbles in the market. The proposed model can be used as a stylized dynamic model of a typical FI in the study of the asset fire sale channel relevant to understanding systemic risk and financial stability.