Portfolio Choice with Illiquid Assets

Abstract

W e present a model of optimal allocation to liquid and illiquid assets, where illiquidity risk results from the restriction that an asset cannot be traded for intervals of uncertain duration. Illiquidity risk leads to increased and state-dependent risk aversion and reduces the allocation to both liquid and illiquid risky assets. Uncertainty about the length of the illiquidity interval, as opposed to a deterministic nontrading interval, is a primary determinant of the cost of illiquidity. We allow market liquidity to vary from "normal" periods, when all assets are fully liquid, to "illiquidity crises," when some assets can only be traded infrequently. The possibility of a liquidity crisis leads to limited arbitrage in normal times. Investors are willing to forgo 2% of their wealth to hedge against illiquidity crises occurring once every 10 years.

Dynamic Trading Volume

“…If prices move quickly against him, the investor has to trade, to avoid insolvency, but trading quickly leads to very unfavorable prices, which cause insolvency anyway. Ang, Papanikolaou, and Westerfield () also find that short sales and leverage of illiquid assets are forbidden, but in their model the illiquid asset trades at exogenous times, hence the investor cannot take action if prices move against him before a trading time arrives. By contrast, in our model illiquidity means finite depth, while continuous trading is allowed.…”

“…Gârleanu and Pedersen () study portfolio choice with a price‐impact function linear in shares traded, using mean‐variance preferences and assets driven by arithmetic Brownian motion. By contrast, the asset prices of Ang, Papanikolaou, and Westerfield () follow geometric Brownian motion, but they model an illiquid asset as one that trades only at exogenous random times, while trading is continuous in our setting.…”

Impact of Time Illiquidity in a Mixed Market Without Full Observation

“…Schwartz and Tebaldi () consider a market with a liquid asset that can be traded continuously, and an illiquid asset that cannot be traded and is liquidated at a terminal date. In a recent paper, Ang, Papanikolaou, and Westerfield (), in an infinite horizon framework with discounted power utility of consumption, take a less restrictive point of view on the tradability of the illiquid asset, assuming, as in Cretarola et al. (), Gassiat, Gozzi, and Pham (), Matsumoto (), Pham and Tankov (), and Rogers and Zane (), that it may be traded at discrete random times.…”

“…Following Ang et al. () and Schwartz and Tebaldi (), we also consider a market with a liquid asset and an illiquid one. In particular, as in Ang et al.…”

“…In particular, as in Ang et al. (), the illiquid asset can be traded at some discrete random dates. From the modeling side, the main novelty of our paper is that it treats the case of incomplete observation of the illiquid asset price between trading dates, modeled through an observation parameter interpolating the two extreme cases of full and no observation.…”