Diversification in Illiquid Market
33 Pages Posted: 20 Sep 2006 Last revised: 30 Jun 2010
We consider a portfolio optimization problem for an investor who can trade liquid and illiquid stocks. The illiquidity of a stock is defined by the presence of a transitory price impact. We analyze the effects from the presence of illiquid stocks on allocations to liquid ones and vise versa. We find that allocations to the two types of stocks are considerably different from those in a liquid market. Moreover, presence of illiquid stocks can have very strong effects on allocations to liquid ones even if the former take a very small fraction of the stock market. This result implies a possibility of a strong comovement between all stocks in the market even if they are seemingly independent and illiquid stocks occupy only a small fraction of the stock market. We find that the liquidity premium for holding illiquid stocks is often very significant and depends on how long this stock remains illiquid. Furthermore, this premium could be very high even if illiquid stocks take a very small fraction of the stock market and the relative exposure of each investor to these stocks is very small. Finally, we confirm the limits to arbitrage by showing that an investor takes a risky position in the presence of arbitrage opportunities.
Keywords: Portfolio Choice, Liquidity, Transaction Costs
JEL Classification: G11
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