Optimal Portfolio Choice in the Presence of Illiquid Assets

Abstract

We propose two models of illiquidity to determine how an investor behaves optimally in the presence of an illiquid asset, which can only be traded infrequently and on random dates. The investor is less willing to invest in the illiquid asset compared to a situation where all assets are liquid, and his optimal amount invested in the illiquid asset is almost half of what it would be if the asset was liquid. The presence of illiquidity also distorts the investor’s willingness to take gambles in his liquid wealth, because he can only meet his immediate obligations with liquid wealth. Together with the fact that the next trading opportunity is random, the investor is less willing to invest in liquid risky asset. We find that investors with shorter investment horizons will never invest any amount in the illiquid asset, and risk-averse investors will need an investment horizon of at least 5 years before they are willing to buy any amount of an illiquid asset that is trade-able on average every year. There is very little difference between long-term investors, as an investor with a investment horizon of 10 year will allocate 1% less in the illiquid asset than an investor with infinite investment horizon. We conclude that the degree of liquidity is an important determinant of the behaviour of the investor. The more illiquid the asset is, the less willing the investor is to buy it, and therefore the more he will need to be compensated in order to invest in it.