Portfolio Dynamics and Expected Returns Under Illiquidity

Using a novel continuous-time framework, this paper explores the effects of illiquidity on portfolio dynamics and expected returns. In summary, the paper makes three key contributions to the existing literature on asset pricing and illiquidity. First, it illustrates that illiquidity leads to portfolio proportions being stochastic processes. The numerical results highlight that investors should be prepared for potentially large and skewed variations in portfolio weights and can be away from optimal diversification for a long time when adding illiquid assets to a portfolio. The second contribution is to show that stochastic portfolio proportions implied by illiquidity increase overall portfolio risk. Interestingly, this effect gets more pronounced when the return correlation between the liquid and illiquid asset is low. Thus, there is a correlation effect in the sense that illiquidity costs, as measured by the increase in overall portfolio risk due to portfolio proportions being stochastic, are inversely related to the return correlation of the liquid and illiquid asset. Third, the paper explores the asset pricing implications of stochastic portfolio proportions. The derived valuation framework shows that the required excess returns of a portfolio can be split into two covariance terms: the first covariance term captures standard market risk, whereas the second term can be interpreted as a required compensation for a form of liquidity risk. This required compensation for liquidity risk increases linearly with the covariance between the proportion invested illiquid in the portfolio and the proportion invested illiquid in the market portfolio, i.e., investors want to be compensated for holding portfolios that become illiquid when the market in general turns illiquid