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The Liquidity Premium in a Dynamic Model with Price Impact

By João Pedro Pereira and Harold H. Zhang


We examine the liquidity premium in a dynamic model with price impact. The liquidity premium is defined as the additional return necessary to compensate the investor for the adverse price impact of trading. Our study reveals that with price impact the optimal stock investment increases with the investment horizon and decreases with the investor’s initial wealth. The liquidity premium is increasing and concave in price impact. It also increases with the investor’s initial wealth and decreases with the investment horizon and the investor’s risk aversion. Allowing for stochastic liquidity, our analysis offers an intuitive theoretical explanation for the “puzzling ” empirical finding that the liquidity premium decreases with the volatility of liquidity. Further, we find that uncertainty about the investment horizon substantially increases the liquidity premium

Year: 2004
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