Parameter Uncertainty: The Missing Piece of the Liquidity Premium Puzzle?

Abstract

I analyze a dynamic investment problem with stochastic transaction cost and parameter uncertainty. I solve the problem numerically and obtain the optimal consumption and investment policy and the least-favorable transaction cost process. Using reasonable parameter values, I confirm the liquidity premium puzzle, i.e., the representative agent model (without robustness) produces a liquidity premium which is by a magnitude lower than the empirically observed value. I show that my model with robust investors generates an additional liquidity premium component of 0.05%-0.10% (depending on the level of robustness) for the first 1% proportional transaction cost, and thus it provides a partial explaination to the liquidity premium puzzle. Additionally, I provide a novel non-recursive representation of discrete-time robust dynamic asset allocation problems with transaction cost, and I develop a numerical technique to efficiently solve such investment problems.