Incomplete Information and the Liquidity Premium Puzzle

Abstract

We examine the problem of an investor who trades in a market with unobservable regime shifts. The investor learns from past prices and is subject to transaction costs. Our model generates significantly larger liquidity premia compared to a benchmark model with observable market shifts. The larger premia are driven primarily by suboptimal risk exposure, as turnover is lower under incomplete information.In contrast, the benchmark model produces (mechanically) high turnover and heavy trading costs. We provide empirical support for the amplification effect of incomplete information on the relation between trading costs and future stock returns. We also show empirically that such amplification is not driven by turnover. Overall, our results can help explain the large disconnect between theory and evidence regarding the magnitude of liquidity premia, which has been a longstanding puzzle in the literature.

An Equilibrium Model for the Cross-Section of Liquidity Premia

“…This is illustrated in Figure 1, which shows that to produce a realistic level of liquidity premia, our model requires a substantial level of heterogeneity in the agents' preferences. This corroborates the partial equilibrium literature on liquidity premia, which finds that additional features such as market closure [14], unobservable regime switches [10], or state-dependent transaction costs [1,29] are needed to reproduce realistic levels of liquidity premia. Incorporating these effects into a general equilibrium analysis is an important but challenging direction for future research.…”

“…However, to match the magnitude of the liquidity premia observed empirically in our model, the risk aversion coefficients of the agents need to be rather heterogenous. In line with the partial equilibrium literature, this suggests that additional features such as market closure [14], unobservable regime shifts [10], or state-dependent trading costs [1,29] also play an important role in this context.…”

“…Moreover, F takes values in the positive semidefinite matrices. 10 With the solution of the matrix Riccati equations (4.8) at hand, we can then construct a solution of the FBSDE system from Lemma 4.2. The latter in turn leads to a Radner equilibrium with transaction costs.…”

“…In particular, S = S + Y t − (c ⊗ Λ) φt is a Radner equilibrium with transaction costs. 10 In much of the literature, positive definite matrices are additionally required to be symmetric. This does not generally hold for F , however, so that the arguments below need to be developed without this convenient property.…”