We find robust portfolio rules for ambiguity-averse fund managers in a financial market with proportional transaction costs. The model proposed in this paper permits a liquidity premium much bigger than those found by most empirical literature. Our liquidity premium is much bigger when using reasonably-calibrated parameters, so transaction costs can have a significant effect on investors' optimal investment behaviors. We also show that a high ambiguity aversion could be an explanation for a puzzling feature of economic crises, where liquidity was greatly reduced in the financial market. Our model shows that a fund manager with a higher ambiguity aversion requires much a bigger liquidity premium at times of down markets than at times of up markets.

"The seminal work of Constantinides (1986) documents how, when the risky return is calibrated to the U.S. market return, the impact of transaction costs on per-annum liquidity premia is an order of magnitude smaller than the cost rate itself. A number of recent papers have formed portfolios sorted on liquidity measures and found a spread in expected per-annum return that is definitely not an order of magnitude smaller than the transaction cost spread: the expected per-annum return spread is found to be around 6-7% per annum. Our paper bridges the gap between Constantinides' theoretical result and the empirical magnitude of the liquidity premium by examining dynamic portfolio choice with transaction costs in a variety of more elaborate settings that move the problem closer to the one solved by real-world investors. In particular, we allow returns to be predictable and transaction costs to be stochastic, and we introduce wealth shocks, both stationary multiplicative and labor income. With predictable returns, we also allow the wealth shocks and transaction costs to be state dependent. We find that adding these real world complications to the canonical problem can cause transactions costs to produce per-annum liquidity premia that are no longer an order of magnitude smaller than the rate, but are instead the same order of magnitude. For example, predictable returns and i.i.d. labor income growth causes the liquidity premium for an agent with a wealth to monthly labor income ratio of 0 or 10 to be 1.68\% and 1.20\% respectively; these are 21-fold and 15-fold increases, respectively, relative to that in the standard i.i.d. return case. We conclude that the effect of proportional transaction costs on the standard consumption and portfolio allocation problem with i.i.d. returns can be materially altered by reasonable perturbations that bring the problem closer to the one investors are actually solving"--National Bureau of Economic Research web site.

Abstract: "An agent solves an infinite-horizon consumption-investment problem when the investment possibilities are a constant-interest-rate, risk-free asset and a stock, modelled as a geometric Brownian motion. There are proportional transaction costs associated with moving wealth between these two assets. The direct utility for consumption is of the form 1/p c[superscript p] for some p [element of] (0,1). The sensitivity of the indirect utility function (or value function) to small transaction costs is found to be of the order of the transaction cost to the 2/3 power."

This paper examines the role of liquidity risk in explaining the cross-section of asset returns using a new measure of liquidity that captures its multi-dimensional nature. This new measure earns a robust liquidity premium that the CAPM and the Fama-French three-factor model cannot explain. I find that a two-factor (market and liquidity) model performs better in explaining the cross-section of stock returns than the CAPM and the Fama-French three-factor model. It not only describes the liquidity premium, but it also subsumes documented anomalies associated with size, book-to-market, cashflow-to-price, earnings-to-price, dividend yield, and long-term contrarian investment. The model also accounts for price momentum after taking into account transaction costs.

In a market with one safe and one risky asset, an investor with a long horizon, constant investment opportunities, and constant relative risk aversion trades with small proportional transaction costs. We derive explicit formulas for the optimal investment policy, its implied welfare, liquidity premium, and trading volume. At the first order, the liquidity premium equals the spread, times share turnover, times a universal constant. Results are robust to consumption and finite-horizons. We exploit the equivalence of the transaction cost market to another frictionless market, with a shadow risky asset, in which investment opportunities are stochastic. The shadow price is also found explicitly.