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.

Liquidity and Asset Prices reviews the literature that studies the relationship between liquidity and asset prices. The authors review the theoretical literature that predicts how liquidity affects a security's required return and discuss the empirical connection between the two. Liquidity and Asset Prices surveys the theory of liquidity-based asset pricing followed by the empirical evidence. The theory section proceeds from basic models with exogenous holding periods to those that incorporate additional elements of risk and endogenous holding periods. The empirical section reviews the evidence on the liquidity premium for stocks, bonds, and other financial assets.

The relationship of stock returns and trading volume is the focus of much recent interest. I examine an economic model of a rational trader who operates in a market with transactions costs and noise trading. The level of trading affects the rational trader’s marginal cost of transacting; as a result, trading volume is a source of risk. This engenders an equilibrium relationship between returns and volume. The model also provides a simple way to scrutinize this relationship empirically. Empirical evidence supports the implications of the model.

Theoretical papers link the liquidity premium to the optimal trading decisions of investors facing transaction costs. In particular, investors' holding periods determine how transaction costs are amortized and priced in asset returns. Using a unique data set containing two million trades, this paper investigates the relationship between holding periods and transaction costs for 66,000 households from a large discount brokerage. The author finds that transaction costs are an important determinant of investors' holding periods, after controlling for household and stock characteristics. The relationship between holding periods and transaction costs is stronger among more sophisticated investors. Households with longer holding periods earn significantly higher returns after amortized transaction costs, and households that have holding periods that are positively related to transaction costs earn both higher gross and net returns. The author shows that there is correlation in the demand for liquid assets across households and, consistent with the notion of flight to liquidity, this demand increases during times of low market liquidity. Households with higher incomes and with higher wealth invested in the stock market supply liquidity when market liquidity is low.

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 relationship of stock returns and trading volume is the focus of much recent interest. I examine an economic model of a rational trader who operates in a market with transactions costs and noise trading. The level of trading affects the rational trader`s marginal cost of transacting; as a result, trading volume is a source of risk. This engenders an equilibrium relationship between returns and volume. The model also provides a simple way to scrutinize this relationship empirically. Empirical evidence supports the implications of the model.