Transaction Costs, Trading Volume, and the Liquidity Premium

TL;DR

This paper derives explicit formulas for optimal trading strategies, welfare, and liquidity premiums in a market with transaction costs, showing their relationships to market spreads and trading volume, applicable across various market conditions.

Contribution

It provides explicit formulas for optimal policies, welfare, and liquidity premiums considering transaction costs, and introduces a shadow price approach for stochastic investment opportunities.

Findings

Liquidity premium equals spread times share turnover times a universal constant.

Results are robust to consumption and finite horizons.

Shadow price explicitly characterized in the model.

Abstract

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.