Transaction Costs, Trading Volume, and the Liquidity Premium

In a market with one safe and one risky asset, an investor with a long horizon, constantinvestment opportunities, and constant relative risk aversion trades with small proportionaltransaction costs. We derive explicit formulas for the optimal investment policy, its impliedwelfare, liquidity premium, and trading volume. At the first order, the liquidity premiumequals the spread, times share turnover, times a universal constant. Results are robust toconsumption and finite horizons. We exploit the equivalence of the transaction cost market toanother frictionless market, with a shadow risky asset, in which investment opportunities arestochastic. The shadow price is also found explicitly.[...]