Transaction Costs, Trading Volume, and the Liquidity Premium

In a market with one safe and one risky asset, an investor with a long

horizon and constant relative risk aversion trades with constant

investment opportunities and proportional transaction costs. We derive

the optimal investment policy, its welfare, and the resulting trading

volume, explicitly as functions of the market and preference parameters,

and of the implied liquidity premium, which is identified as the

solution of a scalar equation. For small transaction costs, all these

quantities admit asymptotic expansions of arbitrary order. The results

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 derived

explicitly. (Joint work with Paolo Guasoni, Johannes Muhle-Karbe, and

Walter Schachermayer)