Transaction Costs, Trading Volume, and the Liquidity Premium

Stefan Gerhold, Paolo Guasoni, Johannes Muhle-Karbe, Walter Schachermayer
2012 Social Science Research Network  
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
more » ... 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. Mathematics Subject Classification: (2010) 91G10, 91G80. JEL Classification: G11, G12.
doi:10.2139/ssrn.1905077 fatcat:l7zzsy7nl5aqxkinwheibbyjya