Transaction Costs, Trading Volume, and the Liquidity Premium
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.
Keywords
Cite
@article{arxiv.1108.1167,
title = {Transaction Costs, Trading Volume, and the Liquidity Premium},
author = {Stefan Gerhold and Paolo Guasoni and Johannes Muhle-Karbe and Walter Schachermayer},
journal= {arXiv preprint arXiv:1108.1167},
year = {2013}
}
Comments
29 pages, 5 figures, to appear in "Finance and Stochastics". arXiv admin note: text overlap with arXiv:1207.7330