This paper deals with the model of transaction costs with one safe and one risky asset and constant investment opportunities. The authors obtain explicitly the optimal trading policy, its welfare, liquidity premium, and trading volume, for an investor with constant relative risk aversion and long horizon. It is shown that the no-trade region is perfectly symmetric with respect to the Merton proportion, if the buy boundary is computed from the ask price, and the sell boundary from the bid price. The liquidity premium and the trading volume are small in the unlevered regime, but become substantial in the presence of leverage. The authors show that share turnover (ShTu), the liquidity premium (LiPr) and the bid-ask spread $$\varepsilon$$ satisfy the asymptotic relation $$\mathrm{LiPr}\approx {3\over 4}\varepsilon~\mathrm{ShTu}$$. Trading boundaries depend on investment opportunities only through the mean-variance ratio. The equivalent safe rate, the liquidity premium, and the trading volume also depend only on the mean-variance ratio if measured in business time. The results are robust to consumption and finite horizon. The authors use the equivalence of the transaction cost market to another frictionless market, with a shadow risky asset, in which investment opportunities are stochastic.
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