  The steady-state turnover of a trading strategy is of clear interest to
practitioners and portfolio managers, as is the steady-state Sharpe ratio. In
this article, we show that in a convenient Gaussian process model, the
steady-state turnover can be computed explicitly, and obeys a clear relation to
the liquidity of the asset and to the autocorrelation of the alpha forecast
signals. Indeed, we find that steady-state optimal turnover is given by $\gamma
\sqrt{n+1}$ where $\gamma$ is a liquidity-adjusted notion of risk-aversion, and
$n$ is the ratio of mean-reversion speed to $\gamma$.
