Costly Trading

TL;DR

This paper analyzes optimal trading strategies considering slippage costs, revealing that the no-trade zone width scales with the square root of the cost parameter in stable return forecasts, differing from stochastic models.

Contribution

It demonstrates that in stable return environments, the no-trade zone scales as the square root of slippage costs, contrasting with previous stochastic setting results.

Findings

No-trade zone width scales as c^{1/2} in stable settings

Optimal trading balances alpha profits, costs, and risk aversion

Analysis uses a physical analogy of forced motion with friction

Abstract

We revisit optimal execution of an active portfolio in the presence of slippage (aka linear, proportional, or absolute-value) costs. Market efficiency implies a close balance between active alphas and trading costs, so even small changes to trading optimization can make a big difference. It has been observed for some time that optimal trading involves a pattern of a no-trade zone with width $\Delta$ increasing with slippage cost parameter $c$. In a setting of a reasonably stable (non-stochastic) forecast of future returns and a quadratic risk aversion, it is shown that $\Delta\sim c^{1/2}$, which differs from the $\Delta\sim c^{1/3}$ scaling reported for stochastic settings. Analysis of optimal trading employs maximization of a utility including projected alpha-based profits, slippage costs, and risk aversion and borrows from a physical analogy of forced motion in the presence of friction.