On the distribution and estimation of trading costs

• I provide an accurate approximation of the ex ante distribution of trading costs.
• I analytically relate the expected trading costs to the asset and portfolio moments.
• I develop novel estimators of the expected trading costs and turnover.
• Expected trading costs can be reduced through a new portfolio choice setting.
• Several numerical experiments confirm the practical value of the results.

This paper investigates the uncertainty about the trading costs associated with a given portfolio strategy. I derive accurate approximations of the ex ante probability distributions of proportional trading costs and portfolio turnover under the conventional assumption of normal asset returns. Based on these approximations, I express the expected trading costs as a function of asset and portfolio characteristics. All else equal, the expected trading costs increase with: i) the deviations of the expected asset returns from the expected portfolio return, ii) the assets' volatility and iii) the portfolio volatility. At the same time, they decrease with the covariance between the assets and the portfolio. Furthermore, I propose novel estimators of the expected turnover and trading costs and show that they offer small bias and low variance, even when the sample size is small. Finally, I incorporate my results into a portfolio selection framework to produce portfolios with low levels of risk and trading costs. Several experiments with real and simulated data confirm the practical value of the results.