Model Trading Frictions in Portfolio Optimization

Extend a single-period statistical-arbitrage objective to reflect real trading frictions. Describe useful terms for commissions and linear costs, bid-ask spread, slippage, nonlinear market impact, turnover, short-borrow fees, and concentration. Explain which terms may overlap, how they are calibrated, and when the resulting optimization remains convex.

Constraints & Assumptions

• h0 is the current portfolio, h is the target, and delta = h - h0 is the trade.
• Point-in-time prices, spread, volume, volatility, and borrow estimates are available.
• Costs should be expressed in the same objective units as expected profit.
• Buy and sell costs may differ.

Clarifying Questions to Ask

• What execution horizon, order type, and participation rate are assumed?
• Are alpha forecasts gross or already net of any cost?
• Should borrow be charged on target shorts or only incremental shorts?
• Which cost components are empirically separable?