Model Trading Frictions in Portfolio Optimization

# 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? ### What a Strong Answer Covers - Trade-dependent linear and convex nonlinear cost functions - Holding-dependent borrow and concentration terms - Unit-consistent calibration with point-in-time execution data - Avoidance of double counting and analysis of convexity ### Follow-up Questions 1. How would asymmetric buy and sell liquidity change the formulation? 2. When can a fixed ticket fee make the problem nonconvex? 3. How would you validate impact estimates without leaking future executions? ```hint Model costs on the change in holdings Execution frictions generally depend on `h - h0`, while borrow and some concentration risks depend on the resulting position. ```