Choose Practical Portfolio Constraints

# Choose Practical Portfolio Constraints For a single-period statistical-arbitrage optimizer, specify practical constraints on target holdings and trades. Cover dollar, beta, and factor neutrality; gross and net exposure; single-name and sector limits; turnover; liquidity; and borrow availability. Explain the risk each constraint controls and how to detect an infeasible or overconstrained problem. ### Constraints & Assumptions - `h` is the target holding vector, `h0` is the current vector, and `delta = h - h0`. - Vectors for market beta, sector membership, and style-factor exposures are available. - Liquidity estimates and short-borrow availability are point-in-time inputs. - The optimizer must remain convex where practical. ### Clarifying Questions to Ask - Are holdings measured as weights, dollars, or shares? - Which neutrality requirements are hard constraints versus soft targets? - What holding period and fraction of daily volume are acceptable? - How should existing positions be handled when borrow disappears? ### What a Strong Answer Covers - Mathematical forms for exposure, position, trade, and liquidity limits - A reason for each constraint and consistent units - Point-in-time borrow and market-data handling - Feasibility diagnostics, slacks, and priority among competing limits ### Follow-up Questions 1. When would beta neutrality be insufficient even with dollar neutrality? 2. Which constraints should become penalties rather than hard limits? 3. How would constraints change for a multi-day liquidation horizon? ```hint Separate holdings from trades Some limits apply to the final portfolio, while turnover and market-capacity limits apply to the change from current holdings. ```