How do you incorporate transaction costs and liquidity constraints into your optimization models?

To put that into laymen’s terms, with the introduction and rapid growth of electronic trading, markets are about speed. Many firms, legal or otherwise, combine advanced traders’ intuition with AI and ML trained to detect big money accounts in the markets attempting to buy sizable stakes or offload large positions. It’s rare they go unnoticed; even the best traders leave bread crumb’s in their wake. Clues become recognizable in repetitive trading patterns and stable block sizes as the big-money hopes to go unnoticed. But steady as she goes gets you caught: unpredictable and erratic behavior may spook the sleuths. Either way, traders use ML to detect buying patterns and front-run big money accounts. Now those are real transaction costs.

Best practices for incorporating transaction costs into optimization models include: 1) Adding a penalty term reflecting costs in the objective function, 2) Using quadratic programming with a budget constraint, and 3) Employing stochastic programming with transaction costs as random variables. For instance, in portfolio optimization, a quadratic programming model minimizes variance while considering transaction costs, ensuring realistic and efficient asset allocation. Key points: account for costs, choose appropriate optimization approach, and consider market conditions.

My experiance teaches me that building allocation models, accurately accounting for trading costs and asset liquidity is crucial. Built an optimization that recommended rebalancing frequently without proper liquidity adjustments. When implemented, the trades faced high slippage and some could not even be executed. Learned to constrain the model by incorporating percentile bands (<-- key) on execution costs based on historical volume data. This prevents overtrading of illiquid assets. The optimizer applies these friction costs when determining allocations, leading to more prudent turnover and trade sizing. Real-world constraints must be modeled to produce actionable portfolio recommendations.

To effectively incorporate liquidity constraints into optimization models, consider modifying expected returns and covariances based on liquidity measures, such as turnover or spread, in a liquidity-adjusted mean-variance model. Alternatively, impose upper and lower bounds on portfolio weights according to asset liquidity levels in a constrained optimization model. For robustness, use a robust optimization model that considers worst-case liquidity shocks and market frictions. By adjusting optimization models to account for liquidity constraints, you ensure more realistic and resilient portfolio management, mitigating the impact of trading limitations on asset allocation decisions.

To effectively navigate the trade-offs between transaction costs, liquidity constraints, and other objectives in optimization models, consider these best practices: 1. Utilize multi-objective optimization to simultaneously optimize returns, risk, transaction costs, and liquidity, generating Pareto-optimal solutions. 2. Conduct sensitivity analysis to assess the impact of varying factors like transaction costs and liquidity measures on portfolio performance and risk. 3. Perform backtesting using historical data to compare optimization model results with benchmark portfolios. By employing these methods, you can make informed decisions that balance competing objectives in portfolio management.

Incorporating transaction costs and liquidity constraints can make an optimization model far more realistic but also computationally intense. One approach that worked well for me was sourcing transaction cost data from multiple brokers and updating it frequently to ensure reliability. When it came to liquidity, using rolling average daily volume (ADV) as a constraint was effective for ensuring that trades could be executed without significantly impacting the market price.

Global nonlinear solvers like DEoptim - global differential evolutionary solvers, etc. & the like can handle transaction costs, slippage, bid/ask spread loss & liquidity specifications as constraints &/or parameters in the optimization routine. The degree of success in the outcome is still heavily reliant on the model builder’s skill & understanding of the industry & particular use case. If the user does not have experience with the situation the optimization is being applied to, she/he should ask several practitioners if her/his assumptions are realistic. For example, an options market-maker would know to adjust for / incorporate give-up from bid/ask spreads & that these widen under conditions of market stress.