Multi-Asset Portfolio Optimization via MIQP
An institutional portfolio construction framework using mixed-integer quadratic programming to enforce real-world allocation constraints across asset classes.
This project is a multi-asset portfolio construction framework designed to move beyond textbook mean-variance optimization and toward the realities of institutional allocation. Instead of assuming frictionless, infinitely divisible portfolios, the system formulates the allocation problem as a Mixed-Integer Quadratic Program so that practical trading and policy constraints are embedded directly into the optimizer.
The pipeline begins with a standard mean-variance objective, but layers on cardinality limits, minimum-lot sizes, and sector concentration caps to reflect the constraints actual managers face when deploying capital. This means the optimizer must choose not only how much to allocate, but also which positions deserve inclusion in the first place. The result is a much more realistic efficient frontier, one that acknowledges the combinatorial structure of implementation rather than abstracting it away.
The framework is built across equity, fixed income, and commodity universes, allowing cross-asset trade-offs to emerge endogenously from the optimization itself. By benchmarking the MIQP solution against both unconstrained MVO and naive 1/N allocations, the project quantifies how much is gained from disciplined optimization and how much is lost when constraints are ignored. Sensitivity analysis further shows which rules bind most tightly and how the portfolio responds as the feasible set is relaxed or tightened.
Interpretability is central to the design. Rather than treating the solver as a black box, the system surfaces which constraints are active, how they reshape the frontier, and where trade-offs between concentration, diversification, and implementability become most severe. That makes the optimizer useful not only for producing allocations, but also for explaining portfolio architecture in a policy or investment committee setting.
Overall, the project demonstrates how integer-constrained optimization can deliver institutionally credible portfolios that are quantitatively rigorous and operationally deployable. Future extensions include turnover penalties, transaction-cost-aware rebalancing, and robust optimization under return and covariance uncertainty.