In a critical back-office operation, a broker-dealer firm must segregate a federally regulated amount of cash and securities in specially protected accounts on behalf of its clients to ensure that clients can withdraw the bulk of their holdings on demand, even if the firm becomes insolvent.
The firm must calculate what it owes to clients and what clients owe to it. If the amount owed to clients exceeds the amount owed from clients, the firm must lock up a portion in a special reserve account. The cash and securities segregated into this account cannot be used by the firm for any purpose, such as trading for its own account or funding its operations. At a single firm, the amount in this account can reach billions of dollars.
The calculation has complex adjustments related to derivatives and lending arrangements. There also are risk levels assigned to various classes of assets, which can modify the computation in complicated ways.
Executives at a broker-dealer had developed a spreadsheet-based prototype of an optimization model for securities collateral. They sought assistance in refining the model’s underlying mathematics and defining its objective function. They required transparency to the optimization results so they could be validated internally by subject matter experts and externally by regulators. Expertise with Gurobi, the firm’s chosen optimization solver to power the solution, was needed.
The executives retained Princeton Consultants for an advanced analytics model review and validation. A team worked with the broker-dealer’s business, operations and analytics executives to define an appropriate mathematical model, including defining multiple objective functions and appropriate constraints that considered issues including: accounting for a possible shortfall in the securities available from the clients to cover the total security requirements; covering deficits in a priority order, if possible; if a deficit must be created, creating the deficits on low-quality assets; and arbitrating choices of securities from different clients via an assessment of quality and rank of the securities. The constraints needed to ensure that new deficits should not be created for the business benefit; total market value should not be greater than a specified allowable value; and total segregated and hypothecated positions should not exceed available positions in the portfolio.
The team tested its model with sample data and multiple days of production data, revised and tuned the performance of Gurobi, and conducted a limited sensitivity analysis of the solution. The team also validated that the Java implementation created by the client was equivalent to the python implementation created by the Princeton Consultants team.
Initially, the broker-dealer firm’s executives wanted to use mixed integer programming (MIP) to get results, but the large quantity of objective functions did not allow the Gurobi mixed integer programming solver to meet the performance requirements. The Princeton Consultants team created a heuristic methodology based on leveraging the Gurobi linear programming solvers and other linear programming techniques that allowed the problems to be solved within the time requirements.
The new system is used nightly to reallocate securities and cash between the securities depository and the clients to meet the stakeholders’ needs. The broker-dealer firm now has a mechanism for allocation that is automatic, transparent, and meets the needs of the regulatory environment. Executives are exploring additional applications of mathematical optimization for the business.
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