Portfolio Optimization with Gurobi Gurobi Anwendertage 2017
swissquant Group: Intelligent Technology For leading companies in different industries State-of-the-art R & D Founded in 2005 as an official spin-off of the ETH Zurich (highest ranked Engineering and Mathematical university in Switzerland) Privately owned by the founders Largest independent Quant team in Switzerland Loyal to Quant R & D roots, with 40% of employed Quant engineers holding PhD s Intelligent Technologies Dynamic Modeling Efficient Computation Toolboxes & Software Forecasting Quant strategies Business Intelligence swissquant translates state-of-the-art technology in quantifiable and sustainable value for its customers in many different disciplines: Trading & Risk Mgmt. Modeling & Analytics Hedging & Procurement Investment Valuations Algorithms / Optimisation Supply Chain & Logistics swissquant Group 1
Client Profiling: increasing client engagement Visualize opportunities and risk interactively Understand the strategy: performance and risk analysis of the different strategies offered by the bank Historical Opportunities: each profile can be analyzed and compared to one or several benchmarks Stress-Tests: understand the risk of the bank s strategies in an comprehensive and interactive way Recovery-times: understand the recovery times after drawdowns and their relation to the risk profile swissquant Group 2
Portfolio construction & optimization Comply with regulatory, client & bank restrictions Customize: client specific investment preferences are included in the portfolio construction Unique: worldwide most granular and only discrete portfolio optimizer (considering instrument quantities and lot sizes) SAA/TAA: systematic alignment of client portfolios with the bank s market view Industrialize: cost reduction and enhanced efficiency in the advisory process swissquant Group 3
Portfolio Health Checks Continuous portfolio review Intuitive report summarizes which Health Checks are met and which ones are breached σ 2 Health Checks may be based on purely quantitative measures such as volatility or VaR >10% Health Checks may also be based on qualitative measures such as rating, issuer risk, bulk risk Strengthen the client relationship as transparency increases and regulatory requirements are met swissquant Group 4
Pre-trade suitability Know the impact of a transaction before executing the trade Instantaneous risk assessment: show the impact of a transaction in a portfolio before the trade is executed Risk assessment on instrument level (PRC) and on portfolio level with full accuracy reflecting correlation, currency risk and hedging as well as effects of linear/nonlinear derivatives Advisory minutes will show the suitability checks and the reasoning for the investment decisions Key to success: increased quality through systematic investment recommendations and Pre-trade checks swissquant Group 5
Portfolio adjustments/optimization Steer the portfolios in the direction of the SAA/TAA Optimization generate automated investment proposals steering the portfolio back to the SAA/TAA Instrument selection based on statistical properties such as risk/return, correlations to the clients portfolio, analyst recommended instruments and client preferences Key to success: Well informed exchange with client through qualitative and quantitative explanation of each investment proposal Advisory minutes will show the suitability checks and the reasoning for the investment decisions swissquant Group 6
Customized Industrialization with the swissquant Approach Return Target Allocation Risk Profiling Client Constraints Each client is mapped to a bank-defined target allocation which is considered optimal for the client s risk profile The client defines which instruments to keep in the portfolio (hold constraints), the maximum turnover and many more Client Portfolio Bank Constraints The bank defines general constraints such as issuer concentration limits, bulk risk constraints and asset allocation bounds Risk Portfolio Optimization The optimization suggests the portfolio which minimizes the tracking error between the client portfolio and the target allocation while fulfilling all of the above constraints swissquant Group 7
The challenge for the solver Business Problem Find the optimal mix of financial instruments amongst a universe of 1 000-10 000 instruments satisfying thousands of bank and client constraints recommending trades in units Mathematical Problem Find a solution to a quadratic objective function of dimenstionaliy at the order of 10 3-10 4 with a similar order of magnitude of linear boundary conditions solved in the mixed-integer space Further complication Optimization has to be performant and produce results in near real-time (few seconds) as it is used in direct clientinteraction on tablet Solver Evaluation Finding the optimal solver in terms of: Speed of the calculation Quality of the optimization (optimiality) Reliability of the solution swissquant Group 15
is best solved by Gurobi Below are results of summary results for large scale tests performed on actual client portfolios Speed Gurobi finds a solution in less than 20 seconds for 98% of all feasible problems, while a Competitor product finds a solution in less than 20 seconds only for 38% of all feasible problems. Quality For 7% of all feasible problems, Gurobi finds a solution with an utility higher by more than 1% of the utility of the Competitor solution. Reliability Gurobi finds an optimal solution for the 90% of all feasible problems, while the Competitor finds an optimal solution only for the 55% of all feasible problems. swissquant Group 16
Portfolio Optimization with Gurobi Use Case Portfolio Management not only requires continuous monitoring of risk and return of client portfolios but also managing a large number of restrictions Automated trade suggestions help resolving restriction breaches Objective Function The objective function is a quadratic utility function in high dimensionality with a large number of restrictions Furthermore, it needs to be solved in the mixed integer space due to indivisibility of financial instruments Solver Challenge The solver has to find a solution in nearreal time in high dimensionality in the mixed-integer space subject to a high number of linear constraints Results Gurobi dominates other commercial solvers for the swissquant portfolio optimization applications It is currently used productively at an increasing number of Swiss and international private banks swissquant Group 20
Disclaimer This material is provided for illustrative purposes only and should not be construed as investment advice or an offer to sell, or the solicitation of offers to buy, any security. Opinions expressed herein are current as of the date appearing in this material. Simulated performance results have inherent limitations. Such results are hypothetical and do not represent actual trading, and therefore may not take into account material economic and market factors, such as liquidity constraints, that would impact the adviser's actual decision-making. Simulated results are also achieved through the retroactive application of a model designed with the benefit of hindsight. The results shown may reflect the reinvestment of dividends and other earnings, but may not reflect advisory fees, transaction costs, and other expenses a client would have paid, which would reduce returns. No representation is made that a client will achieve results similar to those shown. If any of the assumptions used in these examples do not prove to be true, results may vary substantially from the examples shown. Examples are for illustrative purposes only and do not purport to show actual results. The information contained in this presentation is not intended to be used as a general guide to investing, or as a source of any specific investment recommendations, and makes no implied or express recommendations concerning the manner in which any client s account should or would be handled, as appropriate investment strategies depend upon the client's investment objectives. It is the responsibility of any person or persons in possession of this material to inform themselves of and to observe all applicable laws and regulations of any relevant jurisdiction. It should not be assumed that recommendations made in the future will be profitable or will equal the performance of the securities mentioned herein. This presentation does not constitute an offer or solicitation to any person in any jurisdiction in which such offer or solicitation is not authorized or to any person to whom it would be unlawful to make such offer or solicitation. Prospective investors should inform themselves and take appropriate advice as to any applicable legal requirements and any applicable taxation and exchange control regulations in the countries of their citizenship, residence or domicile which might be relevant to the subscription, purchase, holding, exchange, redemption or disposal of any investments. Past performance is not a guide to future performance and the value of investments and the income derived from those investments can go down as well as up. Future returns are not guaranteed and a loss of principal may occur. swissquant Group 11
Contact Matthias Wyss MSc University of Oxford Head ImpaQt Consulting wyss@swissquant.com +41 (0)43 244 30 91 Contact Address swissquant Group AG Kuttelgasse 7 CH-8001 Zürich www.swissquant.com +41 (0)43 244 75 85