The Topology of Macro Financial Flows: An Application of Stochastic Flow Diagrams

44 Pages Posted: 16 Jan 2014 Last revised: 27 May 2014

Neil J. Calkin

Clemson University

Marcos Lopez de Prado

Guggenheim Partners, LLC; Lawrence Berkeley National Laboratory; Harvard University - RCC

Date Written: February 8, 2014


A large portion of Macroeconomic and Financial research is built upon classical applications of Linear Algebra (such as regression analysis) and Stochastic Calculus (such as valuation models). As a result, most Macroeconomic and Financial research has inherited a focus on geometric locations rather than logical relations. Ideally, Econometric models could be complemented with Topological and Graph-Theoretical tools that recognize the hierarchy and relationships between system constituents.

Stochastic Flow Diagrams (SFDs) are topological representations of complex dynamic systems. We construct a network of financial instruments and show how SFDs allow researchers to monitor the flow of capital across the financial system. Because our approach is dynamic, it models how and for how long a financial shock propagates through the system. Practical applications include stress-testing of investment portfolios under user-defined scenarios, and the discovery of Macro trading opportunities. SFDs add Topology to the Econometrics toolkit used by Macroeconomists, and may enlighten long-standing controversies, such as the one involving Keynesians and Austrian-school economists. Our findings have important implications for regulators, market designers and Macro investors.

Keywords: Time Series, Graph Theory, Topology, Financial Flows, Macro Trading

JEL Classification: G0, G1, G2, G15, G24, E44

Suggested Citation

Calkin, Neil J. and Lopez de Prado, Marcos, The Topology of Macro Financial Flows: An Application of Stochastic Flow Diagrams (February 8, 2014). Algorithmic Finance 2014, 3:1-2, 43-85. Available at SSRN: or

Neil J. Calkin

Clemson University ( email )

101 Sikes Ave
Clemson, SC 29634
United States


Marcos Lopez de Prado (Contact Author)

Guggenheim Partners, LLC ( email )

330 Madison Avenue
New York, NY 10017
United States


Lawrence Berkeley National Laboratory ( email )

1 Cyclotron Road
Berkeley, CA 94720
United States


Harvard University - RCC ( email )

26 Trowbridge Street
Cambridge, MA 02138
United States


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