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Presentation held at the 5th Risk Summit organized by Center for Risk Studies at the University of Cambridge. See http://www.risk.jbs.cam.ac.uk/news/events/risksummits/risksummit2014.html
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FINANCIAL CARTOGRAPHY
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23 June 2014 !Risk Summit at Center for Risk Studies The Pulse of Risk: From Big Data to Business Value !!Dr. Kimmo SoramäkiFounder and CEO, FNA Ltd.
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Soramaki et al, 2007
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What can old maps teach us about visualizing complex financial data?!
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!!
A Map is!!
A set of points, lines, and areas all defined both by position with reference to a coordinate system
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Eratosthenes' map of the known world c. 194 BC
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!!
Data is encoded as size, shape, value, texture or pattern, color and orientation of the points, lines and
areas!!
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The Ebstorf map (Mappa mundi), 13th c.
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!!
Maps reduce multidimensional data into !a two dimensional space and filter out details
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20 zoom levels of Google maps, 2014!
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Correlation MapsDifficult to understand large-scale correlation or other dependence structures.!!Especially time series.!!How to filter signal from noise?!!How to put the correlations and their changes in context with changes/returns and volatility?!!!Objective is to efficiently represent a complex system!
…"
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Significant CorrelationsCommon method to visualize large correlation matrices is with heat maps.!!!!!!If we only keep statistically significant correlations with 95% confidence level, the resulting matrix is sparse (with short time periods).
All correlations (last 100 days)!
Statistically significant correlations (last 100 days)!
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Sample Time-series
Corporate Bonds - Gov. Bonds
S&P 500 - Financials
Lehman Collapse
Subprime Crisis
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Correlation NetworksA sparse matrix is often well represented as a network. !!We encode correlations as links between the correlated nodes/assets.!!!Red link = negative correlation Black link = positive correlation!!!Absence of link marks that asset is not significantly correlated.!
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Dimensionality Reduction & FilteringNext, we identify the Minimum Spanning Tree (MST) and filter out other correlations.!!Rosario Mantegna (1999) ‘Hierarchical Structure in Financial Markets’ !This shows us the backbone correlation structure where each asset is connected with the asset with which its correlation is strongest.
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Coordinate SystemWe use a radial tree layout algorithm (Bachmaier & Brandes 2005) that places the assets so that:!!• Shorter links in the tree
indicate higher correlations!!
• Longer links indicate lower correlations!
!As a result, we also see how the assets cluster (analogous to single linkage clustering).!
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Encoding non-spatial dataNode color indicates last daily return!!Green = positive!!Red = negative!!Node size indicates magnitude of return!!!
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“Here be Dragons”Sornette’s Dragon King: “Extreme events can be predicted”!!Mandelbrot’s Volatility Clustering: “Large changes tend to be followed by large changes”!!!-> Identify VaR exceptions (return outside 95% VaR bounds)!!-> Map them as bright green or red nodes!
Track the number of outliers each day
Highlight outliers in their context
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Correlations Maps!Dimensionality Reduction & Filtering!-> Minimum Spanning Tree!!!Coordinate System!-> Radial Tree layout algorithm (correlation distances)!!!System for visual encoding of (non-spatial) data!-> Returns and Outliers!!!
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Cartographer selects only the information that is essential to fulfill the purpose of the map!
!
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Other Financial MapsNetwork of Economic States Interbank Payment Networks
Trade Flow Networks Interbank Exposure Networks
