Financial Cartography - Center for Financial Research

Financial CartographyCFS Seminar

Dr. Kimmo SoramäkiFounder and CEOFNA, www.fna.fi

CFS PhD SeminarFrankfurt, 30 January 2013

“When the crisis came, the serious limitations of existing economic and financial models immediately became apparent. [...] As a policy-maker during the crisis, I found the available models of limited help. In fact, I would go further: in the face of the crisis, we felt abandoned by conventional tools.”

in a Speech by Jean-Claude Trichet, President of the European Central Bank, Frankfurt, 18 November 2010

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We did not have maps …

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Eratosthenes' map of the known world c. 194 BC

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… but what are maps

“A set of points, lines, and areas all defined both by position with reference to a coordinate system and by their non-spatial attributes”

Data is encoded as size, shape, value, texture or pattern, color and orientation of the points, lines and areas – everything has a meaning

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Political map of Europe

… but what are maps (contd.)

Cartographer selects only the information that is essential to fulfill the purpose of the map

Maps reduce multidimensional data into a two dimensional space that is better understood by humans

Maps are intelligence amplification, they aid in decision making and build intuition 

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Map by John Snow showing the clusters of cholera cases in the London epidemic of 1854

I. Mapping Systemic Risk

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II. Mapping Financial Markets

Systemic risk ≠ systematic risk

The risk that a system composed of many interacting parts fails (due to a shock to some of its parts).

In Finance, the risk that a disturbance in the financial system propagates and makes the system unable to perform its function – i.e. allocate capital efficiently.

Domino effects, cascading failures, financial interlinkages, … -> i.e. a process in the financial network

News articles mentioning “systemic risk”, Source: trends.google.com

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Not:

Network Theory can be to Financial Maps what Cartography is to Geographic MapsMain premise of network theory: Structure of links between nodes matters

To understand the behavior of one node, one must analyze the behavior of nodes that may be several links apart in the network

Topics: Centrality, Communities, Layouts, Spreading and generation processes, Path finding, etc.

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Network aspect is an unexplored dimension of data

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Variables

Obs

erva

tions

Time

First Maps Fedwire Interbank Payment Network, Fall 2001

Around 8000 banks, 66 banks comprise 75% of value,25 banks completely connected

Similar to other socio-technological networks

Soramäki, Bech, Beyeler, Glass and Arnold (2007), Physica A, Vol. 379, pp 317-333.See: www.fna.fi/papers/physa2007sbagb.pdf 11

M. Boss, H. Elsinger, M. Summer, S. Thurner, The network topology of the interbank market, Santa Fe Institute Working Paper 03-10-054, 2003.

Source: Bech, M.L. and Atalay, E. (2008), “The Topology of the Federal Funds Market”. ECB Working Paper No. 986.

More Maps: Federal Funds

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1997 - 2006

• 2600 loans worth $335 billion per day

• First Circle: 165Second Circle: 271Rest: 42

Source: Iori G, G de Masi, O Precup, G Gabbi and G Caldarelli (2008): “A network analysis of the Italian overnight money market”, Journal of Economic Dynamics and Control, vol. 32(1), pages 259-278

More Maps: Italian money market

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Italian (very small)Italian (small)Italian (large)Foreign

More Maps: DebtRank

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Source: Battiston et al, Nature Scientific Reports 2-54, 2012

Nodes: Financial institutionsLinks: Impact of an institution to another

Nodes closer to center are more important (as are big and red)

August 2007 to April 2008 October 2008 to April 2010

Where are we today?

Regulatory response to recent financial crisis was to strengthen macro-prudential supervision with mandates for more regulatory data

“Big data” and “Complex Data”-> Providing tools and challenge to understand, utilize and operationalize the data

Financial Networks are starting to get their own literature and metrics different from other fields of Network Theory

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(network is fictional)

Case: Oversight Monitor at Norges Bank

The monitor will allow the identification of systemically important banks and evaluation of the impact of bank failures on the system

Intraday Liqudidy Network -example

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II. Mapping Financial Markets

I. Mapping Systemic Risk

Outline

Purpose of the maps– Identify price driving themes and

market dynamics – Reduce complexity– Spot anomalies– Build intuition

The maps: Heat Maps, Trees, Networks and Sammon’s Projections

Based on asset correlations or tail dependence

These methods are showcased for visualizing markets around the collapse of Lehman Brothers

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Collapse of Lehman

Lehman was the fourth largest investment bank in the US (behind Goldman Sachs, Morgan Stanley, and Merrill Lynch) with 26.000 employees

At bankruptcy Lehman had $750 billion debt and $639 billion assets

Collapse was due to losses in subprime holdings and inability to find funding due to extreme market conditions

Is seen as a divisive point in the 2007-2009 financial crisis

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The Data

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Pairwise correlations of return on 118 global assets in 4 asset classes

9870 data points per time interval

Time windows 2 months before and 2 months after Lehman collapse

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Corporate Bonds

FX Rates

Government Bond Yields

Stock Exchange Indices

January 2007

-1

0

+1

Correlation

i) Heat Maps

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t-2 t-1January 2007

t+1 t+2

Corporate Bonds

FX Rates

GovernmentBonds

Stocks

Corporate Bonds

FX Rates

GovernmentBonds

Stocks

ii) Asset Trees

Originally proposed by Rosario Mantegna in 1999

Used currently by some major financial institutions for market analysis and portfolio optimization and visualization

Methodology in a nutshell

1. Calculate (daily) asset returns2. Calculate pairwise Pearson correlations of

returns3. Convert correlations to distances4. Extract Minimum Spanning Tree (MST)

5. Visualize (as phylogenetic trees) 22

Minimum Spanning TreeA spanning tree of a graph is a subgraph that: 1.is a tree and 2.connects all the nodes together

Length of a tree is the sum of its links. Minimum spanning tree (MST) is a spanning tree with shortest length.

MST reflects the hierarchical structure of the correlation matrix

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Demo: Asset Trees

Click here for interactive visualization

Color of node denotes asset class:

Links between nodes reflect 'backbone' correlations

- short link = high correlation- long link = low correlation

Size of node reflects volatility (variance) of returns

Dow Jones

EUR/USD

Ireland 10 year government bond

EMU Corporate AAA, 1-3 years

Correlation filtering

Balance between too much and too little information, signal vs noise

One of many methods to create networks from correlation/distance matrices

–PMFGs, Partial Correlation Networks, Influence Networks, Granger Causality, NETS, etc.

New graph, information-theory, economics & statistics -based models are being actively developed

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PMFG

Influence Network

iii) NETS

• Network Estimation for Time-Series

• Forthcoming paper by Barigozzi and Brownlees

• Estimates an unknown network structure from multivariate data

• Based on partial correlations

• Captures both comtemporenous and serial dependence (partial correlations and lead/lag effects)

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iv) Sammon’s Projection

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Iris Setosa

Iris Versicolor

Iris Virginica

Proposed by John W. Sammon in IEEE Transactions on Computers 18: 401–409 (1969)

A nonlinear projection method to map a high dimensional space onto a space oflower dimensionality. Example:

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Demo: Sammon Projection

Click here for interactive visualization

Color of node denotes asset class:

Distance between nodes reflects similarity of correlation profiles- close = similar- far apart = different

Size of node reflects volatility (variance) of returns

Dow Jones

EUR/USD

Ireland 10 year government bond

EMU Corporate AAA, 1-3 years

Tail dependence

• Correlation is a linear dependence. The same visual maps can be extended to non-linear dependences.

• Joint work with Firamis (Jochen Papenbrock) and RC Banken (Frank Schmielewski), see www.extreme-value-theory.com

• Instead of correlation, links and positions measure similarity of distances to tail losses

29Tail Tree

(Click here for interactive visualization)Tail Sammon

(click here for interactive visualization)

“In the absence of clear guidance from existing analytical frameworks, policy-makers had to place particular reliance on our experience. Judgment and experience inevitably played a key role.”

in a Speech by Jean-Claude Trichet, President of the European Central Bank, Frankfurt, 18 November 2010

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Blog, Library and Demos at www.fna.fi

Dr. Kimmo Soramäki [email protected]: soramaki