This document summarizes a presentation given by Dr. Kimmo Soramäki on financial cartography and mapping systemic risk and financial markets. The presentation discusses how existing economic models failed during the financial crisis and the need for better tools to understand financial linkages and systemic risk. It then outlines different mapping techniques like heat maps, asset trees, networks, and dimensional reduction techniques that can be used to visualize complex financial data and reduce dimensionality to aid decision making. Examples are provided mapping markets around the collapse of Lehman Brothers.

1. CFS PhD Seminar
Frankfurt, 30 January 2013
Financial Cartography
CFS Seminar
Dr. Kimmo Soramäki
Founder and CEO
FNA, www.fna.fi

2. “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
2

3. We did not have maps …
3

4. Eratosthenes' map of the known world4
c. 194 BC

5. … 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 Political map of Europe
5

6. … 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 Map by John Snow showing the clusters of cholera
cases in the London epidemic of 1854
intuition
6

7. I. Mapping II. Mapping
Systemic Risk Financial Markets
7

8. Systemic risk ≠ systematic risk
News articles mentioning “systemic risk”, Source: trends.google.com
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.
Not:
Domino effects, cascading failures, financial
interlinkages, … -> i.e. a process in the
financial network
8

9. Network Theory can be to Financial Maps
what Cartography is to Geographic Maps
Main 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.
9

10. Network aspect is an unexplored
dimension of data
e
Tim
Variables
Observations
10

11. 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), M. Boss, H. Elsinger, M. Summer, S. Thurner, The
Physica A, Vol. 379, pp 317-333. network topology of the interbank market, Santa
See: www.fna.fi/papers/physa2007sbagb.pdf Fe Institute Working Paper 03-
11
10-054, 2003.

12. More Maps: Federal Funds
1997 - 2006 Source: Bech, M.L. and Atalay, E. (2008), “The Topology of
the Federal Funds Market”. ECB Working Paper No. 986.
• 2600 loans worth $335
billion per day
• First Circle: 165
Second Circle: 271
Rest: 42
12

13. More Maps: Italian money market
Italian (very small)
Italian (small)
Italian (large)
Foreign
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 13

14. More Maps: DebtRank
August 2007 to April 2008 October 2008 to April 2010
Nodes: Financial institutions Source: Battiston et al, Nature
Links: Impact of an institution to another Scientific Reports 2-54, 2012
Nodes closer to center are more important (as are big and red) 14

15. 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
(network is fictional)
Financial Networks are starting to get their
own literature and metrics different from
Case: Oversight Monitor at Norges Bank
other fields of Network Theory
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
15

16. I. Mapping II. Mapping
Systemic Risk Financial Markets
16

17. 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
17

18. 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
18

19. The Data
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
19

20. i) Heat Maps
January
Corporate 2007
Bonds
FX Rates
Government
Bond Yields
Correlation
-1
Stock
Exchange 0
Indices
+1
20

21. January 2007 t-2 t-1
Corporate
Bonds
FX Rates
Government
Bonds
Stocks
t+1 t+2
Corporate
Bonds
FX Rates
Government
Bonds
Stocks
21

22. 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 returns
2. Calculate pairwise Pearson correlations of returns
3. Convert correlations to distances
4. Extract Minimum Spanning Tree (MST)
5. Visualize (as phylogenetic trees)
22

23. Minimum Spanning Tree
A 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

24. Demo: Asset Trees
Color of node denotes asset class:
Dow Jones Size of node reflects volatility
(variance) of returns
Ireland 10 year Links between nodes reflect
government bond 'backbone' correlations
EMU Corporate
AAA, 1-3 years
- short link = high correlation
- long link = low correlation
EUR/USD
Click here for interactive visualization 24

25. Correlation filtering PMFG
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, Influence Network
NETS, etc.
New graph, information-theory, economics
& statistics -based models are being
actively developed
25

26. 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)
26

27. iv) Sammon’s Projection
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 of
lower dimensionality. Example:
Iris Setosa
Iris Versicolor
Iris Virginica
27

28. Demo: Sammon Projection
EMU Corporate
AAA, 1-3 years Color of node denotes asset class:
Dow Jones
Size of node reflects volatility
Ireland 10 year (variance) of returns
government bond
Distance between nodes reflects
EUR/USD similarity of correlation profiles
- close = similar
- far apart = different
Click here for interactive visualization 28

29. 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
Tail Tree Tail Sammon
(Click here for interactive visualization) (click here for interactive 29

30. “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
30

31. Blog, Library and Demos at www.fna.fi
Dr. Kimmo Soramäki
kimmo@soramaki.net
Twitter: soramaki