system shock analysis and complex network effects
DESCRIPTION
Joint presentation with Michelle Tuveson and Dr Andrew Coburn from Cambridge Risk Center at the Conference Board Global Risk Conference in New York, 8 May 2013. Links to conference website: http://www.conference-board.org/conferences/conferencedetail.cfm?conferenceid=2456TRANSCRIPT
Analytical FrameworksSystem shock analysis and complex network effects
The 2013 Global Risk Management Pre-Conference Seminar
Michelle Tuveson, Executive Director, Cambridge Centre for Risk Studies
Andrew Coburn, Director External Advisory Board, Centre for Risk Studies
Dr Kimmo Soramäki, Founder and CEO, Financial Network Analytics
Analytical Frameworks: System shock analysis and complex network effects
Session Outline Michelle Tuveson
Executive Director, Centre for Risk Studies, University of Cambridge– A Framework for Managing Emerging Risks in International Business Systems– Problem statement: emerging risks as a corporate problem, the Cambridge
Framework as a structure for approaching the problem
Dr Andrew CoburnDirector of External Advisory Board, Centre for Risk Studies, University of Cambridge– Developing Scenarios for Managing Emerging Risks – Methodology: structural modeling of scenarios and their consequences; examples of
scenarios for extreme oil prices
Dr Kimmo SoramäkiFounder and CEO, Financial Network Analytics – Understanding Shock Effects on Business Systems and Investment Portfolios– Solutions: networks and interactivity, investment portfolios, illustration of network
modeling
A Framework for Managing Emerging Risks in International Business Systems
The 2013 Global Risk Management Pre-Conference SeminarAnalytical Frameworks: System shock analysis and complex network effects
Michelle TuvesonExecutive Director
Centre for Risk Studies, University of Cambridge
4
Some Recent Events Disrupting International Business
Hurricane Sandy 2012impacted a region that generates 40% of US economy. Flights from many airports disrupted. Eastern sea port closures disrupted international shipping for weeks
Arab Spring 2011-12Impacts on many international businesses. Increased fuel prices. 22% of businesses globally reported that the unrest has a negative impact on their business
Credit Crunch 2008US housing price crash in 2007 caused liquidity crisis impacting all major economies and triggering lengthy recession , impacting global businesses
Japan Tōhoku Tsunami 2011Killed 26,000, destroyed factories and infrastructure, triggered Fukushima nuclear meltdown. Disrupted supply chains for electronics and other high-tech components
Swine Flu Pandemic 2009caused international panic with initial reports of a high virulence virus, leading to travel and business disruption for many weeks
Thailand Floods 2011Manufacturing regions in Chao Phraya flood plains inundated disrupting supply chains for international businesses . Large contingent business interruption claims
And the list goes on… Volcanic eruption of Eyjafjallajökull, Iceland, 2010, closed airports across Europe for two
weeks. Business sectors worst hit, included fresh produce providers, pharmaceuticals, and electronics
In 2010 piracy activity around Horn of Africa reached an unprecedented level of 490 acts of piracy, and an estimated $12bn in costs incurred, leading to re-routing, delays, and cost escalation for shipping routes between Europe and Asia
Unprecedented multi-national General Strikes were coordinated across Portugal, Spain, Italy and Greece in November 2012, leading to impacts on air travel, telecoms, and many other business sectors
7/7 2005 terrorist attack on London caused the closure of the City’s financial centre, airports and local travel systems, and impacted international business activity
North American Blizzard of 2010 affected most of US with record snow levels, suspending travel services, international flights and shipping with waves of snowfall through Feb and March
Deepwater Horizon oil spill in 2010 made large parts of the Gulf of Mexico unnavigable, caused damage to local industries and disrupted international business connected to the region
SARS outbreak in 2003 disrupted airline passenger traffic for five months, depressing tourism, travel and other business
5
The Problem
Modern corporate businesses are finding that their processes are more prone to disruption than they expected
– Each geo-political event causes surprise This is a result of globalization – corporate systems now reach across
the world and are impacted by many more hazards and localized changes than ever before
Global business systems have been optimized to minimize cost – this reduces safety margins
There is a new operational focus on ‘resiliency’ To understand and measure resilience requires a new framework
– The Cambridge Risk Framework Many corporates are espousing new approaches to managing
‘emerging risks’– The Cambridge Risk Framework aims to provide tools for this management
6
Japan Tōhoku CatastropheDisruption to Business Systems
7
“Sony's production and sales were severely affected by the earthquake and tsunami in Japan in March last year.
The twin disasters resulted in supply chain disruptions and a shortage in power supply in Japan, forcing Sony to curtail production.
Its fortunes were hurt further by floods in Thailand later in the year, which saw its factories in the country being affected.”
8
The Cost of Disruption
Examples of daily cost impact of a disruption in a company’s supply network being $50-$100 million
– Rice and Caniato (2003) Studies of ‘long-run’ equity values of companies following disruption to supply
chain show:– Average abnormal stock returns of -40% for firms suffering disruptions– Shareholders lose average of 10% of their stock value at announcement– 14% increase in equity risk in the year following a disruption announcement– Firms do not quickly recover from the negative effects of disruptions– Source: Hendricks & Singhal, 2005 (sample of 827 disruption announcements made during 1989–2000)
2004 Survey of top executives at Global 1000 firms showed supply chain disruptions and associated operational and financial risks to be single greatest concern
– (Green, 2004)
Current trends in best practice for managing the risk of international disruption:– Cost management and efficiency improvements– Supply base reduction– Global sourcing– Sourcing from supply clusters– Source: Craighead et al., 2007, The Severity of Supply Chain Disruptions: Design Characteristics and Mitigation Capabilities
The Current Challenge of Managing ‘Emerging Risk’
Modern businesses face a large number of ‘Emerging Risks’ Many companies maintain an emerging risk committee or have
a formal monitoring system in place– Much of this work is ad-hoc
‘Emerging Risks’ also include emerging recognition of long-standing threats
Is there a systematic process to assess and evaluate the entire range of threats?
How are these threats best managed? Can we also assess the positive opportunities and upside
potential that might be presented by new threats? What financial products or techniques could best answer the
corporate demand for de-risking global business?9
10
Catastrophe Modeling Meets Complex Systems
The Centre for Risk Studies arises from shared interests by the participants in exploring areas of intersection between– Catastrophe modeling and extreme risk analytics– Complex systems and networks failures
Advance the scientific understanding of how systems can be made more resilient to the threat of catastrophic failures
Air Travel Network Global Economy
To answer questions such as: ‘What would be the impact of a [War in Taiwan] on the [Air Travel Network] and how would this impact the [Global Economy]?
Regional Conflict
11
Business Activity as a System of SystemsAir Travel Network Cargo Shipping Networks
Communications Networks
12
Networks, Attacks, and Residual Modeling A framework for assessing the consequences of an event on a system network
Network ‘Attack’ Residual
Describe the topology of the network as nodes and links
Baseline efficiency of the network quantified through standard metrics of Value Function:• Connectivity• Reference path length• Diameter• Social Welfare
Degradation of the network through localized impairment or removal of nodes and links
Attack measured by ‘k-cut’ metrics
Post-attack network either static or adaptive • Network may be fragmented after an attack
Adaptive response of a network adjusts traffic and relationships
May introduce congestion Changes in Value Function are
measured as a result of the attack
13
Components of Cambridge Risk Framework
Threat Observatory
Network Manager
Analytics Workbench
Strategy Forum
http://www.CambridgeRiskFramework.com
14
Cambridge Risk FrameworkThreat Taxonomy
Famine
Water Supply Failure
Refugee Crisis
Welfare System Failure
Child Poverty
Hum
anita
rian
Cri
sis
AidC
at
Meteorite
Solar Storm
Satellite System Failure
Ozone Layer Collapse
Space Threat
Exte
rnal
ity
Spac
eCat
Oth
er
Nex
tCat
Labour Dispute
Trade Sanctions
Tariff War
NationalizationCartel Pressure
Trad
e D
ispu
te
Trad
eCat
Conventional War
Asymmetric War
Nuclear War
Civil War
External Force
Geo
politi
cal C
onfli
ct
War
Cat
Terrorism
Separatism
Civil Disorder
AssassinationOrganized Crime
Politi
cal V
iole
nce
Hat
eCat
Earthquake
Windstorm
TsunamiFloodVolcanic Eruption
Nat
ural
Cat
astr
ophe
Nat
Cat
Drought
Freeze
HeatwaveElectric Storm
Tornado & Hail
Clim
atic
Cata
stro
phe
Wea
ther
Cat Sea Level Rise
Ocean System Change
Atmospheric System Change
Pollution Event
WildfireEnvi
ronm
enta
l Cat
astr
ophe
EcoC
at
Nuclear Meltdown
Industrial Accident
Infrastructure Failure
Technological Accident
Cyber Catastrophe
Tech
nolo
gica
l Cat
astr
ophe
Tech
Cat
Human Epidemic
Animal Epidemic
Plant Epidemic
ZoonosisWaterborne Epidemic
Dis
ease
Out
brea
k
Hea
lthCa
t
Asset Bubble
Financial Irregularity
Bank Run
Sovereign Default
Market Crash
Fina
ncia
l Sho
ck
FinC
at
15
Profile of each Macro-Threat Class
We are preparing a monograph on each of the key threat categories: State-of-knowledge summary of the science Identify the leading authorities and publications
on the subject Catalogue of historical events Map the geography of threat Define an index of severity (‘magnitude scale’) Assess a first-order magnitude-recurrence
frequency (worldwide) Provide illustrative ‘Stress Test’ scenarios of large
magnitude events– For e.g. 1-in-100 (or 1-in-1,000) annual probability
System impact (vulnerability) knowledge Assessment of uncertainties
16
Adopting Cambridge Threat Taxonomyas an Industry Standard
In September 2013, Munich Re will be co-hosting a workshop to review the CRS Threat Taxonomy v2.0 for use in emerging risk management processes
Attendees include major corporations, model developers and insurance companies
Objective is to produce a version 3.0 for use by Munich Re and others for use as an industry standard
Others are welcome to participate– Invitation to attend the workshop– Or review the proposed standard during consultation stage– Participants should be interested in adopting the standard for their own use in
risk management
17
Conclusions
Many international corporates now recognize the importance of managing emerging risks in their global business
Managing emerging risks needs a framework for – Understanding the interlinkages in global business systems– Assessing all the different types of threats that might impact
those business systems The framework can be used to develop shock test
scenarios for use in risk management
Developing Scenarios for Managing Emerging Risks
The 2013 Global Risk Management Pre-Conference SeminarAnalytical Frameworks: System shock analysis and complex network effects
Dr Andrew CoburnDirector of External Advisory Board
Centre for Risk Studies, University of Cambridge
19
Using Scenarios for Risk Management
Many companies use ‘what-if’ scenarios for understanding and managing risk
Management science is well developed– Use of scenarios in business strategy since 1960s
Scenario planning proved to create business value– Companies like Shell place great value in their scenario unit, and
attribute it with anticipation of the 1970s oil crisis, and rapid response to 2008 financial crisis
Scenarios – Create management flexibility – Improve resilience to a crisis– Challenge management assumptions about status quo
20
Seven Key Lessons for Developing Scenarios
1. Make it plausible, not probable
2. Ensure that the scenarios are disruptive and challenging
3. Offer two scenarios for a situation, not one or three
4. Make the suite of scenarios equally likely
5. Quantify the consequences of the scenario
6. Ensure scenarios are ‘coherent’
7. Make the scenarios relevant to the management team
21
Example Scenarios Currently in Development
Cyber Catastrophe RiskMajor compromise of commercial and national infrastructure IT systems by malicious worm attack
Geopolitical Conflict RiskRegional conflict in South China Sea embroiling Western military powers and SE Asian nations
Human Pandemic RiskVirulent influenza pandemic causes 6 months of workforce absenteeism and social and economic disruption
Civil Disorder RiskAusterity-driven riots and strikes across multiple cities in several Eurozone countries
Oil Supply Shock Analysis
22
Hypothetical Scenario of a Geopolitical Crisis in Middle East
Disclaimer
This is a hypothetical scenario developed as a stress test for risk management purposes
It does not constitute a prediction The Centre for Risk Studies develops hypothetical
scenarios for use in improving business resilience to shocks
These are contingency scenarios used for ‘what-if’ studies and do not constitute forecasts of what is likely to happen
04/10/2023
System Shock ProjectHow might…
24
A geo-political event …impact the global price of crude oil…
…and how would that affect a typical investment portfolio..?
$
25
Oil Price Shock Scenarios
Forcing Oil Price to an Unprecedented LowShale oil bonanza from large reserves in China turns China into a net producer, causing rapid oil price collapse on global markets
Forcing Oil Price to an Unprecedented High‘Arab Spring’ regime change in Saudi Arabia deregulates OPEC-Swing oil production and triggers extreme oil price escalation
26
Project Team
Andrew CoburnMichelle TuvesonDanny RalphSimon RuffleGary BowmanLouise Pryor
Kimmo SoramäkiSamantha Cook
Christian Brownlees
With assistance from:
Peace and Collaborative Development NetworkIvan Ureta
Associate Prof in International Relations
Investment FundWill Beverley
Head of Macro Research
27
Sample Investment Portfolio
US Equities
11%
UK Equities
7%
EU Equities
10%
Japanese Equities6%
Asia ex-Japan Equities
6%Small Cap
Equities6%
EM Equities
4%
Government Bonds11%
Corporate Bonds4%
High Yield Bonds12%
Property9%
Private Equity
4%
Gold6%
Commodities3%
Cash2%
28
Historical Oil Price Shocks
Basic Structure: Price of Oil
Demand- Transport
-Transport excl. cars
- Heating/Electricity
Supply
-Saudi & Kuwait- OPEC
-Non OPEC
4. Long term/short term oil price
5. Cost of E&P
2. Budgetary needs3. Geopolitics e.g. war,
embargos
1. Production constraints
3. Population4. Exchange rates
1. Price Elasticity2. GDP
Oil Price
Demand/ Supply
Equilibrium
Oil Prices Driven by Global Growth
Prices of commodities tend to be:• Log-normal-ish, but
• fat-tailed• mean reverting• with sudden jumps
Prices of commodities tend to be:• well-correlated to global economy• cyclical• seasonal
Spot Price($/B)
Initial SpotPrice ($/B)
Price Adjustment
Must be between 0 and 2
PriceAdjustment
DelayDelta: PA Now -
PA Delay
Futures OilPrice ($/B)
Initial FuturesOil Price ($/B)
DifferenceFutures/Spot
Futures/SpotPrice
Adjustment
Future delay($/B)
Futures/FuturesDelay PriceAdjustment
MarketSentiment market adj
Inital MarketSentiment
market adjoutput
<Prod - Cons 1month delay (B/M)>
Ideal Production -Consumption (B/M)
Ideal D/S - ActualD/S (B/m)
Demand/SupplyPrice Adjustment
CommercialInventory Adj
<CommercialInventory Flows
(B/M)>
Exogenousevent
Spot Price 1Month Delay
($/B)
<Strategic InventoryFlows (B/M)>
StrategicInventory Adj
<Prod - Cons 1month delay (B/M)>
ST geopolitics
<Exogenousevent>
<OPEC Supply constraints:Politics/embargos/wars
(B/M)>
Conversion Delay 1Exo Eve
Geopoltics
ST geo
Modeling of Crude Oil Spot Price
32
Scenario Initiation
Two months of initial unrest leads to increasing levels of violence and anti-government protest in Saudi Arabia
Initial dissatisfaction is driven by social conditions but is rapidly taken up by neo-Arab nationalism and minority Shia Islamic fundamentalism
Suspicion of support to rebels being provided by Shia groups in Middle East, including Iran and Hezbollah
33
Seizure of Refineries and Oil Production Mass-movement leads to loss of control
of major oil production facilities as protestors occupy refineries – Ras Taruna (0.5 m barrels/day)– Yanbu (1m barrels/day)– Multiple others
Many thousands of armed protestors occupying sites, taking hundreds of western workers as hostages
Military stand-off as Saudi and US forces are unable to retake facilities without jeopardizing civilian hostages
Sudden loss of production of over 1m barrels a day (10% of Saudi output)
Political chaos as leadership falters
34
Initial StateOverthrow
Scenario Escalation Event Tree
Anti-western regime established
US Military Intervention
Iran Hezbollah Response Regional
EscalationNone -
Forced Standoff
Swift restitution of pro-Western regime Insurgency
Iranian state-backed military invasion
Annexation of regional caliphate
Lengthy military campaign
China backing for military action
Israeli counter-strikes and broader ections
Western coalition forces deployed
Russia annexes areas of Islamic influence
Other coincidental or triggered consequences can increase the severity of a scenario
A
C
D
E
B
Conflict Escalation Across ‘the Oil Corridor’
Potential for scenario to escalate into broader regional conflict
‘Oil Corridor’ contains a third of the world’s oil
Worst case sees prolonged conflict across entire region
36
Arab Spring Timelines
Libya First protests (15 Feb 2011) UN Recognition (16 Sep 2011) End of violence (23 Oct 2011) 251 days
Egypt First protests (25 Jan 2011) Mubarak resigns (11 Feb 2011) Protests end (30 June 2012) 18 days (523 days of unrest)
Tunisia First protests (18 Dec 2010) Regime Change (14 Jan 2011) Protests end (9 Mar 2011) 27 days (82 days of unrest)
Yemen First protests (27 Jan 2011) Ceasefires and Transitions End of protests (27 Feb 2012) 397 days
Syria First protests (15 Mar 2011) 736 days (ongoing)
Oil Production
OPEC produces 40% of the world’s 80 mbbl/d oil and holds three quarters of the world’s 1.6 tr bbl reserves
Oil consumption is well-correlated to global economy – with cyclical and seasonal
patterns Oil Corridor accounts for a
third of all oil production OPEC follows Oil Corridor lead
37
Saudi Arabia; 10
Rest of OPEC; 23Non-OPEC; 45
19651968
19711974
19771980
19831986
19891992
19951998
20012004
20072010
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
Mill
ions
of b
arre
ls o
f oil
per d
ay
World Oil Production millions of barrels a day
Total 80 mbbl/d
Total World
Saudi Arabia
Other OPEC
Middle Eastern Oil Corridor
38
OPEC Swing
Saudi Arabia controls the ‘OPEC-Swing’
OPEC Swing is a pricing regulatory mechanism– releases more reserves as price rises
It damps sudden price rises and constrains market volatility
In this scenario, the OPEC Swing mechanism is effectively disabled
It enables prices to follow market sentiment rather than economic fundamentals
39
Market Reaction: The Black Bubble
Market reactions are severe Negative sentiment feedback and
pessimistic commentary results in a ‘black bubble’
Oil prices peak at $500 a barrel for 3 days
Release of government strategic reserves and political commentary reduces oil pricing to below $300
Sustained period of high oil prices
Modeled Impact on Oil Price
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100$0
$100
$200
$300
$400
$500
$600
Oil Price during Saudi Arabia Crisis Scenario
Crisis (Days)
Oil
Pri
ce p
er b
arre
l
Attack on Ras Tanura
Attack on Yanbu
‘OPEC Swing’ failure
Note – this is a ‘what-if’ illustration of potential extreme price patterns not a prediction or estimation of an actual outcome
Duration of military action
41
Scenario Durations and Impacts
0 20 40 60 80 100 120 1400%
5%
10%
15%
20%
25%
30%
35%
A
B
C
D
E
Duration: Months before restoration of normal oil production
Impact: % of world’s oil productionaffected
ShortRevolution
Successful USIntervention
US fights well-resourced insurgency
Iranian invasion
RegionalConflagration
Duration
Imp
act
42
Sectors Worst AffectedCode Sector Subcode Industry Groups Correlation with Oil Price Shock
10 Energy 1010 Energy High + 315 Materials 1510 Materials High - -3
2010 Capital Goods Medium - -22020 Commercial & Professional Services Low - -12030 Transportation High - -32510 Automobiles and Components Medium - -22520 Consumer Durables and Apparel Medium - -22530 Consumer Services Medium - -22540 Media Medium - -22550 Retailing Medium - -23010 Food & Staples Retailing High - -33020 Food, Beverage & Tobacco Medium - -23030 Household & Personal Products Medium - -23510 Health Care Equipment & Services Low - -13520 Pharmaceuticals, Biotechnology & Life Sciences Low - -14010 Banks Medium - -24020 Diversified Financials Medium - -24030 Insurance Medium - -24040 Real Estate Medium - -24510 Software & Services Low - -14520 Technology Hardware & Equipment Low - -14530 Semiconductors & Semiconductor Equipment Medium - -2
50 Telecommunication Services 5010 Telecommunication Services Low - -155 Utilities 5510 Utilities Medium + 2
35 Health Care
40 Financials
45 Information Technology
20 Industrials
25 Consumer Discretionary
30 Consumer Staples
Few sectors are not negatively impacted by a severe oil price
43
Understanding the Implications of a High Oil Price
Businesses can trace the implications of high oil prices on all their business operation costs and opportunities
Sectoral impacts have marginal differences Affects overall macro-economic environment
– Transportation of all goods to market cause spirals of cost inflation
– Severe curtailment of demand through increased pricing– Recessionary forces– Alternative sources of energy become more attractive and
economically viable A major impact is investment portfolio asset movements
44
What Other Scenarios Should a Business Consider?
As an alternative to contingency planning for a world of extreme high energy prices, there are scenarios for extreme low prices of energy– The Shale Oil Bonanza
These may have opposite implications and contingency requirement
There are also several scenarios for extreme impacts on business systems and operational continuity that are plausible – Pandemics; cyber-catastrophes; severe weather; environmental
collapse; Drives emphasis on flexibility of thinking, and resiliency to
cope with unexpected shocks
45
Conclusions
Scenarios are useful tools for business planning to challenge assumptions about the status quo
Can be used as stress tests to a five-year plan and as contingency plan requirements
Scenarios have proved their business value in helping businesses have more agile reactions to unexpected events
The Cambridge Centre for Risk Studies will be publishing and releasing scenarios for use with models of networked business systems to fully understand potential effects
Understanding Shock Effects on Business Systems and Investment Portfolios
The 2013 Global Risk Management Pre-Conference SeminarAnalytical Frameworks: System shock analysis and complex network effects
Dr Kimmo SoramäkiFounder and CEO
Financial Network Analytics
47
Systemic Risk ≠ systematic risk
The risk that a complex system composed of many interacting parts fails (due to a shock to some of its parts).
Domino effects, cascading failures, financial interlinkages, … -> i.e. a process in the financial network
News articles mentioning “systemic risk”, Source: trends.google.com
Not:
48
Network Theory
Main premise of network theory: Structure of links between nodes matters
Large empirical networks are generally very sparse
Network analysis is not an alternative to other analysis methods
Network aspect is an unexplored dimension of ANY data
49
Variables
En
titi
es
Time
For example:
Entities: 100 banks
Variables: Balance sheet items
Time: Quarterly data since 2011
Link
sLinks:Interbank exposures
Information on the links allows us to develop better models for banks' balance sheets in times of stress
Networks brings us beyond the Data Cube"The Tesseract"
50
Observing vs Inferring
Observing links – Exposures, payment flow, trade, co-
ownership, joint board membership, etc.
– Cause of link is known
Inferring links – Observing the effects and inferring a
relationship e.g. via correlations– Cause of link is unknown– Time series on asset prices, trade
volumes, balance sheet items
Inferring Links from Asset Prices
Issues:– Prices vs Returns (arithmetic vs log)– Controlling for Common Factors (PCA)– Correlation (Pearson, rank, ...) vs dependence (partial correlations, tail,
normal, regimes)– Time period (short vs long)– Significant and Multiple Comparisons -correction
-> Goal is to uncover 'links' or relationships that form a network
52
Benefit of Visualization
Mean of x 9 Variance of x 11
Mean of y ~7.50 Variance of y ~4.1
Correlation ~0.816
Linear regression: y = 3.00 + 0.500x
Anscombes Quartet: Constructed in 1973 by Francis Anscombe to demonstrate both the importance of graphing data before analyzing it and the effect of outliers on statistical properties
Visualizing Correlations
Calculate pairwise correlations for 31 ETFs in various geographies and asset classes (465 correlations)
Color code correlations:
Problem: We are making many estimates, some of which are likely false positives
-1 +1
2007-2008
2012-2013
54
Example - Distribution of correlation in 30 trials with random numbers
20 pairs 50 pairs
100 pairs 200 pairs
Significant Correlations
Keep statistically significant correlations with 95% confidence level
Carry out 'Multiple comparison' -correction -> Expected error rate <5%
Problem: Heatmaps can be misleading due to human color perception
2012-2013
Last month
About Color Perception
A and B are the same shade of gray
About Color Perception
A and B are the same shade of gray
Correlation Network
Network layout allows for the display of multiple dimensions of the same data set on a single map.
Correlation Network
Nodes (circles) represent assets and links (lines) represent correlations between the linked assets
Node size scales with variance of returns.
Thicker links denote stronger correlations (red= negative, black=positive)
60
Hierarchical structure in financial markets
Rosario Mantegna (1999): "Obtain the taxonomy of a portfolio of stocks traded in a financial market by using the information of time series of stock prices only"
Correlations cannot be used as the metric as they don't fulfil the metric axioms– non-negativity: d(x, y) ≥ 0 – coincidence: d(x, y) = 0 – symmetry: d(x, y) = d(y, x)– subadditivity: d(x, z) ≤ d(x, y) + d(y, z)
We transform the correlations into Gower's (1966) distances:
where e.g correlation of -1 -> 2 ; 0 -> 1.41 ; 1 ->0
The resulting distance matrix can be used to look for a hierarchical structure of the assets
Minimum Spanning Tree
A Spanning Tree of a graph is a subgraph that: 1. is a tree and 2. connects all the nodes together
Minimum spanning tree (MST) is a spanning tree with shortest length. Length of a tree is the sum of its links.
Re-positioning the Assets
We lay out the assets by their hierarchical structure using Minimum Spanning Tree of the asset network.
Shorter links indicate higher correlations. Longer links indicate lower correlations.
Negative correlations are shown as red links and positive correlations as black.
Absence of links marks that asset is not significantly correlated with anything
Interactive chart at:http://www.fna.fi/demos/conference-board/charts/correlation-network.html
Data Reduction for Clarity
Node color indicates identified community.
Missing links (clusters) denote no significant correlation.
Interactive chart at:http://www.fna.fi/demos/conference-board/charts/correlation-tree.html
Extensions
Principal Component Analysis and Correlation regimes
GARCH -based forecasts
Alternative link definitions: Granger causality, partial correlation, tail dependence
Outlier detection and alert systems
Stress testing
Partial Correlation
Partial correlation measures the degree of association between two random variables, controlling for other variables
We build regression models for daily returns of e.g. Oil and Gold based on all other assets of interest and look at the correlation of their model residuals (i.e. what is left unexplained by the other factors) -> Partial correlation
Model 1: Regress Gold on all other assets except Oil Model 2: Regress Oil on all other assets except Gold
Gold residuals = vector of differences between observed Gold values and values predicted by Model 1
Oil residuals = vector of differences between observed Oil values and values predicted by Model 2
Partial correlation between Oil and Gold is the correlation between Oil residuals and Gold residuals
65
Partial Correlation Network
Network of statistically significant partial correlations of monthly returns for a wide set ETFs during 2007-2013
Link width is value of partical correlation (range up to 0.85)
We can use the partial correlations to undestand linkages within a standard portfolio stress test model
We organize the network on the basis of distance from the shocked node:
The Network for an Oil Shock
Interactive chart at:http://www.fna.fi/demos/conference-board/charts/oil-shock-01.html
Shocking Multiple Nodes
We use multivariate percentiles (based on the multivariate normal distribution) to simultaneously shock Financials, German Stocks and Gold
First we estimate the mean and covariance matrix of these three asset returns from theobserved data.
Then, for the first percentile, we find the shocks x, y, and z such that the joint probability P(XLF < x AND EWG < y AND GLD < z) = 0.01 and the marginal probabilities are equal, i.e., P(XLF < x) = P(EWG < y) = P(GLD < z)
A similar calculation finds the 99th percentile.
The Network for Multiple Shocks
Interactive chart at:http://www.fna.fi/demos/conference-board/charts/triple-shock-01.html
Is it Correct?
We develop a model where we use the network structure to estimate many small models (some of which are based on estimates)
We see how well cascading predictions works by predicting values for a out of sample data set whose values are known.
We compare results to a normal linear model Result: Predictions based on partial correlation network are as good for
single asset shock, and just slightly worse for multiple asset shock
-> The partial correlations do open up the model and provide more insights into asset dynamics and interdependencies
Caveats: shocks outside 'normal' bounds may not exhibit same behavior. Shocks to correlations, volatilities are not covered.
Summary
Correlation networks can provide visual insights into market dynamics
Partial correlation networks can provide visual insights for portfolios stress testing
Blog, Library and Demos at www.fna.fi
Dr. Kimmo Soramäki [email protected]: soramaki