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 kimmo@soramaki.netTwitter: soramaki