Adaptive Stress Testing

www.riskcommons.org | www.fna.fi Alan Laubsch, alaubsch@gmail.com | Kimmo Soramaki, kimmo@fna.fi
Adaptive Stress Testing
Harnessing Network Intelligence in Stress Testing
and Reverse Stress Testing
ERM Symposium, Chicago April 24 2013

2www.riskcommons.orgwww.riskcommons.org | www.fna.fi Alan Laubsch, alaubsch@gmail.com | Kimmo Soramaki , kimmo@fna.fi 2www.riskcommons.org | www.fna.fi Alan Laubsch, alaubsch@gmail.com | Kimmo Soramaki , kimmo@fna.fi 2
Agenda
1. A Framework for Adaptive Stress Testing
2. Signal or Noise?
3. Introducing StressGrades™
4. Network Approaches to Stress Testing
5. Summary and Conclusions

3www.riskcommons.orgwww.riskcommons.org | www.fna.fi Alan Laubsch, alaubsch@gmail.com | Kimmo Soramaki , kimmo@fna.fi 3
Scenarios are continually emerging and evolving
• Integrate interdisciplinary perspectives
Source: infomous.com/

Implication of Complexity: “Sense and Respond”
Dynamic Steering: continual feedback

Seek to understand systemic fault lines…
• …and how is your portfolio is positioned relative to fault lines.
• Major challenge: disaster myopia (see “Why Banks Failed the Stress Tests”
by A. Haldane, 2009)
Earthquake activity vs Nuclear power plants
Source: http://googlemapsmania.blogspot.com/2011/03/nuclear-power-plants-earthquake.html

I. Macro: identify structural risks (potential risks)
• Stress Library based on Thought Leaders (Innovators)
• Awareness of systemic cycles, in particular credit and asset bubbles
• Financial or economic imbalances (e.g., capital flows, consumption vs. saving)
• Examples: Shiller – (a) tech bubble (2000) and (b) housing bubble (2005)
II. Micro: monitor potential precipitating events (visible risks)
• Focus on short term market movements, especially outliers and regime shifts
• Early Warning: identify amplification mechanisms and critical (tipping) points
• Examples: vol spike in (a) tech stocks and (b) US mortgage securities & financials
Adaptive Stress Testing Framework

Designing an Adaptive Stress Library
Source: Wikipedia; see Geoffrey Moore’s “Crossing the Chasm” (1999)
• Diffusion of ideas and innovation follow a predictable course after a
tipping point is crossed
Two key perspectives for stress testing
1. Stress Library: Innovators
2. Early Warning: Early Adopters
Innovators:
Roubini, Rosenberg, Shiller,
Rogoff, Reinhart, Ferguson, …
Key early adoption signals:
- Outliers clustering, vol spikes,
super-exponential trends
- Adoption by hedge funds and
broker dealers.

US Financials Case Study
Financial Meltdown (“Roubini”) scenario escalates from ’07 and peaks March ’09 and then
declines… inverse Financial Recovery scenario emerges
-20.0%
-15.0%
-10.0%
-5.0%
0.0%
5.0%
10.0%
15.0%
20.0%
Daily 99% VaR Backtest (.94 decay, Student t)
Feb 27 „07 outlier
Source: Alan Laubsch, “Equities as Collateral In U.S. Securities Lending Transactions”,
The RMA Executive Committee on Securities Lending & RiskMetrics, March 2011
March 6 Market bottom
June 1 Market peaks
Chart: U.S. Financials “death star pulse”

Tipping Point Dynamics require early detection and action
• Limited window of opportunity for exerting control
• What are early warning signals of a phase transition?
Source: “Building A Reputation Risk Management Capability”, Diermeier & Loeb, 2011
Invisible/Potential Visible & amplifying

Agenda
2. Signal or Noise?

Exogenous vs Endogenous Crises
• Nassim Taleb’s “Black Swan” claims that crises arise from unknowable
events that cannot quantified or predicted
• Historical examples: Eisenhower heart attack; Lincoln & Kennedy assassinations;
asteroid impact or flood basalt eruptions resulting in mass extinctions; 911;
• Didier Sornette’s “Dragon King” thesis holds that most financial crises are
endogenous in nature and can be diagnosed in advance, can be
quantified, and have some predictability
• Examples of endogenous crises in history: rise of Fascism; rise of dictators
(Hitler, Mao);‟29 Great Depression, ‟87 Black Monday, ‟89 Japan Bubble; ‟01 Tech
Bubble; GFC; current ecological crisis
• Endogenous structural risk combined with exogenous precipitating event
is common (e.g., forest fire)
Source: Alan Laubsch “Integrated Risk Management - Early Overview”, RiskMetrics

Phase transitions can result from amplifying feedback
• Super-exponential instability and change characterizes phase transitions
See: http://www.er.ethz.ch/presentations/Endo_Exo_Oxford_17Jan08.pdf
Source: Sornette et al., Endogenous versus Exogenous Origins of Crises (2008)

Subprime CDO volatilities spiked 7 & 4 months before the meltdown
-100.0%
-80.0%
-60.0%
-40.0%
-20.0%
0.0%
20.0%
40.0%
60.0%
80.0%
100.0%
120.0%
7/19/2006
8/19/2006
9/19/2006
10/19/2006
11/19/2006
12/19/2006
1/19/2007
2/19/2007
3/19/2007
4/19/2007
5/19/2007
6/19/2007
7/19/2007
8/19/2007
9/19/2007
10/19/2007
11/19/2007
12/19/2007
1/19/2008
2/19/2008
3/19/2008
4/19/2008
5/19/2008
6/19/2008
Date
SpreadChange
300%+ increase in vol from
Dec 12 to 21 '06
357% vol spike on
Feb 23 '07
RM 2006 99% VaR bands vs 2006-1 AAA spread changes
One major outlier, a 12 sd move on Feb 23 '07, the day
after the $10.5bn HSBC loss announcement
Backtesting summary:
2.4% upside excessions
0.81% downside excessions
Major ratings agencies initiate reviews and/or
downgrades week of July 9 '07
Source: Alan Laubsch “Subprime Risk Management Lessons”, RiskMetrics
GS exits
subprime

The Dec ‟06 and Feb ‟07 spikes in volatility can be seen as tremors
(foreshocks) that cascaded into a major earthquake
'2006-1 AAA'
0
50
100
150
200
250
300
350
400
450
1/19/2006
2/19/2006
3/19/2006
4/19/2006
5/19/2006
6/19/2006
7/19/2006
8/19/2006
9/19/2006
10/19/2006
11/19/2006
12/19/2006
1/19/2007
2/19/2007
3/19/2007
4/19/2007
5/19/2007
6/19/2007
7/19/2007
8/19/2007
9/19/2007
10/19/2007
11/19/2007
12/19/2007
1/19/2008
2/19/2008
3/19/2008
4/19/2008
5/19/2008
6/19/2008
The first tremor
(vol up 300% Dec 12-21)
Feb 23 '07, first major
outlier, 350% vol increase
in 1 day, 12sd move
June 20 '07, ML tries
to liquidate Bear
Subprime CDO's
Absolute Spread Levels
Major ratings agencies
initiate reviews and/or
downgrades week of
July 9 '07
bp's
• Absolute spread moves were small, but rate of change was super-exponential. Parallels to failure and
rupture process in material science (pressure to break point)

Feb 27 „07 DJIA outlier marks the beginning of a phase transition with
increasing waves of volatility
• Increasing amplitude of volatility is a telltale sign of endogenous crises
-5.00%
-4.00%
-3.00%
-2.00%
-1.00%
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
1/23/2006
3/23/2006
5/23/2006
7/23/2006
9/23/2006
11/23/2006
1/23/2007
3/23/2007
5/23/2007
7/23/2007
9/23/2007
11/23/2007
1/23/2008
3/23/2008
5/23/2008
DJIA daily returns vs 99% VaR bands (.94 decay, t dist)
Feb 27, 6th biggest outlier in DJIA
history 4 days after largest spike in
subprime spreads
Source: Alan Laubsch “Integrated Risk Management - Early Overview”, RiskMetrics

Gold Early Warning

Let‟s look more closely at Outliers

Downside outlier Clustering Escalates from Oct 2012

Agenda
2. Signal or Noise?

Typical stress testing processes generate much data,
but not necessarily intelligence
“We run over 180 stress scenarios against each of our counterparties on a daily
basis. But we don‟t know what to do with the information” – Risk manager at
global bank
Key questions:
• With overwhelming amount of data, which scenarios to focus on?
• …given market conditions (systemic)
• …given our portfolio exposures (specific)

DStress
PStress
Figure: Student t distributions and Z-scores
We estimate DStress w/market implied vols (and correlations for multi factor scenarios) and
PStress using a distributional assumption (e.g., Normal or Student t).
StressGrades™ harness market intelligence highlight
emerging risks
We define three components of StressGrades™:
1. PStress = Market Implied Probability of a Stress Scenario
2. DStress = Distance to stress scenario in standard deviations (z-score)
3. StressQ = Quantile (percentile) historical rank of stress scenario (e.g., StressQ = .82
implies stress levels have exceeded current levels 18% of the time)

Stress Grades™ provide early warning and can be
backtested
S&P 500 Case Study:
• Since 1987, the biggest one day drop in the S&P 500 was a 9.6% fall on Dec 1 ‟08,
which we use to calibrate and backtest our StressGrade scenario.
• DStress escalates from -24sd to -2sd before Dec „08 drop. Regime shift warning
Feb„07

S&P500 cont’d: Super-exponential increase in PStress:
170x on Feb 27 then another 1300x before Dec 1 ’08
• Note log scale on the PStress Chart below (right scale)

ETF analysis reveals systemic risk early warning signals
• Implied Probability of Stress Event (PStress) for major ETFs shows super-
exponential escalation during GFC
LogScale
Source: Alan Laubsch, “Introduction to StressGrades©”, riskcommons.org, 2011

Super-exponential increase in PStress preceded market
crash…
• … and broad declines in PStress from peak levels signaled market recovery
Source: Alan Laubsch, “Introduction to StressGrades©”, riskcommons.org, 2011

Highlight escalating and large risks in StressGrades™ HeatMap
Mouse over to get
more information
about each scenario
StressGrade™ (PStress)
%changeinStresGrade
0 100 200 300 400
10%
-10%
100%
1000%
2. PIGS Inflationary Bust
- StressGrade 385 up 550%
0%
Highest Priority:
Escalating and High
PStress
Early Warning:
Moderate PStress
but escalating

Outlier Analysis can identify regime shifts
Rank % Move in PStress Scenario [each hyperlinked]
1 780% to 389 PStress Sovereign default
2. 690% to 355 PStress Deflationary bust
….
23. 55% to 80 PStress Gold spike
• Sample Outlier Analysis: 5% threshhold StressGradiealyss
• 23 of 80 scenarios were outliers
• 6 Outliers Average over 12 months

Network Graphs allow visualization of interrelationships
• Potential to integrate stress themes into interactive network graphs and
play movie of changing correlation and volatility dynamics over time

Agenda
2. Signal or Noise?
4. Network approaches to Stress Testing

DStress Network
How are asset stresses coordinated?
We calculate the Euclidean distance between
pairwise series of daily DStress values.
Keep only most important links that form the
backbone dependencies, i.e. present a data
reduction.
Size of node scales with risk as defined by
average DStress during the period: Large node,
high risk. Small node, low risk.
The network shows us the coordination of
stress among the assets in a portfolio.
Jan 20 - April 19 2013
http://www.fna.fi/demos/erm/dstress-tree.html

Stress Testing a Portfolio - Opening up the Black Box
Partial correlation measures the degree of
association between two random variables,
controlling for other variables
Network of statistically significant partial
correlations of dailyt returns for a wide set
ETFs during 2009-2013
• link = partial correlation
• green node = positive return
• red node = negative return
• node size scales with absolute return
We can use the partial correlations to
undestand linkages within a standard
portfolio stress test model

Calculating Partial Correlation
• 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
32

The Network for an Oil shock
http://www.fna.fi/demos/erm/cascade-oil-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 schocks 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
http://www.fna.fi/demos/erm/cascade-three-01.html

Is it correct?
The test:
• 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

Agenda
2. Signal or Noise?
4. Network approaches to Stress Testing

Summary: sense and respond to emerging risks
• Use algorithms and visualization techniques to detect signals amidst
noise (e.g., super-exponential rates of change)
• Prioritize attention to relevant macro fault lines and specific
portfolio vulnerabilities
Anticipate
Most of the focus at most companies is on what’s directly ahead. The leaders lack
“peripheral vision.” This can leave your company vulnerable to rivals who detect
and act on ambiguous signals.
- 6 Habits of True Strategic Thinkers, Paul Schoemaker, Mar 20, 2012

Summary: Architect stress tests to adapt to market
intelligence
• As early warning signals are observed:
1. Focus on affected systemic fault lines (and related nodes)
2. Assign higher probability of stress
3. Apply more severe stress scenarios
• Proactive response is essential
1. War game scenarios to better understand potential impacts and
consequences over time, and practice playing out various permutations
of scenarios across the enterprise
2. Take advantage of calm periods to reduce concentration risks, increase
capital and liquidity buffers. Get prepared to weather more severe
storms ahead.

Conclusions
• Adaptive stress testing practices
• Experiment: explore emerging vulnerabilities and seek to
uncover risk concentrations
• Learn: intelligent feedback loops: market signals and
subjective perspectives (scenarios)
• Practice: play through various scenario permutations
• Early detection and adaptation is crucial for systemic risks
• Harness market intelligence to prioritize attention
“The future is already here — it's just not very evenly distributed.”
William Gibson

Adaptive Stress Testing

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