Financial Rogue Waves
Steve Ohana
ESCP Europe
Presentation at the CFA UK Society
Nov, 10th, 2010
Rogue waves correspond to non-linearities in the wave
propagation
1
2
3
Rogue waves (also known as freak waves, monster waves, killer waves, extreme waves, and
abnormal waves) are relatively large and spontaneous ocean surface waves that occur far out in
sea, and are a threat even to large ships and ocean liners. In oceanography, they are more
precisely defined as waves whose height is more than twice the significant wave height (SWH),
which is itself defined as the mean of the largest third of waves in a wave record.
It seems possible to have a rogue wave occur by natural, nonlinear processes from a random
background of smaller waves. In such a case, it is hypothesized, an unusual, unstable wave type
may form which 'sucks' energy from other waves, growing to a near-vertical monster itself, before
becoming too unstable and collapsing shortly after.
Source: Wikipedia
Early warning systems now exist to detect approaching
rogue waves
The tool developed by Professor Nieto from the signal theory department of the Universidad de Alcalá translates the radar image
into a measurement of the elevation of the waves.
In the radar images above, the image on the left corresponds to the raw radar image, while the one on the right is the image once
processed by the software.
Thanks to the color code it can be appreciated that higher waves propagate as a group. This effect is called wave grouping and
has a great relevance for the safety of marine structures such as ships, dikes, platforms.
The software can be used to provide warning of an approaching extreme wave, giving time to prepare and minimize its
effects.
http://www.sciencedaily.com/releases/2007/11/071117091502.html
Black Swans vs Rogue Waves: two opposite conceptions
of extreme market events
• Rise endogenously, conveying expansion signals
• Totally unpredictable
• Early warning signals of dislocation can be observed
• No one is responsible for them (or everyone is!)
• An investor may adjust risk-taking depending on the
observation of an expanding rogue wave and on the
manifestation of early warning signals of dislocation
• An investor can never have any idea of the tails
and should always avoid exposure to them
• Putting an end to speculation is the only way
to prevent them
• Some specific actors play an objective role in their expansion
• Might be prevented if investors’ and public awareness grow
Regulators slowly acknowledge that financial crises look
more like Rogue Waves than Black Swans
New regulation should reduce the risk of future financial crises […] More research [is needed]
on asset price bubbles, market liquidity and decision-making during panics.
Ben Bernanke
http://www.federalreserve.gov/newsevents/speech/bernanke20100924a.html
“A top priority” of regulators assigned to monitor systemic risks should be determining whether
asset prices are signaling the emergence of a bubble. Surveillance of emerging risks is likely to
focus in part on the accumulation of credit and funding risk inside systemically important firms,
and counterparty risks.
Janet Yellen
http://www.bloomberg.com/news/2010-10-11/fed-s-yellen-says-accommodative-policy-mayprompt-excessive-risk-taking.html
The European Commission is investing in a research project to develop new systemic risk
indicators for “early warning systems” that could alert governments and bankers to impending
financial crises in the earliest stages and take early action to stop them from spreading.
European Commission
http://europa.eu/rapid/pressReleasesAction.do?reference=IP/10/1344&format=HTML&aged=0
&language=EN&guiLanguage=en
Outline
1
The financial cardstack
2
The rogue waves machinery: positive feedback loops in
financial markets
3
Navigating through financial rogue waves: towards a
Radar of financial markets
More frequent financial seisms with a more global impact
Japanese crisis
1990-1992
WS crash
1987
Asian crisis
1997
Mexican crisis
1995
Mostly local crises following
bubble implosions
High-tech bubble
implosion
2000 – 2001
Russian default
LTCM debacle
1998
Corporate credit
crisis
2002
Sept 11
2001
Lehman’s demise
2008
Subprime crisis
2007
Mostly broad liquidity crises
evolving into global
financial meltdowns
Players’ integration
Normalized banks’ CDS rates (in number of standard deviations)
Source: Riskelia
Eurozone sovereign
debt crisis
2010
Players integration
Financial Players’ network (source: Riskelia)
Each point stands for a financial institution, the network displays the correlations between normalized banks’
CDS rates
Red lines represent correlations standing above 75%
Bold lines represent correlations standing between 50% and 75%
Thin lines represent correlations standing between 25% et 50%
Source: Riskelia
Players’ integration: hedge fund strategies
Source: Andrew Lo
Asset integration
This indicator corresponds to the proportion of the global asset price daily variations (i.e.
the equities, corporate credit, currencies, bonds, interest rates futures, and commodities’
price variations) which can be explained by a common risk factor, viewed as the
average dynamics of risky assets against bonds.
Source: Riskelia
Relatively diversified markets up to 2006
Asset class network (source: Riskelia)
Each point stands for an asset, the network displays the correlations between assets’ weekly returns
Red lines represent correlations standing above 75%
Bold lines represent correlations standing between 50% and 75%
Thin lines represent correlations standing between 25% et 50%
Risky assets network from 2002 to 2006
Zinc
Nickel
S&P
Copper
DJ Indu
Alu
TSX
Heating Oil
Period 2002-2005
CAC
Oil Brent
DAX
FTSE
Oil WTI
KRW
TPX
HUF
HSI
TRY
KOSPI
ZAR
AUD
BRL
Source: Riskelia
CAD
NZD
Average correlation: 24%
% correlations above 50% : 9%
Integrated financial markets since 2006
Asset class network (source: Riskelia)
Each point stands for an asset, the network displays the correlations between assets’ weekly returns
Red lines represent correlations standing above 75%
Bold lines represent correlations standing between 50% and 75%
Thin lines represent correlations standing between 25% et 50%
Risky assets network from 2006 to 2010
Zinc
Nickel
S&P
Copper
DJ Indu
Alu
TSX
Heating Oil
Period 2006-2010
CAC
Oil Brent
DAX
FTSE
Oil WTI
KRW
Average correlation: 51%
% correlations above 50% : 52%
TPX
HUF
HSI
TRY
KOSPI
ZAR
AUD
BRL
CAD
NZD
Source: Riskelia
The risk on/risk off paradigm: liquidity as the main driver
of financial markets
Source: Riskelia
Outline
1
The financial cardstack
2
The rogue waves machinery: positive feedback loops in
financial markets
3
Navigating through financial rogue waves: towards a
Radar of financial markets
Positive feedback
 A system exhibiting positive feedback, in response to perturbation, acts to increase the magnitude of the
perturbation. That is, "A produces more of B which in turn produces more of A.
 These concepts were first recognized as broadly applicable by Norbert Wiener in his 1948 work on
cybernetics.
Source: Wikipedia
Positive feedblack loop
Positive feedback and systemic risk
 Systemic risk is the risk that an amplification or leverage or positive feedback process is built into a system,
this is usually unknown, and under certain conditions this process can amplify exponentially and rapidly lead
to destructive or chaotic behavior.
 Simple systems that clearly separate the inputs from the outputs are not prone to systemic risk. This risk is
more likely as the complexity of the system increases, because it becomes more difficult to see or analyze
all the possible combinations of variables in the system even under careful stress testing conditions.
 Well-designed complex systems generally have a small amount of friction, or resistance, or inertia, or time
delay to decouple the outputs from the inputs within the system. These factors amount to an inefficiency, but
they are necessary to avoid instabilities.
Source: Wikipedia
endogenous amplification of initial shock
Soros’ reflexivity concept
outputs and inputs are separated
The price of financial assets reflects the anticipations
regarding the real economy
The price of financial assets reflects the beliefs
of individual investors
positive feedback loops
The price of financial assets
shapes the real economy
The price of financial assets
determines the beliefs of individual
investors
The trend following vicious circle
In sociology, a self-fulfilling prophecy is a positive feedback loop between
beliefs and behavior: if enough people believe that something is true, their
behavior makes it true, and observations of their behavior in turn increase
belief (Wikipedia)
The bubble attractor
The deleveraging spiral
There is too much leverage in the system
The cushions of equity capital are consumed
Market liquidity deteriorates
The selling pressure is strong
No buyers in a bearish environment
Failure to honor margin calls
Impossibility to refinance positions
Defaults/foreclosures
Deleveraging spirals within systematic trading systems
Market liquidity deteriorates
The selling pressure is strong
No position buyers in a bearish environment
There is too much leverage in the system
The cushions of equity capital are consumed
The positions are crowded due to systematic trading
Failure to honor margin calls
Impossibility to refinance positions
Defaults
Redemptions
Disruptions in the short-term wholesale funding market: a
modern version of bank runs
Procyclical VaR-based risk management
Funds liquidity crises
The liquidity conundrum
Positive feedback in the dynamic hedging of derivatives
The Fed also feeds a positive feedback loop
Moral hazard
low interest rates
The Fed doom loop
Bubble expansion
Excessive leverage in systemic
institutions
Financial markets as chaotic systems
Definition of a chaotic system
Complex system that shows sensitivity to initial conditions, such as an economy, a stock market, or
weather. In such systems any uncertainty (no matter how small) in the beginning will produce rapidly
escalating and compounding errors in the prediction of the system’s future behavior. To make an
accurate prediction of long-term behavior of such systems, the initial conditions must be known in their
entirety and to an infinite level of accuracy. In other words, it is impossible to predict the future
behavior of any complex (chaotic) system.
http://www.businessdictionary.com/definition/chaotic-system.html
We cannot predict financial rogue waves formation nor their trajectory once they appear
However, we can monitor their expansion and dislocation in real time
by means of a Radar of financial markets
Outline
1
The financial cardstack
2
The rogue waves machinery: positive feedback loops in
financial markets
3
Navigating through financial rogue waves: towards a
Radar of financial markets
3.a
Early detection
3.b
Capital protection and asset allocation
Measuring financial markets turbulence
Subprime crisis
Lehman Brothers
demise
Russian default
LTCM debacle
Sept 11
Corporate
credit crisis
Asian crisis
Source: Riskelia
Eurozone soverei
debt crisis
For a given asset class, the risk aversion indicator rates the reward market participants require for
risk taking. The scores are expressed in numbers of standard deviations to a set of moving
averages (from 3 months to 2 years). They are averaged into a Global Risk Indicator representing
the global level of risk aversion in the market.
Heat map over the recent year
Source: Riskelia
-1,5
Risk seeking behaviour
-0,5
0,0
1,0
2,0
3,0
Very high risk aversion
For a given asset class, the risk aversion indicator rates the reward market participants require for
risk taking. The scores are expressed in numbers of standard deviations to a set of moving
averages (from 3 months to 2 years). They are averaged into a Global Risk Indicator representing
the global level of risk aversion in the market.
Heat map over the recent decade
Source: Riskelia
Characterizing momentum investing and herding behavior
The Trend Indicator represents the net proportion of trending systems going long or short.
50 trend following systems with a horizon of 3 to 24 months watch every asset.
Trends
-100% Very strong negative trend
-50% Strong negative trend
-25% Negative trend
0% Neutral
25% Positive trend
50% Strong positive trend
100% Very strong positive trend
The Bubble Indicator reflects bullish or bearish herding behavior.
It is only based on market prices and scores the regularity of the price moves on various time frames.
Bubbles
0%
25% No risk of bubble
50% Risk of bubble
75% Strong risk of bubble
Source: Riskelia
Almost all bear markets have been the stage of
generalized momentum investing
The Dow Jones bear periods have almost always been associated to
negative trend spirals and occasionally preceded by bubble expansions
start
09/02/66
03/12/68
28/04/71
11/01/73
21/09/76
08/09/78
27/04/81
29/11/83
25/08/87
16/07/90
17/07/98
17/01/00
19/03/02
09/10/07
Bear periods
end
DJ variation
07/10/66
-25%
26/05/70
-36%
23/11/71
-16%
06/12/74
-45%
28/02/78
-27%
27/03/80
-16%
12/08/82
-24%
24/07/84
-16%
19/10/87
-36%
11/10/90
-21%
31/08/98
-19%
21/09/01
-30%
07/10/02
-30%
09/03/09
-54%
Bubble score
start
end
-58%
48%
-51%
34%
69%
-15%
-55%
42%
-70%
37%
21%
-18%
35%
-31%
-42%
49%
70%
41%
32%
-22%
41%
-20%
-29%
38%
-45%
1%
-76%
48%
Trend score
start
end
-82%
73%
-70%
71%
81%
-56%
-72%
70%
-83%
47%
63%
-50%
69%
-61%
-69%
66%
81%
-12%
72%
-62%
59%
-24%
-71%
62%
-76%
24%
-72%
59%
Bold red: indicator above (resp. below) 90% (resp. 10%) quantile
Red: indicator above (resp. below) 75 (resp. 25%) quantile
250
200
150
100
roll adjusted Hang Seng futures prices
300
Replicating trend following strategies
The case of the Hang Seng Index
2002
2004
2006
2008
2010
2000
2002
2004
2006
2008
2010
0.0
-0.5
Trend score
0.5
2000
250
200
150
100
roll adjusted Hang Seng futures prices
300
Monitoring bubble expansion
The case of the Hang Seng Index
2002
2004
2006
2008
2010
0.0
-0.5
Bubble score
0.5
2000
2000
2002
2004
2006
2008
2010
The role of the bubble score as an early warning indicator
of fat-tailed distribution
0.1
0.2
Dispersion of DJ monthly returns following an observation of the bubble score
returns
0.0
Mean return
-0.2
-0.1
1% quantile
-0.3
0.5% quantile
Min return
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
Bubble scores preceding the observations of monthly returns
The role of the bubble score as an early warning indicator
of fat-tailed distribution
0.6
unconditional return
(right tail)
conditional mean
0.0
unconditional mean
-0.2
returns
0.2
conditional return
(right tail)
0.4
dispersion of DJ returns
conditional on bubble score more than 0.6
-0.4
conditional return
(left tail)
unconditional return
(left tail)
0
50
100
150
200
250
Lag in number of days
The role of the risk aversion score as an early warning
indicator of fat-tailed distribution
dispersion of crude oil WTI monthly returns
conditional on global risk aversion
0.0
returns
0.0
-0.2
-0.1
-0.4
-0.2
-0.3
returns
0.1
0.2
0.2
0.4
dispersion of SP 500 monthly returns
conditional on global risk aversion
-1.5
-1.0
-0.5
0.0
0.5
Risk aversion score preceding the observations of monthly returns
-1.5
-1.0
-0.5
0.0
0.5
Risk aversion score preceding the observations of monthly returns
The role of the risk aversion score as an early warning
indicator of fat-tailed distribution
dispersion of SP500 returns
conditional on risk aversion score less than -0.5
-0.4
-0.4
-0.2
-0.2
0.0
0.0
returns
returns
0.2
0.2
0.4
0.4
0.6
0.6
dispersion of SP500 returns
conditional on risk aversion score more than 0.5
0
50
100
150
200
0
250
Lag in number of days
50
100
150
200
250
Lag in number of days
The role of the trend score as an early warning indicator of
fat-tailed distribution
dispersion of crude oil WTI monthly returns
conditional on trend score
0.0
returns
0.0
-0.2
-0.1
-0.4
-0.2
-0.3
returns
0.1
0.2
0.2
0.4
dispersion of SP 500 monthly returns
conditional on trend score
-0.5
0.0
0.5
Trend score preceding the observations of monthly returns
-0.5
0.0
0.5
Trend score preceding the observations of monthly returns
The role of the trend score as an early warning indicator of
fat-tailed distribution
0.6
unconditional return
(right tail)
unconditional mean
0.0
returns
0.2
conditional return
(right tail)
0.4
dispersion of DJ returns
conditional on trend score less than -0.5
-0.2
conditional mean
-0.4
unconditional return
(left tail)
0
50
100
150
200
250
conditional return
(left tail)
Lag in number of days
The role of the trend score as an early warning indicator of
fat-tailed distribution
dispersion of Hang Seng returns
conditional on trend score less than -0.5
1.0
conditional return
(right tail)
returns
0.5
unconditional return
(right tail)
conditional mean
0.0
unconditional mean
-0.5
conditional return
(left tail)
unconditional return
(left tail)
0
50
100
150
Lag in number of days
200
250
Outline
1
The financial cardstack
2
The rogue waves machinery: positive feedback loops in
financial markets
3
Navigating through financial rogue waves: towards a
Radar of financial markets
3.a
Early detection
3.b
Capital protection and asset allocation
Enhancing passive strategies with early warning systems
The use of the risk aversion signal
7
Long prompt-month WTI Crude Oil futures
6
Passive strategy
3
4
5
Enhanced with Global Risk
Aversion signal
1
2
Cut when RA
exceeds 0.5
2000
2002
2004
volatility
max Drawdown
skewness
gross sharpe
annual return
2006
passive
38%
83%
-0,10
0,20
7,6%
2008
with risk aversion signal
28%
43%
0,07
0,68
19,2%
2010
Enhancing passive strategies with early warning systems
The use of the trend signal
7
Long prompt-month WTI Crude Oil futures
6
Passive strategy
3
4
5
Enhanced with trend signal
1
2
Cut when trend
falls below -0.5
2000
2002
2004
volatility
max Drawdown
skewness
gross sharpe
annual return
2006
passive
38%
83%
-0,10
0,20
7,6%
2008
2010
with trend signal
29%
45%
-0,21
0,50
14,8%
Building bubble-proof trend following strategies
Simulation strategy using trends, risk aversion with or without bubbles
4.5
4
with bubble immunization
3.5
without bubble immunization
3
Universe of 80 assets
(equities, bonds, currencies, commodities)
Weekly rebalancing
Includes transaction costs
2.5
2
1.5
1
2003
Source: Riskelia
2004
2005
2006
2007
2008
2009
2010
A score is attributed to each asset depending on its trend, bubble
score and global risk aversion
Volatility
Max drawdown
skewness
Gross sharpe
Annual Return
Without bubbles immunization
10%
14%
-0.54
1.4
16.6%
With bubbles immunization
10%
7%
+0.1
1.9
19.5%
Building resilient asset allocation strategies
Maximal leverage: 200%
No short positions allowed
Building resilient asset allocation strategies (continued)
 Including transaction costs
 Weekly rebalancing
2
 Each asset is attributed a score
depending on its trend, bubble rating
and global risk aversion
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1
2002
2003
2004
2005
Source: Riskelia
2006
2007
2008
2009
2010
Start Date
16/ 10/ 2001
EndDate
4/ 8/ 10
Annual Return
9,2%
Annual Vol
5,3%
Sharpe
1,7
Max DD
5,8%
ReturnOverMaxDD
1,6
Building resilient asset allocation strategies (continued)
Asset classes contributions
Equities
Gold
Bonds
Total
2002
-2,4%
4,2%
8,8%
10,6%
2003
12,5%
2,4%
0,1%
15,1%
2004
3,4%
0,5%
0,8%
4,7%
2005
10,3%
1,1%
0,1%
11,6%
2006
7,2%
0,1%
-1,1%
6,2%
2007
4,9%
2,5%
0,8%
8,2%
2008
-2,6%
-0,5%
6,4%
3,3%
2009
9,9%
1,5%
0,2%
11,6%
Equities boom
9,0%
Eurozone sovereign debt
crisis
2010 (asof September)
0,8%
1,4%
6,8%
Corporate credit crisis
Emerging countries boom
Subprime crisis
Lehman’s demise
Concluding remarks on crisis prevention
 If market crises are preceded by early warning signals, then it becomes possible
for investors to adjust their level of risk-taking
 Deleverage when risk-aversion surges or a negative trending spiral sets off
 However, the generalization of systematic crisis-response models would produce new positive
feedback loops that could have unintended consequences for market stability…
 Ultimately, only counter-cyclical behavior can produce the negative feedback
loops that could restore financial stability
 Some proposals:
 Introduce inefficiencies/frictions in the system to rein in positive feedback loops by a tax on
financial transactions (Tobin tax)
 Tax behaviors producing positive feedbacks (short-term debt, leverage, systematic trading,
momentum investing…)
 Encourage long-term investment:
 tax financial transactions (Tobin tax again)
 reward buying (selling) in bear (bull) bubbles, reward liquidity providers during liquidity crises
 promote indicators of long-term risk-adjusted performance
 Promote contra-cyclical capital rules (e.g. reward excess capital cushions in periods of booms)
Thank you
Steve Ohana, PhD
[email protected]
+33 6 09 56 08 79
www.riskelia.com