Financial Markets Crisis:

Lessons learned and future implications

Paul Embrechts

Department of Mathematics

Director of RiskLab, ETH Zurich

Senior SFI Chair

www.math.ethz.ch/~embrechts

ICA 2010 CIA, Cape Town, South Africa

hopefully

This talk is very much based on the

following 2009 RiskLab publication (*):

Catherine Donnelly and Paul Embrechts,

The devil is in the tails: actuarial

mathematics and the subprime crisis

Astin Bulletin 2010, to appear

(*) It contains more technical details

Mathematics and Financial Crises

• 1907, 1914, 1929-33, 1980 (S&Ls), …

• 1987: (October 19, Black Monday)

electronic/algorithmic trading, portfolio

insurance, Value-at-Risk (VaR), …

• 1998: (LTCM disaster) normal-based risk

management systems (VaR again),

leverage, personalities, …

• 2007 - ???: (Subprime Crisis) numerous

accusations, content of this talk:

By 2006 we should have learned about:

• (I)liquidity

• Leverage (investments banks 30+:1)

• Model uncertainty

• Non-normality, Extreme events

• Regulatory arbitrage

• Off-balance positions, OTC (shadow banking)

• Greed, Non-rationality, Human factors

• Short-term financing of long-term risks

• Accounting deficiencies

• Global financial networks, IT vulnerability

• Etc … etc …

Well we didn’t, previous events were just

peanuts compared to the Perfect Storm

that came to us around late 2007, and is

still going on!

And indeed the feeling very much was one

of “SOS for the World’s Financial System”:

Or “The scream” of the banker:

“Blame the mathematicians!” (*)

For some it was however clear:

Here are some examples:

(*) Financial Engineers, Quants, Actuaries, …

Recipe for Disaster: The Formula That Killed

Wall Street

By Felix Salmon 23 February, 2009

Wired Magazine

Error, )

The Turner Review

A regulatory response to the

global banking crisis

March 2009, FSA, London (126 pages)

1.1 (iv) Misplaced reliance on sophisticated maths

There are, however, fundamental questions about

The validity of VAR as a measure of risk (see Section

1.4 (ii) below). And the use of VAR measures based

on relatively short periods of historical observation

(e.g. 12 months) introduced dangerous procyclicality into the assessment of trading-

book risk for the reasons set out in Box 1A (deficiencies of VAR).

The very complexity of the mathematics used to measure and manage risk, moreover,

made it increasingly difficult for top management and boards to assess and exercise

judgement over the risks being taken. Mathematical sophistication ended up not con-

taining risk, but providing false assurance that other prima facie indicators of increa-

sing risk (e.g. rapid credit extension and balance sheet growth) could be safely ignored.

The Financial Times:

Of couples and copulas by Sam Jones (April 24, 2009)

In the autumn of 1987, the man who would

become the world’s most influential actuary

landed in Canada on a flight from China.

He could apply the broken hearts maths to

broken companies.

Li, it seemed, had found the final piece of a risk ma-

nagement jigsaw that banks had been slowly piecing

together since quants arrived on Wall Street.

Why did no one notice the

formula’s Achilles heel? Johnny Cash and June Carter

Wall Street’s Math Wizards Forgot a Few

Variables,Steve Lohr, September 12, 2009, NY Times

• From 3 to N Dimensions (mean, variance, …)

• Social Networks, Global Networks

• Market Psychology, Irrationality, Human Factor

• More RM, Less Complex Products

• New Frontiers for FE and RM

• More Dimensions of Uncertainty

• The Adaptive (not Efficient) Market Hypothesis

• Understanding of Contagion

• …

Number-crunchers crunched: The uses and

abuses of mathematical modelsThe Economist, February 13th-19th 2010,

Special Report on Financial Risk

• The eggheads are now in the dock

• A US congressional panel is investigating the role of models in the crash

• Only so far with VaR

• Models (may) change markets

• Similarity of risk models used

• Keynes: “Better to be roughly right than exactly wrong”

• Poor risk aggregation

• Stress tests, rare events, …

• “Why some banks did much better than others?”

• and much more (interesting report)

These are rather serious allegations, so let us look

at some examples of financial products (*) and

investigate where the mathematics “went wrong”

(*) Credit Derivatives

As examples of credit derivatives:

CDS = Credit Default Swap

A relatively simple instrument

CDO = Collateralized Dept Obligation

A rather complex instrument

A stylized Credit Default Swap Set-Up

PF1 F-BB

RAIC-AArating

rating

1 bio USD

10%/year

1%/year Insurance on

F-BB’s debt

PF2/F2

PF3/F3 PFn/Fn… HF1 HFk

…

Betting on default, no link

Credit Default SwapsSecuritisation

construction

The investors

(Synthetic)

Before we say something about pricing, let

us first reflect about volume(*), in particular

what order of magnitude are we talking

about for these markets?

(*) “Where is all the credit risk hiding?” (+/- 2005)

50 000 000 000 000 $ *

• CDS is almost a brand new investment vehicle, but the market is already 20 times its size in 2000. The principal amount of CDS outstanding equals $50 trillion, or more than three times the U.S. Gross Domestic Product and bigger than all the U.S. credit markets put together. And the CDS has been a huge source of "financial engineering" profits, both for Wall Street and the hedge fund community over the last few years.

• World GDP is about $66 trillion.

• First CDS about 1995.

• Total nominal volume of OTC derivatives 550 Tri. $

* 3.7 Tri. $ after netting

And yet

The conventional wisdom – 2006 (!!!!!)

“ There is growing recognition that the dispersion of credit

risk by banks to a broader and more diverse group of

investors, rather than warehousing such risk on their

balance sheets, has helped make the banking and overall

financial system more resilient.

The improved resilience may be seen in fewer bank failures

and more consistent credit provision. Consequently the

commercial banks may be less vulnerable today to credit or

economic shocks ”

IMF Global Financial Stability Report, April 2006

This very much clashed with an older view:

Economists’ Voice: www.bwpress.com/ev November, 2008

“I went on to explain how securitization can give rise to perverse incentives …

Has the growth in securitization been result of more efficient transactions

technologies, or an unfounded reduction in concern about the importance of

screening loan applications? … we should at least entertain the possibility that

it is the latter rather than the former.”

At the very least, the banks have demonstrated

an ignorance of two very basic aspects of risk:

(a) the importance of correlation, and

(b) the possibility of price decline.

So according to Stiglitz (1992!) the issues to

concentrate on are:

• Downside risk: extremes

• Correlation: dependence

And let me add as an intermezzo:

Chapter on Extreme Value Theory

beyond Normality

Chapter on Dependence Modelling

beyond Linear Correlation

… (2005) contains

and much more …

LCFIs and “Securitization” (*)

together with excessive leverage (**)

End of 2001: $ 767 bio

2004: $ 1.4 tri

December 2006: $ 2.7 tri

(*)

Now to the real culprits!

Remark on “.”

(**) 30-60:1

From: “Manufacturing Tail Risk: A Perspective on

the Financial Crisis of 2007-09”, Acharya et al.,

NYU Stern School, 2010

LCFI = Large, Complex Financial Institution

“These LCFIs ignored their own business

model of securitization and chose not to

transfer credit risk to other investors. Instead

they employed securitization to manufacture

and retain tail risk that was systemic in

nature and inadequately capitalized.” Regulatory arbitrage

On UBS, Citigroup and AIG:

From the same paper:

“Starting in 2006, the CDO group at UBS noticed

that their risk-management systems treated AAA

securities as essentially riskless, even though

they yielded a premium (the proverbial free

lunch). So they decided to hold onto them

rather than sell them! After holding less than

$5 bio of them in 2/06, the CDO desk was

warehousing a staggering $50 bio in 9/07.”…

“Similarly, by late summer of 2007, Citigroup had

accumulated over $55 bio of AAA-rated CDOs.”

From Donnelly-Embrechts: the AIG-story:

• AIGFP sold protection on super-senior tranches of CDOs, where the underlying portfolio con-sisted of loans, debt securities, asset-backed securities and mortgage-backed securities.

• “The likelihood of any payment obligation by AIGFP under each transaction is remote, even in severe recessionary market scenarios“ (2006, AR)

• “It is hard for us, without being flippant, to even see a scenario within any kind of realm of reason that would see us losing one dollar in any of those transactions.“(8/2007, CEO of AIGFP)

And yet:

• AIG, a company of around 100,000 employees brought to its knees by a small subsidiary of 400 employees, is an example of a failure of risk management, both at the division and the group level. AIG almost went bankrupt because it ran out of cash.

• As at December 31 2007, AIG had assets of $1,000 billion dollars.

• Problems with collateral posting and securities lending pro-gram also affecting its credit rating, etc …

• On September 16 2008, the Federal Reserve Board, with the support of the U.S. Department of the Treasury, announced that it had authorized the Federal Reserve Bank of New York to lend up to $85 billion to AIG.

Liquidity – Speed – Size

In order to understand the CDO-mispricing (*)

issue, consider the following stylized example

very clearly showing that extremes and

dependence matter very much:

(*) (*)

(*) These so-called AAA-rated “riskless”

securities

The normal distribution

Extremes matter

Correlation matters

micro-

?

Eq. Mez. Sen.

The waterfall principle

Hence the pricing and hedging of CDO

tranches* is confronted with considerable

model uncertainty!

* “Economic catastrophy bonds”

(Coval, Jurek and Stafford, 2008)

Some further issues:

1) Securitization of mezzanine tranches leading to CDO squared and cubed !!!

2) Hedging of CDO tranches

3) IT and Accounting complexity

4) Tranche valuation under stress scenarios

5) Various types and current use

6) Other credit derivatives

7) …

Back to “Recipe for Disaster: The

Formula That Killed Wall Street”

Why did no one notice

the formula’s Achilles

heel?

We did, but nobody

listened!

Two results from the 1998 RiskLab report

Remark 1: See Figure 1 next page

Remark 2: In the above paper it is shown that

A very early warning!

1960

Indeed we did warn about the Achilles heel!

Standard - model Stress - model

(3) (12)

Some comments by mathematicians:

• (L.C.G. Rogers) The problem is not that

mathematics was used by the banking industry,

the problem was that it was abused by the

banking industry. Quants were instructed to build

models which fitted the market prices. Now if the

market prices were way out of line, the

calibrated models would just faithfully reproduce

those wacky values, and the bad prices get

reinforced by an overlay of scientific

respectability!

A further example of an early warning by

academics that was dismissed as

“that’s academic”

and one by a concerned risk manager

that was totally ignored!

Charles Ponzi

1910

Harry Markopolos

Embrechts, P. et al. (2001): An academic response to Basel II.

Financial Markets Group, London School of Economics.

(Mailed to the Basel Committee)

(Critical on VaR, procyclicality, systemic risk)

Markopolos, H. (2005): The world’s largest

hedge fund is a fraud. (Mailed to the SEC)

(Madoff runs a Ponzi scheme)

Bernard Madoff

In summary (Acharya et al., 2010)

“The new banking model * of

“originate-distribute-and-hold”

incurred massive systemic tail-risks

that brought the financial sector

down!”

* Always beware when “new” appears!

Further topics not discussed:

1) The insurance universe and the crisis

2) Fundamental differences in funding of

insurance versus banking

3) Why did some countries (banks) fared

better, e.g. Canada

4) Regulatory environment: Basel II versus

Solvency 2, how further

5) Consequences for education and research

6) …

Back to the role of mathematics:

The overall societal relevance, importance and

success of mathematics is beyond any doubt:

• Medical Statistics and Epidemiology

• Statistical Quality Control

• Maxwell’s Theory of Electromagnetism

• Calculus and Newtonian Mechanics

• Number Theory and Cryptography

• Differential Geometry and Einstein’s Relativity Theory (GPS-application)

• Markov Chain Theory and Web based Search Engines like Google

• … and many more examples!

Mathematics is of key importance for

• understanding and clarifying models used in insurance and economics

• making heuristic methods mathematically precise

• highlighting model conditions and restrictions on applicability

• working out numerous explicit examples

• leading the way for stress testing and robustness properties

• … a relevant mathematical theory on its own!

• And it would be bad if the current crisis would induce a shying away from mathematics.

New generations of students will have to use the tools

and techniques of QRM wisely in a world where the

rules of the game will have been changed.

Always be scientifically critical, as well as socially

honest, adhere to the highest ethical principles,

especially in the face of temptation … which will

come!

A message for my students

QRM = Quantitative Risk Management

And on the boundedness of our knowledge:

There are more things in heaven and earth,

Horatio, than are dreamt of in your

philosophy!

William Shakespeare

(Hamlet I.v. 166)

Thank You!

Thank you!