Transcript Diapositiva 1

Funding Liquidity Risk
Advanced Methods of Risk Management
Umberto Cherubini
London Finance Graduate Program
Birbeck College, 18/03/2011
Outline
• How the crisis started
– Securitization structures
– Toxic assets?
• How the crisis expanded
– Counterparty risk
– Liquidity and the accounting standards
• Where the crisis ended (did it end?)
– Public debt and banks
– The Government budget crisis
• What’s next?
2
Lessons from crises
• September-October, 1998: LTCM, the lesson to
be learned is liquidity, and the incomplete
market problem
• November-December 2001: Enron, the theme is
lack of transparency of balance sheet data,
problem of incomplete information
• May 2005: the crisis on securitization following
downgrading of GM to junk. The theme is break
in correlation. Hedge funds affected.
3
The crisis of 2008, 2009, 2010…
• Credit crisis: “subprime” mortgages were the
trigger of the crisis.
• Liquidity crisis: difficulty to unwind positions has
exacerbated the crisis, like in the LTCM case
• Accounting transparency crisis: fair-value
accounting has been a vehicle of contagion,
Enron’s “lite accounting” has become the practice
of the banking system. Use of derivative contracts
for “window dressing”: councils, Greece, Italy??
4
How the crisis started
• Credit crisis: the crisis began with fear of insolvency on
asset-backed-securities (ABS), that is bonds guaranteed
by pools of assets as collateral.
• Question: bonds guaranteed by collateral, whatever it can
be, cannot be riskier than bonds guaranteed by no
collateral at all. So why the crisis sprang from these
assets, and not from the unsecured ones?
•
Possible answers: unsecured investment are monitored
more closely that collateralized ones (moral hazard);
securitized investments are marked-to-market (fair value
accounting standards)
5
Gaussian factor model (Basel II)
• Assume a model in which there is a single
factor driving all losses. The dependence
structure is gaussian. In terms of
conditional probabilility
 N 1 u   m 

PrDefaultM  m  N 
2


1




where M is the common factor and m is a
particular scenario of it.
6
Vasicek model
• Vasicek proposed a model in which a large
number of obligors has similar probability of
default and same gaussian dependence
with the common factor M (homogeneous
portfolio.
• Probability of a percentage of losses Ld:
 1   2 N 1 L   N 1  p  
d

PrL  Ld   N 
2





7
16
Vasicek density function
14
12
10
Rho = 0.2
Rho = 0.6
Rho = 0.8
8
6
4
2
0
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
8
Vasicek model
• The mean value of the distribution is p, the value of
default probability of each individual
• Value of equity tranche with detachment Ld is
Equity(Ld) = (Ld – N(N-1(p); N-1 (Ld);sqr(1 – 2))
• Value of the senior tranche with attachment equal to
Ld is
Senior(Ld) = (p – N(N-1(p); N-1 (Ld);sqr(1 – 2))
where N(N-1(u); N-1 (v); 2) is the gaussian copula.
9
Vampires, zombies, toxic assets…
• We are “fairly” confident that vampires and
zombies do not exist: what about toxic assets?
• A toxic asset is a creature with 30% attachment.
Under which conditions can we create a toxic
asset? We mean an asset that is worth 70% of its
value.
• Assume a homogeneous portfolio of exposures
and perfect correlation of the losses in the pool.
Then, a toxic asset would require a pool with an
average delinquency rate of 30%. Can it be
serious? Or is it just another horror movie?
10
Fréchet bound
• Men get reflected in mirrors (if they are not vampires) and
assets cannot exceed super replication bounds (if they are
not toxic). According to the Vasicek formula, superreplication bounds are given by the bounds admitted for
copulas (unless you define a new class that
you may
call vampire copulas).
• Say two risks A and B have joint probability H(A,B) and
marginal probabilities Ha(A) and Hb(B). We have that
H(A,B) = C(Ha , Hb), and C is a copula function.
• C(u,v) = uv, independence
C(u,v) = min(u,v), perfect positive dependence
The perfect dependence cases (we overlook negative
dependence here) are called Fréchet bounds.
11
Price bounds of a senior tranche
1
0,9
0,8
0,7
0,6
Rho = 0
Rho = 1
0,5
0,4
0,3
0,2
0,1
0
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
12
Toxic assets: the definition
• “Financial assets the value of which has fallen
significantly and may fall further, especially as the
market for them has frozen. This may be due to
hidden risks within the assets becoming visible or
due to changes in external market environment”
FT lexicon
• It seems then to be a problem of
– Liquidity (market frozen)
– Ambiguity (hidden risk becoming visible)
13
How the crisis expanded
• “Default losses on US sub-prime mortgages
about 500 billion dollars.
• But in a mark-to-market world, deadly losses are
valuation losses
– Valuation losses as high as 4 trillion
– Major banks failed without single penny of default
• BIS study of rescue package: EUR 5 trillion in
committed resources”
Eli Remolona,IV Annual Risk Management Conf., Singapore, July 2010
14
Recipe for contagion
• Ambiguity: assets for which you do not know whether they
are collateralized or not or the quality of the collateral are
traded at discount
• Counterparty risk: you do not trust your neighbour, in spite
of safety nets (netting, collateral). What went wrong?
• Liquidity: funding liquidity (compete for funds from
everyone except your neighbor) and market liquidity (try to
unwind positions in assets)
• Accounting: losses due to whatever (included liquidity) are
marked-to-market and impair the balance sheet.
15
Ambiguity
• Knightian uncertainty: uncertainty is when you do not
know the odds. Risk refers to unambiguous bets.
• Ellsberg paradox, 1961: agents prefer unambiguous bets
over ambiguous bets, that is agents are uncertainty
averse
• Gilboa Schmeidler (1989): multiple prior approach, MaxMin-Expected Utility (MMEU): probabilities are
represented by intervals, rather than numbers.
• Gilboa (1987), Schmeidler (1982,1989): Choquet utility
(sub-additive measures represent uncertainty aversion)
16
Ambiguity and the crisis
• Toxic assets are ambiguous bets. The effect of
ambiguity is that:
– Investors require a premium for uncertainty
– Bid-ask spread larger
– Portfolio inertia (people do not participate in the market
when uncertainty increases)
• Ambiguity reduces market liquidity.
• Changes in ambiguity can be triggered by events
specific to a single issuer (or issue), or by shocks
affecting other issuers (or issues). This is called
information-based contagion (i.e. Enron).
17
Counterparty risk and the crisis
• In 2008 the market was expecting a default of a
big bank. On March 15 Bear Stearns was
rescued. On September 15 Lehman Brothers was
left to his destiny and went bust
• The crisis was a test for the risk mitigating system
applied in the banking practice. The system was
severely shaked, but in the end it worked (we do
not know whether with the help of Governments,
and what would have happened without).
• It is difficult to say whether the counterparty risk
emergency is over or not.
18
Risk mitigating techniques
• In order to reduce the credit risk in their
derivative transactions, banks apply risk
mitigating techniques that are inspired by
futures market. These are implemented in
the so called ISDA standard Credit Annex
• The risk mitigating techniques are:
– Net exposure of the all open contracts (open
interest account, in futures market jargon)
– Deposit of collateral of profit and losses every
week (margin in the language of futures)
19
A simple example
• Assume a counterparty A has p forward contracts
CFi open with counterparty B.
• The value of each exposure is given by
CFi = max([Si(t) – P(t,Ti)Fi],0)
where  = 1 represents long positions and  = – 1
denotes short positions.
• Notice that the exposure is a short position in a
portfolio of call options for long positions and put
options for short positions.
20
Netting
• Assume that counterparty B defaults at time . In
the presence of a netting agreement, exposure in
this case will be given by a an option of a basket,
rather than a basket of options


max Si    A ,0
 i 1

p
p
A    P , Ti Fi
i 1
21
Monte Carlo simulation
• Counterparty risk is evaluated by Monte Carlo
simulation
• Algorithm:
• Choose a set of dates: {t1,t2,…tn} and for each
one of these evaluate a basket option
(counterparty risk exposure)
• For each date ti the value of counterparty risk will
be
[Q(ti-1) – Q(ti)]Basket (S1, …Sp, ti; A(ti), ti)
with Q(ti) the survival probability beyond time Q(ti)
22
Collateral
• The impact of collateral amounts to resetting the strike in
favor of the party that receives the deposit (again as it
happens in the futures markets).
• Collateral is deposited in cash or very safe securities. In
come cases, however, the senior tranches were actually
used as collateral.
• If one accounts for collateral, the CVA amounts to a short
position in cliquet options.
• If risky collateral is used, it is typical to apply a “haircut” (a
given amount of collateral provides guarantee for a lower
amount of exposure)
23
What went wrong?
• Risk mitigating arrangements: the Lehman
Bros default provided a test. It seems that it
took about 15 days to compute and notify
losses, due to negatives externalities:
shortage of lawyers, difficulty to have third
party fair valuation.
• Interbank market: the interbank market was
left outside the risk mitigating arrangement.
Credit risk haunted to the Euribor/Libor
rates (difference between 3m Euribor/OIS)
24
From credit to liquidity
• If you do not trust your neighbor and do not trust
your assets, you are in liquidity trouble
• Funding liquidity: you must come up with funding
for your assets, but the market is dry. Solutions: i)
chase retail investors ii) rely on quantitative easing
(won’t last long)
• Market liquidity: you are forced to unwind positions
in periods of market stress, and you may not be
able to find counterparts for the deal, unless at a
deep discount. Solution: quantitative easing (place
illiquid bonds as collateral)
25
From liquidity to accounting
• Fair value accounting: bonds available for sale must be
evaluated at fair value and profits and losses must be
reported in the balance sheet.
• What is fair value? The price as close as possible to the
market evaluation? But: what is a market?
• Types of assets:
• Type 1. Price is available on a transparent market
• Type 2. A variable needed to compute the price can be
calibrated from a liquid market
• Type 3. Neither the price or market parameters can be
observed
26
Accounting and the crisis I
• What is a market? Two people exchanging one good is a
market? Or do we need more people to say that we have a
market? Sorites paradox (how many grains make a heap of
sand?)
• In a market in which people do not trust their neighbors
(counterparty risk) and do not trust their assets (ambiguity)
accounting may have a perverse effect
• Assume counterparty A is in desperate need of cash and is
obliged to unwind a position worth 100 overnight (say a
senior tranche). Say no one wants to buy, and finally one
finds a counterpart for 70. If this is considered a market, all
institutions in the world will record a loss of 30 on the same
asset. And tomorrow many others will be in need of cash…
27
“Lite accounting”
• Lite accounting was a term used for Enron to denote the
fact that much of Enron’s debt and most of Enron
managers’ bonuses where hidden in about 1 000
companies controlled by Enron, but not consolidated in its
balance sheet. Enron crisis was triggered by the request
of consolidation from the auditing company (Arthur
Andersen)
• SIV (Structured Investment Vehicle): lite accounting for
banks. Off-balance sheet institutions, controlled by banks,
issuing short term liabilities (commercial paper) and
investing on long term bonds (senior tranches) to earn the
difference in spread (carry). A receipe to boost leverage.
28
Accounting and the crisis II
• Reconsider the modern version of Sorites paradox with
lite accounting and SIV.
• Financial institution A has SIV , and in an illiquid market
has difficulty to raise commercial paper to fund the assets.
Then it is forced to look for a financial institution B to sell
the assets. But financial institution B should buy the asset
through its vehicle  which is also struggling to place
commercial paper to fund his own assets.
• Notice: the first SIV in history were launched by Citigroup
in 1988 and were given the names Alpha and Beta
Finance Corporations.
29
Where did the crisis end?
• The crisis could end nowhere but in the only
balance sheet that is not computed at fair value,
namely Government and municipal entities
balance sheets.
• Bail-out from the Government: special purpose
interventions (see AIG, Fortis, and the like) and
general purpose committments
• Central bank intervention: quantitative easing, to
provide liquidity to the system and prevent
contagion. It is almost over in Europe, still alive in
the US.
30
“Monstruous siamese brotherhood”?
• In the aftermath of the 29 crisis the most famous Italian
banker, Raffaele Mattioli, founder of COMIT (BCI) denoted
“mostruosa fratellanza siamese” the evolution of the
relationship between banks and corporate clients. The
“physiological symbiosis” typical of “universal banking”
(that is lending and providing risk capital) had brought, in
a period of credit crisis, the banks to take control of
industrial firms.
• Today, the same “monstruous siamese brotherhood” is
looming in the relationship between Government and the
banking system.
31
The “siamese brotherhood”
• Banks have exposures to Government. Once monetary
base was directly created by the central bank by lending
to Government. Now lending is intermediated by banks.
Government issue securities that are bought by banks in
the primary market and placed as collateral with the
central bank. Default of a Government would severely
jeopardize the banking system.
• In these days the regulators are designing a new stress
test of the soundness of the banking system in front of a
public debt crisis ending with default. The old stress test
tried in September was only based on the value
impairment of a crash in the public debt securities market.
32
Fail or be rescued?
• The other face of “siamese brotherhood” is the implicit
guarantee offered by the Government to banks
• Too big to fail (or to big to save?). The debate is about
whether it is possible to allow big institutions (systemically
important financial intermediary, SIFI) to go bankrupt
• Taxation on SIFI: they would pay for insurance from the
public. Pros: makes moral hazard more costly. Cons: who
is SIFI? Any volunteer?
• Living wills: should (or could) big banks prepare their own
funeral? Pros: assets are perishable goods. Reduces
moral hazard because makes default credible. Cons: how
to plan externalities? Can you be credible if you state that
you will walk into the grave on your own?
33
Marshall Olkin copula
• Marginal survival probabilities
• P(1 > T) = exp(– (1 + 12)(T – t )) = u1
• P(2 > T) = exp(– (2 + 12)(T – t )) = u2
P(1 > T, 2 > T) = u1u2 min(u1-1 u2 - 2)
with -i = 12 /(i + 12)
• This is known as Marshall Olkin copula
34
Portfolio intensity
• The idea of Marshall Olkin distribution is that
different shocks bring about defaults of
subsets of names.
• The problem is that there may exist an
arbitrarily large number of shocks and this
makes calibration of the model very difficult.
• Factor model specification
n
   i  123....n
i 1
35
Filters of common shocks
• Call m the cross-section average intensity
• Given 1/ (average of inverse Kendall’s )
and 1/ (average of inverse Spearman’s ).
123...n 
2
1
1

m 123...n


4 1

3 1 1
3 




 m


36
01/09/2010
01/07/2010
01/05/2010
01/03/2010
01/01/2010
01/11/2009
01/09/2009
01/07/2009
01/05/2009
01/03/2009
01/01/2009
01/11/2008
01/09/2008
01/07/2008
01/05/2008
01/03/2008
01/01/2008
Italy
0,2
0,18
0,16
0,14
0,12
Govt
0,1
Systemic
0,08
Financial
0,06
0,04
0,02
0
37
01/09/2010
01/07/2010
01/05/2010
01/03/2010
01/01/2010
01/11/2009
01/09/2009
01/07/2009
01/05/2009
01/03/2009
01/01/2009
01/11/2008
01/09/2008
01/07/2008
01/05/2008
01/03/2008
01/01/2008
Spain
0,3
0,25
0,2
Govt
0,15
Systemic
Financial
0,1
0,05
0
38
01/09/2010
01/07/2010
01/05/2010
01/03/2010
01/01/2010
01/11/2009
01/09/2009
01/07/2009
01/05/2009
01/03/2009
01/01/2009
01/11/2008
01/09/2008
01/07/2008
01/05/2008
01/03/2008
01/01/2008
Portugal
0,4
0,35
0,3
0,25
Govt
0,2
Systemic
Financial
0,15
0,1
0,05
0
39
01/09/2010
01/07/2010
01/05/2010
01/03/2010
01/01/2010
01/11/2009
01/09/2009
01/07/2009
01/05/2009
01/03/2009
01/01/2009
01/11/2008
01/09/2008
01/07/2008
01/05/2008
01/03/2008
01/01/2008
Greece
0,7
0,6
0,5
0,4
Govt
Systemic
0,3
Financial
0,2
0,1
0
40
01/09/2010
01/07/2010
01/05/2010
01/03/2010
01/01/2010
01/11/2009
01/09/2009
01/07/2009
01/05/2009
01/03/2009
01/01/2009
01/11/2008
01/09/2008
01/07/2008
01/05/2008
01/03/2008
01/01/2008
Ireland
0,45
0,4
0,35
0,3
0,25
Govt
0,2
Systemic
Financial
0,15
0,1
0,05
0
41
01/09/2010
01/07/2010
01/05/2010
01/03/2010
01/01/2010
01/11/2009
01/09/2009
01/07/2009
01/05/2009
01/03/2009
01/01/2009
01/11/2008
01/09/2008
01/07/2008
01/05/2008
01/03/2008
01/01/2008
U.K.
0,2
0,18
0,16
0,14
0,12
Govt
0,1
Systemic
0,08
Financial
0,06
0,04
0,02
0
42
01/09/2010
01/07/2010
01/05/2010
01/03/2010
01/01/2010
01/11/2009
01/09/2009
01/07/2009
01/05/2009
01/03/2009
01/01/2009
01/11/2008
01/09/2008
01/07/2008
01/05/2008
01/03/2008
01/01/2008
Netherlands
0,2
0,18
0,16
0,14
0,12
Govt
0,1
Systemic
0,08
Financial
0,06
0,04
0,02
0
43
01/09/2010
01/07/2010
01/05/2010
01/03/2010
01/01/2010
01/11/2009
01/09/2009
01/07/2009
01/05/2009
01/03/2009
01/01/2009
01/11/2008
01/09/2008
01/07/2008
01/05/2008
01/03/2008
01/01/2008
France
0,14
0,12
0,1
0,08
Govt
Systemic
0,06
Financial
0,04
0,02
0
44
01/09/2010
01/07/2010
01/05/2010
01/03/2010
01/01/2010
01/11/2009
01/09/2009
01/07/2009
01/05/2009
01/03/2009
01/01/2009
01/11/2008
01/09/2008
01/07/2008
01/05/2008
01/03/2008
01/01/2008
Germany
0,14
0,12
0,1
0,08
Govt
Systemic
0,06
Financial
0,04
0,02
0
45
01/09/2010
01/07/2010
01/05/2010
01/03/2010
01/01/2010
01/11/2009
01/09/2009
01/07/2009
01/05/2009
01/03/2009
01/01/2009
01/11/2008
01/09/2008
01/07/2008
01/05/2008
01/03/2008
01/01/2008
Austria
0,4
0,35
0,3
0,25
Govt
0,2
Systemic
0,15
Financial
0,1
0,05
0
46
Portugal
Ireland
Italy
Greece
Spain
Germany
France
UK
Netherland
Austria
Table 5. Mark-to-market of the implicit guarantee to a systemic shock (bn euro)
Intensity
DP
LGD
Government Commitments
Liability Liability
Commitments
6,04%
26,06%
312,12
73,68
20
53,68
7,15%
30,05%
980,4
266,85
430
-163,15
2,65%
12,42%
2248,62
252,98
20
232,98
12,12%
45,45%
295,14
121,51
28
93,51
4,73%
21,06%
2068,08
394,57
329
65,57
0,94%
4,57%
4461,66
184,89
480
-295,11
1,36%
6,56%
4594,02
273,00
288,95
-15,95
2,07%
9,85%
5677,2
506,61
444,66
61,95
1,70%
8,15%
1330,2
98,23
200
-101,77
2,79%
13,02%
618,12
72,90
90
-17,10
Total
2245,23
2330,61
-85,38
47
600
500
Germany
y = 0,8025x + 52,877
R2 = 0,3876
U.K.
Ireland
Commitment
400
France
300
Spain
Netherlands
200
100
Austria
Greece
Italy
Portugal
0
0
100
200
300
400
500
600
Government Liability
48
The Government crisis, finally
Table 6. Bail-out Government liability and
Debt/GDP
Total
Liability/GDP
Debt/GDP
Portugal
121,76%
44,96%
76,80%
Ireland
227,17%
163,17%
64,00%
Italy
132,43%
16,63%
115,80%
Greece
166,26%
51,16%
115,10%
Spain
90,74%
37,54%
53,20%
Germany
80,88%
7,68%
73,20%
France
91,91%
14,31%
77,60%
UK
100,44%
32,34%
68,10%
Netherlands
78,13%
17,23%
60,90%
Austria
92,83%
26,33%
66,50%
49
Ingredients of the crisis
• Credit crisis: example of Greece and the so called
PIIGS (GIPSI). Unsustainable debt with respect to
credible future primary surpluses.
• Liquidity crisis: funding liquidity experienced for
the GIPSI at the beginning of the year, primary
market closely monitored by regulators
• Accounting crisis: no fair value (thanks God), but
lot of accounting creativity. Lite accounting? May
be…
50
Public debt transparency
• Derivatives have been used to “window dress” public debt
accounting data: the case is Greece (and rumours about
Italy). The technique is fairly easy. Instead of plain loans,
investment banks offer swap transactions with large
upfront in favour of the Government (and large
commissions hidden in the deal). You receive money for
your current deficit in exchange for higher deficits that
next generations will pay.
• Lite accounting? We are not sure. But in some situation
one could suspect a transfer of debt from the central
Government to the municipal Governments in much the
same way as debt was transferred from Enron to the
subsidiaries. This is something that is worth studying.
51
A sovereign liquidity model
• Assume that an obligor issues a long term bond
for an amount D0. The bond expires in N
periods.
• The curve of the obligor is v(t0,ti)
• In every period, the obligors receives net cash
flows Si, and it pays interest rates on debt Ri =
1/v(ti,ti+1) – 1.
• The difference between Ri Di –1 and Si increases
or decreases the amount of debt Di.
52
A structural model of sovereign debt
• Given a path of primary surplus, measured in
euros, S, the amount of debt in n years is
n
D0
1
DN 

v(t0 , ti )Si

v(t0 , t N ) v(t0 , t N ) i 1
• At time tN, default occurs if DN > DK, with DK a
default threshold (unobserved)
• Probability of default at time t0 is P(DN > DK )
53
Mathematics
N
 D0

1
P( DN  DK )  P

vt0 , ti Si  DK  0 

 vt0 , t N  vt0 , t N  i 1

N


 P D0 1  vt0,t N    vt0 , ti Si  vt0,t N DK  D0   0 
i 1


N
and, dividing by  vt0 , ti 
i 1
N


 P D0 RN   i Si   N DK  D0   0 
i 1


N


 P D0 SRN  ASWN    i Si   N DK  D0   0  or else...
i 1


N



Si 



 P D0 ASWN  D0  i  f i 
  N DK  D0   0  where f i are forwardrates

D0 
i 1



54
Distance to default
• Assume a dynamics of primary surplus. We speficy it in
terms of ratio to GDP: si = Si/Yi and di = Di/Yi.Assume a
simple model si = s + i, i iid with 0 mean and st.dev. 
Then,the distance to default DDN over time horizon tN
turns out to be

N
DDN 
s  i  d 0 RN   N d K 1  g   d 0
i 1

N

N
2

 i
i 1
wit h g t heaveragerat eof growt h of GDP and i  i 1  g 
i
55