london finance graduate program birbeck college, 18/03/2011 funding liquidity risk advanced methods...
TRANSCRIPT
London Finance Graduate Program
Birbeck College, 18/03/2011
Funding Liquidity Risk
Advanced Methods of Risk Management
Umberto Cherubini
2
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?
3
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.
4
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??
5
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)
6
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
where M is the common factor and m is a particular scenario of it.
2
1
1Pr
muN
NmMDefault
7
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:
2
1121Pr
pNLN
NLL dd
8
Vasicek density function
0
2
4
6
8
10
12
14
16
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
Rho = 0.2
Rho = 0.6
Rho = 0.8
9
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.
10
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?
11
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, super-replication 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.
12
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
Rho = 0
Rho = 1
Price bounds of a senior tranche
13
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)
14
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
15
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.
16
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, Max-Min-Expected Utility (MMEU): probabilities are represented by intervals, rather than numbers.
• Gilboa (1987), Schmeidler (1982,1989): Choquet utility (sub-additive measures represent uncertainty aversion)
17
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).
18
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.
19
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)
20
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.
21
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
p
iii
p
ii
FTPA
AS
1
1
,
0,max
22
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)
23
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)
24
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)
25
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)
26
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
27
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…
28
“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.
29
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.
30
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.
31
“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.
32
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.
33
• 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?
Fail or be rescued?
34
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
35
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
n
ii ....123
1
36
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 ).
mnmn
131
1
3
41
1
2...123...123
37
Italy
0
0,02
0,04
0,06
0,08
0,1
0,12
0,14
0,16
0,18
0,2
01/0
1/20
08
01/0
3/20
08
01/0
5/20
08
01/0
7/20
08
01/0
9/20
08
01/1
1/20
08
01/0
1/20
09
01/0
3/20
09
01/0
5/20
09
01/0
7/20
09
01/0
9/20
09
01/1
1/20
09
01/0
1/20
10
01/0
3/20
10
01/0
5/20
10
01/0
7/20
10
01/0
9/20
10
Govt
Systemic
Financial
38
Spain
0
0,05
0,1
0,15
0,2
0,25
0,3
01/0
1/20
08
01/0
3/20
08
01/0
5/20
08
01/0
7/20
08
01/0
9/20
08
01/1
1/20
08
01/0
1/20
09
01/0
3/20
09
01/0
5/20
09
01/0
7/20
09
01/0
9/20
09
01/1
1/20
09
01/0
1/20
10
01/0
3/20
10
01/0
5/20
10
01/0
7/20
10
01/0
9/20
10
Govt
Systemic
Financial
39
Portugal
0
0,05
0,1
0,15
0,2
0,25
0,3
0,35
0,4
01/0
1/20
08
01/0
3/20
08
01/0
5/20
08
01/0
7/20
08
01/0
9/20
08
01/1
1/20
08
01/0
1/20
09
01/0
3/20
09
01/0
5/20
09
01/0
7/20
09
01/0
9/20
09
01/1
1/20
09
01/0
1/20
10
01/0
3/20
10
01/0
5/20
10
01/0
7/20
10
01/0
9/20
10
Govt
Systemic
Financial
40
Greece
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
01/0
1/20
08
01/0
3/20
08
01/0
5/20
08
01/0
7/20
08
01/0
9/20
08
01/1
1/20
08
01/0
1/20
09
01/0
3/20
09
01/0
5/20
09
01/0
7/20
09
01/0
9/20
09
01/1
1/20
09
01/0
1/20
10
01/0
3/20
10
01/0
5/20
10
01/0
7/20
10
01/0
9/20
10
Govt
Systemic
Financial
41
Ireland
0
0,05
0,1
0,15
0,2
0,25
0,3
0,35
0,4
0,45
01/0
1/20
08
01/0
3/20
08
01/0
5/20
08
01/0
7/20
08
01/0
9/20
08
01/1
1/20
08
01/0
1/20
09
01/0
3/20
09
01/0
5/20
09
01/0
7/20
09
01/0
9/20
09
01/1
1/20
09
01/0
1/20
10
01/0
3/20
10
01/0
5/20
10
01/0
7/20
10
01/0
9/20
10
Govt
Systemic
Financial
42
U.K.
0
0,02
0,04
0,06
0,08
0,1
0,12
0,14
0,16
0,18
0,2
01/0
1/20
08
01/0
3/20
08
01/0
5/20
08
01/0
7/20
08
01/0
9/20
08
01/1
1/20
08
01/0
1/20
09
01/0
3/20
09
01/0
5/20
09
01/0
7/20
09
01/0
9/20
09
01/1
1/20
09
01/0
1/20
10
01/0
3/20
10
01/0
5/20
10
01/0
7/20
10
01/0
9/20
10
Govt
Systemic
Financial
43
Netherlands
0
0,02
0,04
0,06
0,08
0,1
0,12
0,14
0,16
0,18
0,2
01/0
1/20
08
01/0
3/20
08
01/0
5/20
08
01/0
7/20
08
01/0
9/20
08
01/1
1/20
08
01/0
1/20
09
01/0
3/20
09
01/0
5/20
09
01/0
7/20
09
01/0
9/20
09
01/1
1/20
09
01/0
1/20
10
01/0
3/20
10
01/0
5/20
10
01/0
7/20
10
01/0
9/20
10
Govt
Systemic
Financial
44
France
0
0,02
0,04
0,06
0,08
0,1
0,12
0,14
01/0
1/20
08
01/0
3/20
08
01/0
5/20
08
01/0
7/20
08
01/0
9/20
08
01/1
1/20
08
01/0
1/20
09
01/0
3/20
09
01/0
5/20
09
01/0
7/20
09
01/0
9/20
09
01/1
1/20
09
01/0
1/20
10
01/0
3/20
10
01/0
5/20
10
01/0
7/20
10
01/0
9/20
10
Govt
Systemic
Financial
45
Germany
0
0,02
0,04
0,06
0,08
0,1
0,12
0,14
01/0
1/20
08
01/0
3/20
08
01/0
5/20
08
01/0
7/20
08
01/0
9/20
08
01/1
1/20
08
01/0
1/20
09
01/0
3/20
09
01/0
5/20
09
01/0
7/20
09
01/0
9/20
09
01/1
1/20
09
01/0
1/20
10
01/0
3/20
10
01/0
5/20
10
01/0
7/20
10
01/0
9/20
10
Govt
Systemic
Financial
46
Austria
0
0,05
0,1
0,15
0,2
0,25
0,3
0,35
0,4
01/0
1/20
08
01/0
3/20
08
01/0
5/20
08
01/0
7/20
08
01/0
9/20
08
01/1
1/20
08
01/0
1/20
09
01/0
3/20
09
01/0
5/20
09
01/0
7/20
09
01/0
9/20
09
01/1
1/20
09
01/0
1/20
10
01/0
3/20
10
01/0
5/20
10
01/0
7/20
10
01/0
9/20
10
Govt
Systemic
Financial
47
Table 5. Mark-to-market of the implicit guarantee to a systemic shock (bn euro) Intensity DP LGD Government
Liability Commitments Liability -
Commitments Portugal 6,04% 26,06% 312,12 73,68 20 53,68 Ireland 7,15% 30,05% 980,4 266,85 430 -163,15
Italy 2,65% 12,42% 2248,62 252,98 20 232,98 Greece 12,12% 45,45% 295,14 121,51 28 93,51 Spain 4,73% 21,06% 2068,08 394,57 329 65,57
Germany 0,94% 4,57% 4461,66 184,89 480 -295,11 France 1,36% 6,56% 4594,02 273,00 288,95 -15,95
UK 2,07% 9,85% 5677,2 506,61 444,66 61,95 Netherland 1,70% 8,15% 1330,2 98,23 200 -101,77
Austria 2,79% 13,02% 618,12 72,90 90 -17,10 Total 2245,23 2330,61 -85,38
48
y = 0,8025x + 52,877
R2 = 0,3876
0
100
200
300
400
500
600
0 100 200 300 400 500 600
Government Liability
Co
mm
itm
ent
Austria
Portugal
Greece Italy
Netherlands
Germany
Ireland
FranceSpain
U.K.
49
Table 6. Bail-out Government liability and Debt/GDP
Debt/GDP Liability/GDP Total Portugal 76,80% 44,96% 121,76% Ireland 64,00% 163,17% 227,17%
Italy 115,80% 16,63% 132,43% Greece 115,10% 51,16% 166,26% Spain 53,20% 37,54% 90,74%
Germany 73,20% 7,68% 80,88% France 77,60% 14,31% 91,91%
UK 68,10% 32,34% 100,44% Netherlands 60,90% 17,23% 78,13%
Austria 66,50% 26,33% 92,83%
The Government crisis, finally
50
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…
51
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.
52
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.
53
A structural model of sovereign debt
• Given a path of primary surplus, measured in euros, S, the amount of debt in n years is
• At time tN, default occurs if DN > DK, with DK a default threshold (unobserved)
• Probability of default at time t0 is P(DN > DK )
i
n
ii
NNN Sttv
ttvttv
DD
1
000
0 ),(),(
1
),(
54
Mathematics
rates forward are where0
else...or 0
0
,by dividing and, 0,1
0,,
1
,)(
01 0
00
01
0
01
0
100,0
10,00
10
00
0
iKN
N
i
iiiN
KN
N
iiiNN
KN
N
iiiN
N
iiKN
N
iiiN
K
N
iii
NNKN
fDDD
SfDASWDP
DDSASWSRDP
DDSRDP
ttvDDttvSttvttvDP
DSttvttvttv
DPDDP
55
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
iii
N
ii
N
i
NKNNi
N
gg
dgdRdsDD
1 and GDP ofgrowth of rate average thewith
1
1
2
100