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Diversification estimating correlation with historicaldata
Laurent Balthazar
17/09/2007, London
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Agenda
Economic Capital Frameworks and Diversification
Overview of litterature
Choosing the driversHistorical correlation measures and proposed values
Quantifying impacts
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Economic Capital Frameworks and DiversificationEconomic Capital definition:
Amount of capital necessary to cover losses linked to decrease of assets value/
increase of liabilities values, at a given confidence interval (= given a specific
risk appetite), taking into account diversification effects
Depends on specific bank risk profile
Depends on risk appetite/ aversion
It integrates diversification between risk types and businesses
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Economic capital: a stylized example
ABC Bank
Credits
EquityCurrencie
s
Bonds
Insurance
Funding
Deposits
Debts
CapitalCredit Risk !
Market Risk !
Liquidity Risk !
Behavioral risk!Insurance Risk !
Spread Risk !
Operational risk!
Compliance Risk!ALM risk!
Economic Capital
1- Risk Cartography
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Economic capital: a stylized exampleEconomic Capital
2- Risk measurement
Some standards begin to emerge for some risk types,
often simulation (VAR) approaches.
Credit Risk : Credit VAR
Equity Risk: Equity VAR
Interest rate risk: Interest rate VAR
Operational Risk: Basel 2AMA (=op. risk VAR) or standardized approach
Spread Risk: Spread VAR
Behavioral risk: ex prepayment models to emulate customers behavior
Insurance risk: solvency 2 simplified formulas available
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Economic capital: a stylized exampleEconomic Capital
3- Risk aggregation
Capital=f(Risk distribution)
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Agenda
Current situation and goal of update
Overview of litterature & parctices
Choosing the driversHistorical correlation measures and proposed values
Quantifying impacts
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Overview of litterature & practicesHow diversification should be
measured theoretically
We should measure correlation of
historical losses of the bank over
each risk type
Correlation measure should be
adapted to each form of the loss
distributions (Normal, Beta,
Lognormal, )
Correlation should be measured in
tails (stress events)
In practice
No internal historical data to isolate
losses on all risk types
We do not know precisely
distribution of all risk types
(hypothesis)
No enough observations to
measure tail events
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Overview of litterature & practicesApproaches seen in the industry
Aggregation by Business Line
=> Diversification estimated between the BL, may be based on P&L historical
Correlation.
=> But to correctly integrate intra-risk diversification, Ecap usually measured
through risk silos.Approach by BL may complicate correlation structure.
Risk
Type 1
Risk
Type 2
Risk
Type 3
Risk
Type 4
Risk
Type 5
Business Line 1 => Ecap BL1
Business Line 2 => Ecap BL2 Diversification effects
Business Line 3 => Ecap BL3 Global Ecap
Business Line 4 => Ecap BL4
Business Line 5 => Ecap BL5
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Overview of litterature & practicesApproaches seen in the industry
Aggregation by Risk Types
=> Economic capital
globally computed byrisk type for the wholebanking group
=> Intra-riskdiversification already
included in the variousmodels
=> Final diversificationlayer= diversificationbetween the risk types
Risk
Type 1
Risk
Type 2
Risk
Type 3
Risk
Type 4
Risk
Type 5
usiness ine 1
usiness ine 2
usiness ine 3
usiness ine 4
usiness ine 5
=>
=>
=>
=>
=>
Ecap
redit
Risk
Ecap
Market
risk
Ecap
oper risk
Ecap
usiness
risk
Ecap
insurance
risk
Di
i
i
i
Global Ecap
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Overview of litterature & practicesCurrent Market Practices
Methods based on VAR / CoVAR are the more used (hypothesis of similar
distributions)
Methods Based on copula theoretically more precise but no data tocalibrate them. Choosing one copula or the other might impact 30% ormore final figures
Agregation techni ue Remar Use in industry
ypothesis of independence ot enough prudent o
ypothesis of perfect correlat ion oo conser ati e o but regulatory approach in Basel
VAR/ CoVAR aproach - tde
ends to o erestimate
cap igh
VAR/ CoVAR aproach - capends to
underestimate capigh
Copulas ard to calibrate Very lo
Joint historical simulation ard to calibrate Very lo
BAABBABAULULULULUL V2
22!
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Overview of litterature & practicesKuritzkes (Wharton Paper)
Own researchTable 17.11 Correlation matrix - Ranges
Corr l. M trix Cr it risk M rk t risk O
r tional risk B siness risk
Cr it risk 100%M rk t risk 50%-100% 100%
r ti l risk 0%-50% 0%-50% 100%
t r risks 30%-70% 30%-70% 0%-50% 100%
Broadreferences ofcorrelationmatrix
Range ofestimatedcorrelations stillhigh
Source: RiskMeasurement, RiskManagement andCapital Adequacy inFinancialConglomerates Working paper -Kuritzkes,
Schuermann, Weiner,2002
Source: From Basel
1 to Basel 3 Bookat Mac Milan Editions- Balthazar, 2006
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Overview of litterature & practicesSolvency 2 proposed values in QIS
Credit Vs Market Risk
Inside Market Risk
Attention: amortizing effect of profit sharing for market risk is taken intoaccount, this could justify lower correl than for banking activities.Also,traditional interest sensitivity is not the same as the banking groups.
Market efault
Market 100% 25%
Def lt 25% 100%
SCRmktaggregation Interest Equity Spread Forex
Interest 100% 50% 25% 25%
Equity 50% 100% 25% 25%
Spread 25% 25% 100% 25%
Forex 25% 25% 25% 100%
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Overview of litterature & practicesRisk Cartography
Attention: Typically, banks communicate on 3-4 broad risk types
Source: From Basel 1 to Basel 3 Book atMac Milan Editions - Balthazar, 2006
Ba k
Co zb nk JP o g n
Ch
NG
o
C financial
g oupCSFB
ABN Amro
CIBC
Citigroup
Ecap average split -
Benchmarking study
of10 large banks
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Overview of litterature & practices
But to measure diversification correctly, one would need to go to finer risktypology
-Default risk
- Spread risk
- Transfert Risk
- Migration risk
- -Interest risk
- Equity risk
- Forex Risk
-
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Overview of litterature & practicesDiversification benefits
Defined as 1- Final Ecap figure \ sum of economic capital stand alone
In Kuritzkes, Schuermann, Weinerdiversification benefit of bank-insurancegroup estimated between between 15-28%
In Economic Capital Modelling Concepts, Measurement and
Implementation Risk Books, edited by Iman van Lelyveld, a survey
shows, 2006 2003Citigroup 10.02%
Deutsche Bank 7.20%
JPMorgan 12.38%
Credit uisse 33.49%
Commerzbank 21.78%
Dresdner Bank 22.64%
De ia 15.00%
average 17.50%
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Overview of litterature & practicesConclusions
Diversification is still an open question for the industry
No clear consensus on a single leading technique
Diversification is anyway an important issue: effect on Ecap can be
roughly estimated between 10 and 30%
Lack of data and uncertainty about functional form (e.g. Copula) creates
large buckets of uncertainty around estimates
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Overview of litterature & practicesProposed Framework
1) Define for each risk type a representative proxy
2) Collect historical data on this proxy
3) Measure linear correlation between the various proxies4) Challenge correlation with expert approach
economic theory
5) Add a layer of conservatism in function of uncertainty
on the results
6) Refine\ enrich with time internal data
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Agenda
Current situation and goal of update
Overview of litterature
Choosing the driversHistorical correlation measures and proposed values
Quantifying impacts
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Choosing the drivers
The goal is to identify for each risk type a
key driver/ proxy representing potential
losses for the bank, to be able to
measure historical correlations.
Credit Risk
We propose Default rates. Public data is
available from rating agencies
Refined approach might use internal Defaultrates collected for Basel 2
Synthetic proxies might be constructed to
reflect more precisely particular portfolio
structure
Yearorporate efault
rate
1983 0.962%
1984 0.922%
1985 1.007%
1986 1.901%
1987 1.499%
1988 1.355%
1989 2.336%1990 3.587%
1991 3.216%
1992 1.300%
1993 0.977%
1994 0.558%
1995 1.021%
1996 0.511%
1997 0.650%
1998 1.249%
1999 2.197%
2000 2.487%
2001 3.907%
2002 3.047%
2003 1.704%
2004 0.821%
2005 0.654%
2006 0.543%
Source-S&P
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Interest Risk: We can use ALM risk sensibilities (= loss for the bank in
case of interest move). The proxy proposed is a synthetic P&L constructed
applying our current sensitivities to historical interest rates move.
Ex:
Choosing the drivers
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Currency Risk: ex: Main currency risk currently= positions in SD. Proposed
proxy equals then E R/ SD exchange rate. In case SD increase, higher
profit for the bank. If it decreases, loss for the bank.
Choosing the drivers
In case big positions in several
currencies, proxy is a weighted index
function of size of positions
SD/E R E R/ SD
Nov-1982 0.813373 1.229448Nov-1983 0.739713 1.351876
Nov-1984 0.667222 1.498752
Nov-1985 0.768838 1.300664
Nov-1986 0.959081 1.042665
relative variation
year SD/E R E R/ SD
Nov-1982
1983 Nov-1983 -9% 10%
1984 Nov-1984 -10% 11%
1985 Nov-1985 15% -13%
1986 Nov-1986 25% -20%
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Price Risk: risk is decrease of equity portfolio value. Proxy used is the
historical returns that would have been registered by our current portfolio
using a mapping of each position to a reference index.
Choosing the drivers
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For some risk types, it is difficult to find a driver. Typically: Business,
operational, model, legal, reputation, risks. If no driver can be found, a
conservative estimation will have to be used. Anyway, credit and market risk
are usually most important par of Ecap consumption (78% in our survey)
Choosing the drivers
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R
eviewing
inter
risk
correl
ation
Current situation and goal of update
Overview of litterature
Choosing the driversHistorical correlation measures and proposed values
Quantifying impacts
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Simplified Bank example:
- Exposed to S Corp
- Exposed on rate increase
(=risk), av maturity 5 years
- Equity positions in S
industrial stocks
- Balance sheet in E R and
large positions unhedged in
SD
! Sign should be changed for
equity and currency
Historical correlation measures and proposed values
credit ri Interest rate risk Equit risk currency risk
year
efault rate 5 year IR
ean
elta S& P 500 return EUR/USD
elta
1983 0.962% -0.56% 17% 10%
1984 0.922% 0.09% 1% 11%
1985 1.007% -1.90% 26% -13%
1986 1.901% -1.77% 15% -20%
1987 1.499% 0.10% 2% -16%
1988 1.355% -0.14% 12% 4%
1989 2.336% 1.46% 27% 5%
1990 3.587% 0.48% -7% -20%
1991 3.216% -0.99% 26% 9%
1992 1.300% -1.49% 4% -2%
1993 0.977% -1.42% 7% 9%
1994 0.558% 1.85% -2% -9%
1995 1.021% -2.15% 34% -5%
1996 0.511% -0.80% 20% 2%
1997 0.650% 0.05% 31% 11%
1998 1.249% -1.42% 27% -2%
1999 2.197% 1.37% 20% 13%
2000 2.487% 0.12% -10% 21%
2001 3.907% -0.61% -13% -4%
2002 3.047% -0.73% -23% -11%
2003 1.704% -0.09% 26% -15%
2004 0.821% -0.66% 9% -10%
2005 0.654% 0.10% 3% 10%
2006 0.543% 0.77% 14% -9%
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Correlation matrix
Historical correlation measures and proposed values
First rough correl matrix
Then we have to challenge it
with economic theory
Propose a level function of
confidence in estimates
And integrate risks without
proxies
Correlation
atri
credit
risk
Interestr
ate
risk
Equityri
sk
currency
risk
credit risk100% 6% 41% 12%
Interest rate risk100% 20% -17%
Equity risk100% 11%
currency risk100%
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CREDIT RISK
Vs Equity: 41%. Expected strong positive correl:
Merton Model
Link to
economic cycle
=> We propose to
retain 50%
Historical correlation measures and proposed values
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CREDIT RISK
Vs Interest: 6%
During DR shock (90
and 01), IR stable
Analysis on S rates
(instead E ), correl
-31%with
5y,
-19%with10y
Historical correlation measures and proposed values
Default rates Vs interest rates
-2.5%
-2.0%
-1.5%
-1.0%
-0.5%
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
198319841985198619871988198919901991199219931994199519961997199819992000200120022003200420052006
years
deltaIR1
0y
0.000%
0.500%
1.000%
1.500%
2.000%
2.500%
3.000%
3.500%
4.000%
4.500%
DR
delta Interest Rates US 10
Default Rate
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In literature, IR used in Moodys model to predict DR, but one factor out 6
(limited weight)
Monetary policy coherent with results: in periods of slow down (DR
increasing), growth policy to rates cut, which could justify the slightlynegative correlation for the bank.
BCE policy a little bit different (priority to fight againts inflation), results
expected to be more close to zero.
=> We propose to retain 25%
Historical correlation measures and proposed values
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CREDIT RISK
Vs Currency: correl of12%. Weak link from economical perspective
between exchange rate and credit risk in developed countries. In
developing countries, conclusions may be different
We propose to retain 25%
Historical correlation measures and proposed values
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EQ ITY RISK
Vs Interest: 20%
Equity risk linked to credit risk, and weak correl between credit risk and
interest risk (see above)
50% correl proposed in solvency 2
In economic theory, increase of rates linked to decrease of equity , weshould then observe positive correlation between those 2 risks
We propose to use 25%
Historical correlation measures and proposed values
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EQ ITY RISK
Vs Currency :11%. Low correlation. It means that decrease of SD value is
not directly linked to increase of S stocks (time lag or no link ?). No cleardirect link for all companies (depending on % of exportations, of% of hedge
of foreign activity, )
=> We propose to use 25%
Historical correlation measures and proposed values
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INTEREST RISK
Vs Currency: -17%. Exchange rate is in principle linked to the difference in
interest rate between 2 currencies, not to the interest rate itself. Expected
correlation is then weak.
We propose to use 15%
OPERATIONAL RISK
By nature, should be low correlation
benchmarking and references usually mention 0-50%
We propose to take upper limits: 50%
Historical correlation measures and proposed values
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Retained values
Historical correlation measures and proposed values
Correlation
matrix
creditr
isk
Interes
trate
risk
Equity
risk
curr
ency
risk
credit risk100% 6% 41% 12%
Interest rate risk100% 20% -17%
Equity risk100% 11%
currency risk100%
Correlation
matrix
cred
itr
isk
Inter
estrate
risk
Equi
tyr
isk
curre
ncy
risk
Oper
ationalrisk
credit risk100% 25% 50% 25% 50%
Interest rate risk100% 25% 15% 50%
Equity risk100% 25% 50%
currency risk100% 50%
Operational risk100%
After challenging and economic analysis
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Reviewinginterriskcorrelation
Current situation and goal of update
Overview of litterature
Choosing the driversHistorical correlation measures and proposed values
Quantifying impacts
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Quantifying impacts
Impact: suppose typical Ecap split
Applying the correlation matrix we have:
Undi ersifiedEconomicCapital
credit risk 50
Interest rate risk 15
Equity risk 10
currency risk 5
Operational risk 20
TOTAL 100
Correlation
matri
credit
risk
Interestrate
risk
Equity
risk
currency
risk
Operationalrisk
credit risk100% 25% 50% 25% 50%
Interest rate
risk 25% 100% 25% 15% 50%
Equity risk50% 25% 100% 25% 50%
currency risk25% 15% 25% 100% 50%
Operational
risk 50% 50% 50% 50% 100%
credit
r
isk
Interest
rate
r
is
k
Equity
ris
k
cu
rrency
ris
k
Op
eration
al
ris
k
50 15 10 5 20
credit risk 50
Interest rate risk 15
Equity risk 10
currency risk 5
Operational risk 20
X X= 77
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Quantifying impacts
Impact: comparing diversification rates
We got 77 for undiversified Ecap of100, a diversification rate of23%
Compared to our benchmarks: 15-30%, we are in line
Sensitivity analysis: +10% on all correl
=> Ecap= 82
=> Diversification down to18%
Correlation
matri
credit
risk
Interestrate
risk
Equity
risk
currency
risk
Operationalrisk
credit risk100% 35% 60% 35% 60%
Interest rate risk35% 100% 35% 25% 60%
Equity risk60% 35% 100% 35% 60%
currency risk35% 25% 35% 100% 60%
Operational risk60% 60% 60% 60% 100%
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Conclusions
Conclusions
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Conclusions
Conclusions
Current Problems with diversification
No standard, industry wide accepted method
Issue Nr1 on distribution forms: no standard, copula the most elegant
theoretically but too sensitive to hypothesis => VAR \ COVAR seems to be used
more common practice
Issue Nr2 on data: poor internal historical data. Past representative of future ?
B T
Diversification exists, then a conservative estimates is better than nothing
First insight can be gained on historical data (high- average- low- negative
Correlation ?)
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Conclusions
Conclusions
A simple method
We illustrated a simple method
Basic idea is to identify public or internal proxies representative of various risktypes for the bank and measure correlation
Results should be challenged with expert\ economic theory
Method is itterative and can be refined with time: internal data, more precisestructure of exposures to currencies, interest,
We believe open debate should currently be the priority in the industry,
regarding the dialogue that will occur with regulators underBasel 2
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