Slides Diversification London 2007

8/6/2019 Slides Diversification London 2007

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Diversification estimating correlation with historicaldata

Laurent Balthazar

17/09/2007, London


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Diversification Workshop

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


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




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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




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:



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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.


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.



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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)



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R

eviewing

inter

risk

correl

ation




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


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%



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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


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%



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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%



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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%



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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%



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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%



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Retained 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




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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Documents

Slides Diversification London 2007