Beyond Credit Risk Economic Capital Models %e2%88%92 News and Views ...

8/8/2019 Beyond Credit Risk Economic Capital Models %e2%88%92 News and Views ...

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Beyond Credit Risk:

Economic Capital Models

News and Views

March 2006


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Economic Capital Model: The Consultancy's View


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Four questions...

What is Philosophy?

What should we do ?

What can we know ?

What is a human being ?

What may we hope for ?

(Immanuel Kant, 18th century)


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Four questions concerning Economic Capital

What should we do ?

What can we know ?

What is a human being ?


What should we do ?

What can we measure ?

What is EC ?


What is Philosophy ?

(Immanuel Kant, 18th century)

What is an EC Model ?

(K.B. 21th century)


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What is Economic Capital?


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Questions

How do we choose between

- an increase of EUR 20 mn in 1-day market VaR

- an increase of EUR 10 bn of exposure in private customers?

What effect does an acquisition have on the overall risk profile

of our bank?

Does our bank have enough capital to sustain potentially

extreme losses with sufficient high probability?

Suppose you are management board member of a bank...


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EC = Loss at very high CL (quantile) Expected Loss (EL)


and the answer...

We need a uniform risk measure across risk types,

business lines, regions, products, etc.

Here, risk is the unexpected loss of economic value over a certain

time period, calculated at very high confidence level

Economic Capital measures risk from the debt holder perspective

(potential loss of value) rather than from the equity holder

perspective (volatility)

Economic Capital


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Economic Capital at HVB

Mean q99,95%

Loss

Economic Capital is based on a Value-at-Risk (VaR) with

a time-horizon of one year

a confidence level of 99.95 %.

ECEL

covered

by net

margin

income

losses against it

would be uneconomical

to hold capital


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What can we measure?


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Economic Capital by risk types

Risk types amenable for quantification

market

4%

credit34%

oprisk

13%

business

14%

real estate

4%

financial inv.

31%

market risk

credit risk

operational risk business risk

real estate risk

financial investment risk


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Aggregation of risk: Overview (1)

Diversification is a competitive advance and should be

taken into account- between business units

- between risk types.

Dependence between different risk types is based on

realistic correlation estimates (InterCorrelation).

Currently, the overall diversification benefit by InterCorrelation

is about 35 %.


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Aggregation of risk: Overview (2)

1. Determine EC for each risk type separately, including

diversification effects between business units.2. Aggregate those EC numbers into one EC for the entire bank.

Risk types

Busines

s

units

EC per risk type Total EC

InterCorr.


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InterCorrelation: Var-covar approach

Correlations estimates between risk types are based on the

loss drivers as well as expert opinions.- what drivers to use for time-varying positions in market risk?

- loss drivers for operational risk?

Normal distribution: Quantiles can be expressed as multiples

of the standard deviation,

21

2

2

2

1 2 ++=total

2122

21 2 VaRVaRVaRVaRVaRtotal ++


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InterCorrelation: Copula approach

1. Choose appropriate marginal distributions for each risk type, e.g.

- market risk: normal distribution, Student tdistribution- credit risk: beta distribution, Vasicek distribution

- operational risk: lognormal distribution

2. Choose a parametric copula based on a correlation matrix

Student t

copula

Gaussian

copulatail dependence

degree of freedom 1


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InterCorrelation: Total EC after portfolio effects

-14 %

aboutEUR 9 bn

Total EC+ 4 %


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What should we do?


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What should we do?

Bank internal

use of EC

Value based management

Analysis of risk taking capacity

?

Regulatory

requirements

Basel II

MaRisk


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Pillar 1 Pillar 2 Pillar 3

Minimum capital requirements Supervisory Review

Process (SRP)Enhanced Disclosure

What should we do?

Regulatory requirements

Basel II Framework

emphasizes the need for aqualitative approach to

supervising banks.

quantitative and qualitativeguidelines.

Internal Capital Adequacy

Assessment Process (ICAAP).

- internal models for OpRisk

- no internal models for

credit risk!

Wh h ld d ?


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Does the bank have enough capital to support the risks it takes?

What should we do?

Risk taking capacity

Capital cushion basically consists of

Net income forecast

price and property reserves

Hybrid capital instruments

IFRS Shareholders equity

minus Goodwill

Capital cushionTotal EC

(incl. diversification)

other risks

model risk

estimation errors

?

?Risk Appetite:

What is enough?


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What may we hope for?


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Better knowledge transfer from theory into practice


Treatment of Hard-to-measure risks



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"a little knowledge is more successful

than complete knowledge: it conceives

things as simpler thanthey are, [and is therefore] more

comprehensible and persuasive."

[Friedrich Nietzsche, Human, all too human (1878)]


Theory-practice gap

Knowledge

Theory / Academics

Practise / Industry

There is a decrease of knowledge when moving from theory to practice.



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Little knowledge: Risk control

is a cost-intensive regulatoryrequirement and diminishes

the bank's profit.


Decrease of knowledge: an example

Complete knowledge: Risk control

is not only a regulatoryrequirement, but is an important

contribution to success in banking.

0 E E'

complete knowledge

profit distribution

profit0 EE'

little knowledge

profit distribution

profit

profit without RM

profit with RM


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It would be a mistake to conclude that the only

way to succeed in banking is through

ever-greater size and diversity.

Indeed, better risk management may be the only trulynecessary element of success in banking.

Alan Greenspan,

Speach to the American Bankers Association, October 5, 2004



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Not everything that counts

can be counted...

[Albert Einstein (1879 -1955)]


Can a bank's total EC be quantified?

However:

It is better to light one candle than

to curse the darkness.

[unknown]



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Regulatory requirements

Qualitative Quantitative

anticipate

monitor

mitigate

Management by "intuition"

in order to

these risks.

"Light one candle" and try to at

least approximate these risks.

VaR

EC Model

Risk taking capacity

Basel II: "Although the Committee recognizes that other risks []

are not easily measurable, it expects industry to further developtechniques for managing all aspects of these risks."



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"Convictions are more dangerous enemies of truth than lies"[Friedrich Nietzsche]

lame duck

lively rabbit


Strategy Evaluation

Corporate strategies often focus on expectations about future

earnings, which are based on the "most likely" future scenario.

Scenario

t

earnings

(cash flows)

0 1 2 3 4 5

= +

=

1 )1(ii

i

r

E

P

Present value:
http://images.google.de/imgres?imgurl=http://www.peppitext.de/WiCoOstern2005/Hase.gif&imgrefurl=http://www.peppitext.de/WiCoOstern2005/html/hasen_einfach_so.html&h=400&w=604&sz=5&tbnid=TdnUzscY6Oi15M:&tbnh=88&tbnw=133&hl=de&start=24&prev=/images%3Fq%3Dhase%26start%3D20%26svnum%3D10%26hl%3Dde%26lr%3D%26sa%3DN


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Good Strategy or Bad Strategy?

Ludwig Wittgenstein (1889-1951)

(1953/1958).



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The natural risk measure for strategic risk is VaR!

The goal of every strategy is to generate cash flows

A good strategy meets or exceeds expectations

A bad strategy results in earnings below expectation,

thereby diminishing the market value of the company

y p

Strategic risk: A question of measure



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A simple model for strategic risk

,0,)()(0

)(

=

tsdEetP

t

ssr

Definition: The present value in continuous time is given by

is referred to as cumulated earnings at time horizon t.

and

=t

sdEtE

0

)()(

Recall the definition of present value:

= +

=

1 )1(ii

i

r

EP



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To account for the uncertainty of future earnings, we introduce an

earnings process given by

where is deterministic and is a 1-dim. Brownian motion.

.),()()( consttdWdtttdE =+= 0

)(t

tE

)(t )(tW

20 40 60 80 100t

10

15

20

25

30

35

earnings

5.01.0)(

==

t

http://images.google.de/imgres?imgurl=http://www.peppitext.de/WiCoOstern2005/Hase.gif&imgrefurl=http://www.peppitext.de/WiCoOstern2005/html/hasen_einfach_so.html&h=400&w=604&sz=5&tbnid=TdnUzscY6Oi15M:&tbnh=88&tbnw=133&hl=de&start=24&prev=/images%3Fq%3Dhase%26start%3D20%26svnum%3D10%26hl%3Dde%26lr%3D%26sa%3DN


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Let rbe a constant discount rate and the earnings process

given above. Then, the present value is given by the value

process ,

with

)()()()( 210

tItIsdEetP

t

sr +==

0)( ttP)(tP

0)( ttE

=

tsrdtestI

0

1 )()(

,)()(0

2

=t

srsdWetI



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Properties of the Ito Integral

,)1(2

])([)](var[0

22

222

22 ===

t

trsre

rdsetIEtI

it is a martingale, in particular .0)]([ 2 =tIE

the variance is given by

:)()(0

2 =

t

srsdWetI

it is normally distributed.



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Distributional properties of : )()()( 21 tItItP +=

Fort > 0, the distribution function of is a normal distribution with)(tP

)()]([0

=

t

srdsestPE

,)1(2)](var[)](var[2

2

2

tr

ertItP

==

is the standard normal distribution function and the confidence level

)()(

11

2

)2exp(1)](var[

==

r

trtPVaR

EaR


A i l d l f i i k


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For strategic VaR simplifies to

),(

EaRr

VaR2

1=

t

Limits:

0 2 4 6 8 10

0

0.5

1

1.5

2

2.5

3

For small values ofrwe obtain

( ) ),(

EaRrOtVaR += )(

0r

1.0=r

5

time

r

tr

2

)2exp(1


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Thank you very much

for your attention!

Beyond Credit Risk Economic Capital Models %e2%88%92 News and Views ...

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