Quantitative methods

in risk management

Introduction part 1

Pavol Jura

palo.jurca@gmail.com

Miestnos: M266 (konzultan hodiny len po dohode)

Web: http://www.iam.fmph.uniba.sk/institute/jurca

Pracovisko: Nrodn banka Slovenska

Odbor regulcie a finannch analz

Macroprudential analysis section

(analytik rizk)

Externe: KAM

Main topics

Motivation and objective of this course

Light intro to risk management

Process of risk identification, management and measurement

Problems in risk management

Problematic / controversial assumptions

Impact of the ongoing crisis on risk management

Motivation

Risk management departments frequent career start after

graduating from EFM

2010/2011 and 2011/2012: around one third out of 50 offers in the field of

risk management

Link between theoretical knowledge and practice

Each year 1-3 defended diploma theses in the are of risk management

application (2008 8 theses!)

Exploiting of the main benefits of: focus on quantitative methods

Opportunities for further development of methods many things have

been affected by the crisis

Complex mathematical formulas appearing directly in the laws!

Mathematics in laws

Decree no. 4/2007 on the bank's capital requirements and the

capital [], 43, para. 2, letter a):

Mathematics in laws Decree no. 4/2007 on the bank's capital requirements and the

capital [], 147, para. 1:

... even in street names!

Course objectives

Overview of quantitative methods that are used or could be used in

risk management

More focus on broad overview than technical details

Strong emphasis on practical applicability: the application of

methods (examples in Excel, Eviews, Matlab, brief description of

specific problems addressed in NBS)

Use your existing knowledge of mathematics and statistics to

understand the basic assumptions, strengths and weaknesses of

each method

Possibilities for further research (a diploma thesis, PhD?)

However, the objective is not to learn risk management as a whole

(we will skip qualitative requirements, the organization's internal

processes, data processing, legislation, personal skills of a risk

manager ...)

Grading principles / examination

The course evaluation is based on a PROJECT (70 %) practical

part:

Will be specified in the next few weeks

Risk analysis of a simple portfolio, comparison of several methods

Possible work in pairs

Deadline: beginning of december

Written TEST (30 %) theoretical part:

The main focus on a comprehensive overview and understanding of the

lectures

Date: half of december

Strict policy of honour code adherence!

Grading principles / examination

Grading scale

A: At least 90

B: At least 80, but less than 90

C: At least 70, but less than 80

D: At least 60, but less than 70

E: At least 50, but less than 60

FX: Less than 50

Course sylabus

The "classic" risk measure - Value at Risk

Methods for generating stress scenarios in case of multidimensional data

principal components analysis

models based on a mixture of several normal distributions

Methods for modeling of a dependence structure - copulas

Credit risk measurement (different approaches)

Credit derivatives and their valuation

Dealing with extreme events - extreme value theory

Appendix: The models used in the management of operational risk and in

(non-life) insurance

Main literature

Your feedback

Your (early) feedback is crucial in order to organize the course in

such a way that you can benefit from it as much as possible

Hence, any feedback would be

very appreciated at any time!

Process of risk management

Identification of risks

Where and what type of risk?

What are the risk factors?

Each individual transaction includes several types of risks!

Risk Measurement

The system allows the measurement (data collection, internal processes ...)

Appropriate quantitative techniques - intensity proportional materiality

Risk Management

Determination of the strategy, what I want to embrace risk (risk appetite)

Limits chosen level of risk for the operation

Stress testing

Back-testing

Mitigation (risk mitigation, hedging)

What is a (financial) risk?

Financial risk = a potential future financial loss related to a given financial

isntrument or to a given portfolio of financial instruments

The definition is not harmonized!

Unexpected profits?

Expected loss? [initial loan loss provisions to a new loan]

Losses already incurred, but still not calculated / reported? [increase in

unemployment]

Opportunity costs?

[I have a mortgage with a five-year fixation of rate, but the interest rate start to decline]

What is the appropriate loss benchmark?

[the bank incurred losses due to a jump in unemployment rate, although lower than expected]

Two basic (and relatively independent) parts of risk:

Probability of an event

Size of the potential impact

What is a (financial) risk?

General principle:

A risk is related to uncertainty

Combination of techniques from financial mathematics, probability theory,

statistics, time series analysis, actuarial mathematics and stochastic

processes theory

The term stochastic comes from Greek:

Stochazesthai = to aim, to guess

Stochastikos = good at aiming ( = aim)

Basic principles of bank regulation

In principle, banks can take any size of risk, but it has to be sufficiently

covered by their own funds (i.e. capital)

Capital adequacy ratio:

(however, the European banking authority currently expects at least 9%)

Examples:

Traditional corporate loan: 8% covered by own funds (risk weight: 100%)

Equity investment: 12 % covered by own funds

Mortgage loan: 4 % covered by own funds (risk weight 50%)

Interbank claim: 1.6 % covered by own funds (risk weight 20%)

Slovak government bond: 0 % covered by own funds (risk weight 0%)

%8assets weighted-risk

fundsown

Risk weights (generally) depends on the debtors credit quality

Approaches

Standardized approach

Using of a banks proprietary model (internal rating based approach)

Demanding qualitative criteria (mainly for internal processes, data quality

etc.)

Upon prior approval by the competent regulatory authority (NBS)

Theoretically, lower capital requirement (conditional on specific cases)

Regulatory requirements do not replace a well-established risk

management

A bank is obliged to cover ALL significant risks (including such as

strategic risk, legal risk, reputational risk

So-called internal (economic) capital concept

Basic principles of bank regulation

Annual report 2010, VB

Basic principles of bank regulation

Legislative implementation:

BAZILEJ II (New Basel Capital Accord)

Non-binding international agreement for large internationally active banks

Basel committee for banking supervision, 2004, Bank for International Settlement

link: http://www.bis.org/publ/bcbsca.htm

Capital requirement directive (2006/48/EC a 2006/49/EC) implemented Basel II in EU law

SR:

Law on banks (No 483/2001 as amended...)

NBS Decree No. 4/2007 on the bank's capital requirements and the capital []

Basic principles of bank regulation

http://www.bis.org/publ/bcbsca.htm

Basel II scheme

Types of risks

Main risks:

Credit risk

Market risks

Counterparty risk

Operational risk

Liquidity risk

Additional risks

Strategic risk

Legal risk

Reputational risk

Model risk

Systemic risk

Credit risk

Credit risk = a risk that a borrower fails to deliver payments which he

or she is obliged to pay in case of different type of claims (bonds,

loans, settlement of financial derivatives ...) because he or she is

unable or unwilling to do so

In addition this "traditional" concept, credit risk also includes, e.g.:

Settlement risk

Risk from guarantees granted

The risk related to unused overdraft facility (eg credit cards)

The risk of a bond impairment due to a reduction in the credit rating of

the issuer

Example of settlement risk: Dexia Banka Slovensko,a.s., 2008 (loss

amount: 82 mil. EUR)

Source: http://firmy.etrend.sk/firmy-a-trhy-financny-sektor/slovenska-

dexia-prisla-o-miliardy-korun.html

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Market risks Market risk = a risk of an adverse impact of movements in market factors

(equity prices, interest rates, FX rates, commodity prices) on the value of

financial instruments

Market risk types

Interest rate risk

Equity risk

FX risk, currency risk (crisis => re-denomination risk)

Commodity risk

Credit spread risk

Different types of impacts:

General risk (overall market) vs. specific risk (only the relevant counterparty)

Changing values, prices, volatilities, ...

Further impacts: Change in the shape of yield curve, change in dividend

policy

Interest rate risk Various type of interest rates - EURIBOR, EUR-LIBOR, FRAs, swaps,

bonds, loans, deposits

Construction of the yield curve by combining different financial instruments

Technical issues

Different day convention

Liquidity of different instruments

Many risk factors: inflation, banks credibility, sovereign risk, expectations

about the development of the economy, monetary policy, banks interest

rate policy

Two views on interest rate risk:

Bond revaluation risk

Risk of changes in interest income

Example: A five-year bond with a variable coupon, parallel upward shift of

the yield curve:

In the beginning: the reduction in the fair value

Later: gradual increase of the real value to the nominal (after 1 year), then the

increase in interest income related to coupon payments

Operational risk Operational risk includes:

Improper or faulty internal processes in the bank

Human error

Failure of the banks internal system

External or internal fraud

External events (eg natural disasters)

Closely associated with the functioning of internal processes (focus on qualitative side)

Difficult to measure

it is present everywhere, but the identification of proper loss amounts is tricky

extreme events, potentially very high impact

Example: Calculate the extent to which the bank is exposed to losses caused by earthquake damage or internal fraud

e.g. loss of 4.9 billion. at Socit Gnrale (Jrme Kerviel, 2008)

Liquidity risk

Liquidity risk = potential loss due to the fact that the bank is unable

to meet its obligations on the contractual basis due to a lack of liquid

funds

Key aspects:

Short-term liquidity risk

Bank for insufficient funds to pay obligations when they are due no liquid

assets that could be sold without much loss

Market liquidity risk

Example: A bank needs to sell its securities to obtain sources of liquidity (fire

sales), but the stock market is not liquid enough (only a small volume might

be sold at the quoted price, then the price drops)

The problem in turbulent market (widening bid-ask spread)

Funding liquidity risk

Example: The bank is financed by short-term interbank deposits constantly

renewed. At the time of distrust between banks, it might be significantly

more expensive to continue with these funds