risk analysis and management - theoretical approaches and applied

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RISK ANALYSIS ANDMANAGEMENT -

THEORETICAL APPROACHESAND APPLIED CHALLENGES

Krzysztof Jajuga

Department of Financial Investments andInsurance

Wroc aw University of Economics



1. Some historical remarks

2. Risk analysis and management - state-of-art

3. Theoretical advances - innovations

4. Applied challenges

Plan



Methods based on the concept of RISK

- Two old seminal contributions:

Bernoulli (1738), Bachelier (1900)

- Classical contributions - milestones and others:

Markowitz (1952), Roy (1952) - portfolio theory

Black, Scholes (1973), Merton (1973) - derivatives

Modigliani, Miller (1958, 1963) - arbitrage concept

Historical remarks



Most significant changes in last decade

- growth of risk transfer market

- integration of segments of financial market

- integration of banking, insurance and (pure) financial markets

Markets - today



MOST SIGNIFICANT CHANGE IN LAST DECADE

INNOV AT ION S !!!!

Markets - today



Innovations

- theory - increasing sophistication and precision

- practice - increasing technology dependence and wide range

- theory is easily verified in the financial market

- practice stimulates theoretical advances

Markets - today



Merton (1995): Mathematical models of modern finance contain some of

the most beautiful applications of probability and optimization theory.But of course, all that is beautiful in science need not also be practical;

and surely not all that is practical in science is beautiful. Here we have

both. With all their seemingly abstruse mathematical complexity, the

models of finance theory have nevertheless had a direct and significant

influence on finance practice.

Markets - today



Types of risk

1. Classical

market risk, credit risk, operational risk

2. N ew - strictly financial

systemic risk, E-risk

3. N ew - coming from other areas

energy risk, insurance risk, weather risk, catastrophe risk, bandwith risk

Risk analysis and management - state -of - art



Risk measurement - Market risk

V olatility measures

standard deviation and other distributional types of measures

Sensitivity measures

duration, ³greeks´, beta




Risk measurement - Market risk - Downside risk

V alue at Risk - popularity - deserved or undeserved?

Incremental V aR - amount of risk that position is adding to the portfolio

Marginal V aR - sensitivity of V aR to the changes in the portfolio holdings




Risk measurement - Market risk

V alue at Risk - what is wrong?

- we do not really know how to estimate

- does not provide the information of the size of losses (if V aR is

exceeded)

- is not subadditive: risk of portfolio could be higher than sum of

individual risks




Risk measurement - Market risk- Downside risk

O ther downside risk measures:

Lower Partial Moment

Xloss (version of Expected Shortfall) - short horizon, abnormal market

Chance of Losing Money (version of aspiration level) - long horizon,

normal market

Worst Case Performance - long horizon, abnormal market




Risk measurement - Credit risk

Credit risk models should reflect:

- spread risk

- downgrade risk

- default risk

- recovery rate risk

- concentration risk




Risk measurement - Credit risk

Credit risk models:

- Credit migration approach (CreditMetrics, Credit V aR)

- O ption pricing approach (KM V )

- Actuarial approach (Credit Risk+)

- Reduced form approach




Risk management methods

- Insurance (classical)

- ALM - Asset and Liability Methods

- ³Home made´ protection - collateral, guarantees, etc.

- Hedging - derivatives




Regulations

Basle Committee for Banking Supervision

Basle Accords - moving to internal models




Financial sector standards -examples

G roup of Thirty - Derivatives, Practices and Principles (1993)

Coopers and Lybrand - G enerally Accepted Risk Principles (1996)

G roup of Twelve: Counterparty Risk Managament Policy G roup -

Improving Counterparty Risk Management Practices (1999)

Algorithmics - Mark to Future (2000)




Financial sector standards - RiskMetrics type approaches (initially

started by JPMorgan)

O ctober 1994 - first edition of RiskMetrics

December 1996 - RiskMetrics Classic (market risk)

April 1997 - CreditMetrics (credit risk)

April 1999 - CorporateMetrics (enterprise market risk)

April 1999 - LongRun (forecasting and scenario generation methods)




Some common features of modern approaches

Cross-fertilization of methods in different areas

- finance and insurance

- econophysics

- behavioral finance





Application of financial market type methods in corporate finance

- enterprise-wide risk: Cash Flows at Risk, Earnings at Risk, Earnings Per

Share at Risk

- valuation:Real O ptions V aluation





Integrated risk management - tailoring risk management solutions to the

needs of particular institution taking into account correlation of

different types of risk

Alternative Risk Transfer - designed by (re)insurance sector, for example

captives





Risk Adjusted Performance Measurement (RAPM) - risk adjusted return

measures:

- RAR O

C type approaches (e.g. RAR O

RAC)

- Return on V aR (Ro V aR)





Risk Budgeting - allocating an allowable measure of potential loss to

different aspects of the investment process, monitoring whether those

pieces of investment have exceeded their measure, taking corrective

action when a measure is exceeded and using risk measurement

process to evaluate risk adjusted return




Theory - main drawbacks of classical approaches

- Unrealistic assumption of normal distribution and geometric Brownian

motion

- In many cases not justifiable assumption of complete market

- Unrealistic assumption of stability of models derived using past data or Monte Carlo simulations

Theoretical innovations



Theory - main drawbacks of classical approaches

- Markets are incomplete

- High liquidity not present in unstable periods




Some warnings

Finance is not physics

N icely packed and promoted products may contain rubbish!

People always try to make money on overvalued products before the

others discover overvaluation

Model risk - TBD




More plausible distributions

- stable distributions

- hyperbolic distributions

- mixtures of distributions




More plausible processes of financial prices

- mean-reverting process

- jump-diffusion process (combination of Wiener and Poisson) stable

distributions

- gamma process




Theoretical advances -some other models

- non-linear models (full revaluation instead of linear sensitivities)

- scenario analysis

- stress testing (type of scenario analysis)




Theoretical advances -emphasis on extremes

- tail estimation (Hill, Pickands, etc.)

- Extreme V alue Theory

a) looking for distribution of maximal loss (Frechet?)

b) looking for distribution of excess loss ( G eneralized Pareto?)




Integration of different types of risk

Different types of risk (e.g. market, credit) not perfectly correlated,

therefore advantages from ³diversification´

Not so much work except for integration of market and credit risk

Applied challenges



Normal versus extreme risk

Too small capital allocated exposes institution to excessive levels of risk

Too large capital allocated raises costs and reduces profitability

This problem arises also for clearing institutions

Applied challenges




Remedy - calculate two measures of risk:

normal risk measure, extreme risk measure

then switch between two regimes

Problem: detect switching time

Applied challenges




Possible measures:

V alue at Risk - normal risk, Expected Shortfall - extreme risk

Applied challenges



Model risk

Financial model risk arises from the fact that the effect of the application

of particular model to the activity on the financial market (valuation,

hedging etc.) may be different from the expected effect

Sometimes considered as operational risk

Applied challenges



Model risk

- inapplicability of modeling

- incorrect model

- incorrect solution

- inappropriate use

- errors in model processing

Applied challenges



Model risk

Estimation risk

Risk measures are estimated therefore estimation error should be given

V aR = 10 mln USD may really mean:

With the probability of 0.95

the interval [8.5 mln USD; 11.5 mln USD] contains V aR

Applied challenges



Merton (1997): At times we can lose sight of the ultimate purpose of the

models when their mathematics become too interesting. The

mathematics of financial models can be applied precisely, but the

models are not all precise in their application to the complex real

world. Their accuracy as a useful approximation to that world varies

significantly across time and place. The models should be applied in

practice only tentatively,with careful assessment of their limitations in

each application.

Applied challenges



Estimation of volatility

V olatility - measure of individual risk

How to estimate?

Historical - drawback: long time series needed, no prevailing model

Implied - drawback: model dependent, market dependent

Estimation risk - measured by vega

Applied challenges



Estimation of correlation

Correlation - ³heart´ of risk management

Linear correlation may give misleading conclusions

Linear correlation suitable for elliptical distributions

Linear correlation shows weak tail dependence

Applied challenges



Measuring dependence with copulas

More general measure of dependence

Can extract from multivariate structure:

- univariate ³marginal structure (individual risks)

- dependence structure

Applied challenges



Practical implementation problems

- intellectual risk (education badly needed)

- data (past, simulated?)

Applied challenges



Practical implementation problems - Accounting issues

Working G roup for IAS: Draft Standard:

- more fair value accounting (if market prices are unobservable, use

theoretical valuation model)

- remove hedge accounting

Applied challenges



Other issues - Risk of risk management

Risk management may require risky tools (as derivatives)

G ains from the use of risk management tools should be larger than risks of

implementing these tools

Applied challenges



Fundamental question to be answered:

How much risk is too much?

Conclusion



THANK YOU VERY MUCH

THIS IS IT

risk analysis and management - theoretical approaches and applied

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