Asmah Mohd Jaapar

0900002

Outline of the Presentation Introduction Integrating Market, Credit and Operational Risk Approximation for Integrated VAR Integrated VAR Analysis: Data Types

Data Integrated Risks Indicator Returns Data Integrated Losses

Integrated VAR Analysis: Example of Parameters Integrated VAR Analysis: Approaches Assumptions for Parametric VAR Approach Distribution of Random Values Defining the Shocking Values Defining the Historical and Random Values Monte-Carlo Simulation Concluding Remarks

In the past, risks were considered separately from each other and hedged one at a time.

VAR for market risk is treated as distinct from credit risk and operational risk.

All sources of risk are integrated to a certain extent and VAR models should include correlations among market, credit and operational risk.

Integrated VAR is a transformation of VAR methods from measuring individual risks toward tool for strategic decisions at the highest level of institution.

INTRODUCTION

INTEGRATING MARKET, CREDIT AND OPERATIONAL

RISK

Market Credit Operational TotalVolatility 0.58% 0.19% 0.04% 0.11%Skewness 0.2 -1.3 -4.5 -1.1Kurtosis 3.7 16.1 35.3 9.699.9% quantile -1.81% -1.20% -0.37% -0.43%99.9% VAR -0.06% -0.35% -0.25% -0.43%

Adding up VAR for each risk CONSERVATIVE! Overestimates the true VAR by 52%

Assuming normal distribution WRONG assumption! Underestimate by 46%

Hybrid combination of VAR for each risk source with correlations

Get close to the true VAR Slight overestimate by 13%

APPROXIMATION FOR INTEGRATED VAR

2122

21 2 VARVARVARVARVARH

MarketVAR

OpVARCreditVAR

Returns of theportfolio products

Losses of the credit portfolio

Returns and lossesof the operational risk

IntegratedVAR

Returns of integrated risk indicators(IKRIs) and integrated losses

INTEGRATED VAR ANALYSIS:DATA TYPES

Variables: returns of the integrated risk indicators or portfolio

performances

where t refers to time series, a, b, c are weighted factors and Pmr, Pcr, Por are the parameters referring to market, credit and operational risk accordingly

Note: IKRI must have parameters from at least two different types of risks.

significance level To evaluate:

FactorsRisk

P e,Performanc Portfolio Integrated

orcrmrt cPPbPafIKRI ,.,.

DATA INTEGRATED RISKS INDICATOR RETURNS

Variables: exposure values distribution of losses

To evaluate:

ExposuresRisk

VAR

DATA INTEGRATED LOSSES

INTEGRATED VAR ANALYSIS:EXAMPLE OF PARAMETERS Portfolio Structure

A/L maturity mismatches that create interest rate risk A/L currency mismatches that create foreign exchange

risk Credit quality of governments, companies, and

individuals to which the institution has loaned money and that affect the risk of adverse rating changes and default

The level of geographic and economic sector concentration (diversification) on the asset portfolio that affects portfolio credit risk

The level of seniority and security for the loans in the portfolio that substantially affects the recovery rates on loans that may default

Off-balance-sheet transactions that either reduce (i.e., hedge) or increase institution’s risk level

Source: Barnhill, Papapanagiotou, and Schumacher (2000), IMF Working Paper

Non-Parametric: Historical simulationBased on integrated indicators:

Past historical information Integrated losses record

Parametric: Monte Carlo simulationUses a random sets for different holding

periodsThe random sets are used to shock both

integrated risks indicator returns and integrated losses

INTEGRATED VAR ANALYSIS:APPROACHES

The risk factors are approximately ~lognormal

The relationship between the portfolio priceand the risk factors is linear

The time value of the contracts may be neglected

ASSUMPTIONS FOR PARAMETRIC

VAR APPROACH

Data integrated risks indicators returnFollow the distribution of the integrated

returns

Data integrated lossesFollow the distribution of integrated losses

within the probabilities and impact axes

Important features to define:1) The strength of the shocked values2) The bandwidth (value zones)

DISTRIBUTION OF RANDOM VALUES

Integrated VAR can be estimated by shocking the decomposed matrix AT with vectors of historical or random values

The decomposed matrix AT is based on The corr.matrix CR as defined by matrix of return

KR referring to integrated risksIKRIs The time framework of the returns is defined by KR

The corr.matrix LR as defined by matrix of the loss returns RP

The holding period is harmonised by the conversion factor CF

RPmr

=

P1mr I1

mr E1mr

P2mr I2

mr E2mr

_ _ _ _ _ _ _ _Pn

mr Inmr En

mr

RPcr=P1

cr I1cr E1

cr P2

cr I2cr E2

cr

_ _ _ _ _ _ _ Pn

cr Incr En

cr

RPor=P1

or I1or E1

or P2

or I2or E2

or

_ _ _ _ _ _ _ _ Pn

or Inor En

or

, ,

DEFINING THE SHOCKING VALUES

Historical or random values can be used to shock the integrated risks returns/losses.

These values can be obtained from fixed or variable distribution bandwidth and volume

The variation is derived from: Significant value of the risk parameters

referring to the integrated risks indicators returns

Exposure degree for integrated losses data

DEFINING THE HISTORICAL AND RANDOM VALUES

New set of the historical/random numbers-normalised into the scale of random values

:The new set of the initial historical or random values:A constant value smaller than one:Degree of significance value for integrated risks return:The exposure value of the integrated losses

2)exp( cornew

SV

2)exp( vnew

h

new

2corSV2vh

DEFINING THE HISTORICAL AND RANDOM VALUES (cont.)

Monte-Carlo algorithm can be applied to estimate the integrated VAR from the set of shocking values and historical/random values as defined earlier.[Refer to “Integrating Market, Credit and Operational Risk: A complete guide for bankers and risk professionals” book pg 24, 148]

Monte-Carlo dynamic simulation method to estimate integrated VAR is notoriously difficult to applied BUT recommended to be implemented in the financial industry.

Gives more realistic results on potential values for the unexpected integrated risks or losses that may occur.

MONTE-CARLO SIMULATION

CONCLUDING REMARKS The regulatory capital under Basel II

which is essentially additive is fundamentally at odds with VAR, which is subadditive measure.

Thus, rather than separate market risk, credit risk, and operational risk elements for capital requirements, an integrated VAR approach would measure overall risk incorporating all sources of volatility.

References Kalyvas, L, Akkizidis, I, Zourka, I and Bouchereau, V.

(2006) Integrating Market, Credit and Operational Risk: A complete guide for bankers and risk professionals. Laurie Donaldson.

Philippe Jorion (2007) Value at Risk: The new benchmark for managing financial risk. McGrawHill.

Barnhill, Papapanagiotou, and Schumacher (2000) Measuring Integrated Market and Credit Risks in Bank Portfolios: An Application to a Set of Hypothetical Banks Operating in South Africa. IMF Working Paper

Thank you.