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.