Asmah Mohd Jaapar

 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

 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%

Market VAR OpVAR Credit VAR Returns of the portfolio products Losses of the credit portfolio Returns and losses of the operational risk Integrated VAR 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: DATA INTEGRATED RISKS INDICATOR RETURNS

 Variables: exposure values distribution of losses  To evaluate: DATA INTEGRATED LOSSES

 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 simulation  Based on integrated indicators: Past historical information Integrated losses record  Parametric: Monte Carlo simulation  Uses a random sets for different holding periods  The 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 price and the risk factors is linear The time value of the contracts may be neglected ASSUMPTIONS FOR PARAMETRIC VAR APPROACH

 Data integrated risks indicators return  Follow the distribution of the integrated returns  Data integrated losses  Follow the distribution of integrated losses within the probabilities and impact axes  Important features to define: 1) The strength of the shocked values 2) The bandwidth (value zones) DISTRIBUTION OF RANDOM VALUES

 Integrated VAR can be estimated by shocking the decomposed matrix A T with vectors of historical or random values  The decomposed matrix A T is based on  The corr.matrix C R as defined by matrix of return KR referring to integrated risks  IKRIs The time framework of the returns is defined by KR  The corr.matrix L R as defined by matrix of the loss returns RP The holding period is harmonised by the conversion factor CF RP mr = P 1 mr I 1 mr E 1 mr P 2 mr I 2 mr E 2 mr _ _ _ _ P n mr I n mr E n mr RP cr = P 1 cr I 1 cr E 1 cr P 2 cr I 2 cr E 2 cr _ _ _ _ _ _ _ P n cr I n cr E n cr RP or = P 1 or I 1 or E 1 or P 2 or I 2 or E 2 or _ _ _ _ P n or I n or E n 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 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

 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.

 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.