SBCE Concentration Risk Research André Morandi – Pricing & Risk Manager Portfolio Management Meeting Rome, October, 2006

Outline Basel II – Internal Ratings-Based Approach Models (IRB) and Pillar 2 Portfolio Concentration Risk: Why it is a problem? Tail Risk! (Portfolio Economic Capital & Tail Risk Management) Measuring Concentration Risk & Underwriting new business: Pricing & Economic Capital under a RAROC Approach Managing Concentration Risk References

Basel II – IRB Models (Pillar 1) Definitions and Risk Components Basel II F-IRB and A-IRB: Portfolio-Invariant Approaches Provisions = Expected Losses (EL) Capital Requirement = Unexpected Losses @ 99.9% confidence interval (UL) = Stand-Alone Economic Capital @ Risk (EC) PD = Probability of Default (%) LGD = Loss Given Default (%) = loss in case of default = (1- Recovery Rate) EAD : Exposure At Default ($) M : Exposure Effective Maturity (Duration);

Basel II – IRB Models (Pillar 1) Estimation of Risk Components EL = PD x LGD x EAD = Mean of the Loss distribution UL = (PD – PD2)1/2 x LGD x EAD = Standard Deviation of the Loss distribution (proxy to Basel II Capital Charge) UL (99.9%) = Stand-Alone Regulatory Capital (RC) under Basel II Premium Charge Based on Basel II Risk Components = EL + % RC %RC ($) = Opportunity Cost of RC (e.g, spread over risk free rate, etc.) Capital Required ($) = RC = Solvency Margin (Stand-Alone Risk Contributions on a Transaction Basis)

Basel II – IRB Models Graphical overview Tail Risk

1) Basel II – Pillar 2 Managing Concentration Risk: Diversification (correlations? concentration?) Concentration Limits (obligor, countries, industries) Collateralization (Asset-Backed Transactions) Risk Transfer (e.g., Reinsurance, Credit Derivatives, Swaps) Securitisations

Why it´s a problem: Tail Risk! 2) Concentration Risk: Why it´s a problem: Tail Risk! Turning now to the portfolio analysis: In the presence of exposure concentration the portfolio loss distribution must be accordingly adjusted and consequently the capital requirements (Basel II addresses concentration risk on Pillar 2, only) Both Idiosyncratic risks (Large single exposures) and Systematic risks ( groups of correlated exposures) must be taken into account when looking at the portfolio´s UL (x Stand-Alone Basel II Capital Charges). In this study we will focus on measuring and managing large single exposures.

3) Measuring Concentration Risk 3 different measures of Concentration Risk were tested : Herfindahl-Hirschman Index (HH) Theil Entropy Index Gini Index These indexes have been widely used in the literature.

3) Measuring Concentration Risk 3 dimensions of concentration were looked at: Country Sector * Buyer *It is worth noting that this sphere takes into consideration mostly global players, and even then, is hard to quantify.

) ( I / I ) (I I / = F ( I / I ) 3) Measuring Concentration Risk We calculated the (risk) contribution of each dimension, so as to form a concentration factor (F). This was done for all three indexes. = F ( I / I ) ( I / I ) (I I ) / 1 X country 1 sector X 1 importer Where I0 is the concentration index today and I1 is the index at t +1 (with new transactions).

3) Measuring Concentration Risk & underwriting new business Our transactional based (stand-alone) capital requirement is then ajusted by the concentration factor (F) to its marginal risk contribution to (portfolio) Economic Capital : CR1 = F X CR0 Once portfolio concentration is taken into account, new transaction limits for the different dimensions may be set (based on a revised solvency margin)

3) Measuring Concentration Risk & underwriting new business Out of the 3 indexes, the Gini index turned out to be the most effective. It showed the least sensitivity to the portfolio´s current diversification level. Has a very useful graphical representation.

3) Measuring Concentration Risk & underwriting new business Where the vertical axis represents the cumulative distribution function of exposure and the horizontal axis represents the cumulative percentage of the relevant subdivision (i.e sector, country, debtor). The Gini Coefficient is the area between the line of perfect equality and the observed Lorenz curve, as a percentage of the area between the line of perfect equality and the line of perfect inequality.

3) Measuring Concentration Risk & underwriting new business Where the vertical axis represents the cumulative distribution function of exposure and the horizontal axis represents the cumulative percentage of the relevant subdivision (i.e sector, country, debtor). The Gini Coefficient is the area between the line of perfect equality and the observed Lorenz curve, as a percentage of the area between the line of perfect equality and the line of perfect inequality.

3) Measuring Concentration Risk & underwriting new business: Example

3) Measuring Concentration Risk & underwriting new business The Next Step: Correlation Analysis We need now to turn our attention to groups of correlated debt exposures. The concentration index must be adjusted by possible correlations between exposures at default (scarcity of market data for buy & hold portfolios, difficult to model: joint default probability functions): I´= ρ + (1- ρ) * I Where I´ = Concentration index, adjusted by correlation ρ = Matrix of correlation coefficients on portfolio exposure I = Non-adjusted concentration index

3) Measuring Concentration Risk & underwriting new business Implications to Pricing: Risk-Adjusted Return on (Economic) Capital (RAROC): ECA’s Hurdle Rate? Implications to Portfolio Economic Capital (Solvency Requirements): Tail-Risk Management through judgemental concentration limits (obligor, sector, country).

4) Managing Concentration Risk Diversification (correlations? concentration?) Concentration Limits (obligor, countries, industries) Collateralization (Asset-Backed Transactions) Risk Transfer (e.g., Reinsurance, Credit Derivatives, Swaps) Securitisations

5) References Basel Committee on Banking Supervision, 2005. An explanatory note on the Basel II IRB Risk Weight Functions. Diez-Canedo, J. (2002), A simplified credit risk model for emerging markets, that measures concentration risk and explicitly relates credit risk to capital adequacy and single obligor limits. Working paper. Fitch Ratings, Structured Finance. Quantitative Financial Research Special Report (2005). A Comparative Empirical Study of Asset Correlations. Gordy, M. (2002), A Risk-Factor Model Foundation for Ratings-Based Bank Capital Rules. Working paper. Heitfield, E. (2005), The effects of name and sector concentration on the distribution of losses for portfolios of large wholesale credit exposure. Working Paper Tasche, D. (2005), Risk Contributions in an asymptotic multi-factor framework, Workshop “Concentration risk in credit portfolios”.

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