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

2. 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

3. 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 99.9% confidence interval (UL) = Stand-Alone Economic 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);

4. 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)

5. Basel II – IRB Models
Graphical overview
Tail Risk

6. 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

7. 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.

8. 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.

9. 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.

10. ) ( 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).

11. 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)

12. 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.

13. 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.

14. 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.

15. 3) Measuring Concentration Risk
& underwriting new business: Example

16. 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

17. 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).

18. 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

19. 5) References
Basel Committee on Banking Supervision, 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”.

20. THE END