1. 1 Applied Business Statistics Case studies Basel II - Introduction Mauro Bufano Risk Management – Banca Mediolanum Spa

2. 2 Basel II – motivations  In a market economy, every company is free to determine its own capital, basing on shareholders’ preferences  This is not true for banks! Financial institutions have minimum capital requirements imposed by regulators. Why? a) Centrality of banks in the overall economy b) Contagion effect: a bank’s default can affect the entire economic system (see Lehman Brothers 2008) c) In banks’ liabilities we have families’ savings (in many cases, with a State guarantee within a limit) d) How much does it cost to save banks from default?

3. 3 Basel I agreement-1988  The first international agreement on banks’ capital was made in 1988 by the “Basel committee” it’s an international institution established in 1974 by the G10 countries. It reports directly to the Central Banks of G10  The main reasons of this agreement were: To prevent banks’ crisis, avoiding excessive risk taking To prevent banks’ crisis, avoiding excessive risk taking To harmonize different capital requirements in developed countries, that could have caused distortions in the market To harmonize different capital requirements in developed countries, that could have caused distortions in the market To ensure financial stability of the banks, impacting directly on consolidated balance sheet To ensure financial stability of the banks, impacting directly on consolidated balance sheet

4. 4 Basel I agreement-1988  The first agreement regulated only capital requirements on credit risk, by applying the rule of “8%”  The regulatory capital had to be at least 8% of the risk weighted assets  Regulatory capital constituted by: Tier I capital: share capital, disclosed reserves, general provisions, innovative capital instruments Tier I capital: share capital, disclosed reserves, general provisions, innovative capital instruments Tier II capital: undisclosed and revaluation reserves, hybrid capital instruments and subordinated debt Tier II capital: undisclosed and revaluation reserves, hybrid capital instruments and subordinated debt Tier III capital (from 1996): short term subordinated debt covers only market risk, was not present in the first agreement Tier III capital (from 1996): short term subordinated debt covers only market risk, was not present in the first agreement

5. 5  The 1988 agreement had some “weights” in order to determine “risk weighted assets” a)w i =0% for cash and exposure vs central governments, central banks and EU b)w i =20% for exposures vs banks and public sector c)w i =50% for mortgage loans d)w i =100% for private sector exposures, equities, subordinated loans, hybrid instruments  Problems: There was few or no differentiation of exposures at allThere was few or no differentiation of exposures at all It encouraged “regulatory arbitrages”It encouraged “regulatory arbitrages” It didn’t take into account many other risks present in banks’ business (market risk, operational risk and so on)It didn’t take into account many other risks present in banks’ business (market risk, operational risk and so on) Basel I agreement-1988

6. 6 Basel II agreement - 2004  Basel II agreements in 2004 is a more complex one than its “parent” in 1988  It’s based on 3 pillars: 1.Pillar I: Minimum capital requirements 2.Pillar II: Internal Capital Adequacy Assessment Process (ICAAP) + Supervisory Review Process (SREP) 3.Pillar III: Market discipline  Its aims are: New rules for capital requirements (+ differentiations, + risk factors) New rules for capital requirements (+ differentiations, + risk factors) Supervision of banks by regulators (e.g. Bank of Italy) Supervision of banks by regulators (e.g. Bank of Italy) + information to the market on the capital adequacy (and risk bearing) of a bank + information to the market on the capital adequacy (and risk bearing) of a bank Possibility to use (after validation by the regulator) internal capital models Possibility to use (after validation by the regulator) internal capital models From “single exposure” approach“portfolio” approach From “single exposure” approach“portfolio” approach towards

7. 7 Basel II – Pillar I  The first pillar of Basel II is also the most important, because it states minimum mandatory capital requirements for banks  In Pillar I three types of risks are considered Credit risk Credit risk Market risk Market risk Operational risk Operational risk  Minimum capital requirements can either be determined by: Standardized risk weights Standardized risk weights Internal models they have to be validated by the regulator: they need an internal complex process and IT sources Internal models they have to be validated by the regulator: they need an internal complex process and IT sources For this reason only major banks can use internal models for capital requirements’ purposes. Smaller banks can use for Pillar I the standardized approach

8. 8 Pillar I – Credit risk  Even in the standardized approach, credit risk estimation has advanced a lot from 1988 agreement  Risk weights are no more based only on the nature of exposure, but also on the credit worthiness, stated by the agency ratings (Moody’s, S&P, Fitch etc.)

9. 9 Pillar I – Credit risk  Internal models: a bank can estimate its internal capital via internal model (Internal Rating Based – IRB). In this case for each exposure it’s necessary to estimate. Probability of default (PD) Probability of default (PD) Loss given default (LGD) Loss given default (LGD) Exposure at default (EAD) Exposure at default (EAD) Maturity (M) Maturity (M)  In order to ensure that not only biggest banks adopt internal models, there are two approaches: Foundation: only the PD is estimated by the bank. LGD, EAD and M are given by the regulator Foundation: only the PD is estimated by the bank. LGD, EAD and M are given by the regulator Advanced: the bank estimate all of the 4 parameters given above Advanced: the bank estimate all of the 4 parameters given above

10. 10 Pillar I – Credit risk  Once the “single exposure” parameters are estimated, we can determine expected losses and unexpected losses. Expected losses: EL = EAD*PD*LGD Expected losses have to be budgeted in the profit and loss account Expected losses: EL = EAD*PD*LGD Expected losses have to be budgeted in the profit and loss account Unexpected losses: these losses represent a “tail event” in the loss distribution. Given a confidence level of 99.9 % (as stated by Basel II for Credit risk), we have that minimum capital requirement (for exposure i) is Unexpected losses: these losses represent a “tail event” in the loss distribution. Given a confidence level of 99.9 % (as stated by Basel II for Credit risk), we have that minimum capital requirement (for exposure i) is

11. 11  The IRB formula represent the unexpected loss (i.e. the 99.9% loss quantile), calculated under the Vasicek- Gordy model (2000)  Its assumptions are: An infinitely granular portfolio An infinitely granular portfolio One common risk factor One common risk factor Normal distribution of the unique risk factor Normal distribution of the unique risk factor The correlation with the risk factor is modelled via a Gaussian copula function The correlation with the risk factor is modelled via a Gaussian copula function The correlation factor ρ is not estimated by the bank, but given by the regulator (it’s generally a decreasing function of the PD) The correlation factor ρ is not estimated by the bank, but given by the regulator (it’s generally a decreasing function of the PD) Pillar I – Credit risk

12. 12 Pillar I - Market risk  Also for market risk we have a standardized and an advanced approach Standardized approach: it consists in weights and haircuts based on: Standardized approach: it consists in weights and haircuts based on: The maturity of the security The maturity of the security Its duration Its duration The credit worthiness of the issuer The credit worthiness of the issuer Compensation for netting long/short positions Compensation for netting long/short positions Internal model: it’s based on the concept of Value at Risk (VaR) Internal model: it’s based on the concept of Value at Risk (VaR)

13. 13 The VaR must have the following characteristics: A confidence level of (at least) 99% A confidence level of (at least) 99% A time horizon of (at least) 10 working days A time horizon of (at least) 10 working days Historical sample for volatility at least 1 year Historical sample for volatility at least 1 year Update of volatility and correlation at least quarterly Update of volatility and correlation at least quarterly Total VaR obtained by summing VaR of different risk factors (correlations equal to 1 among risk factors) Total VaR obtained by summing VaR of different risk factors (correlations equal to 1 among risk factors) Reflect non-linear risk profile of option contracts Reflect non-linear risk profile of option contracts Calculated on a daily basis Calculated on a daily basis The factor F is a number between 3 and 4, it reflects the quality of internal model Default risk must be calculated with the model adopted for credit risk (IRB) Pillar I - Market risk

14. 14 Pillar II Pillar II consists in two different aspects ICAAP: it’s a process internal in the bank itself. Its aim is to determine the capital adequacy for unexpected losses ICAAP: it’s a process internal in the bank itself. Its aim is to determine the capital adequacy for unexpected losses SREP: it’s a review of the risk measurement process carried out by the individual banks, requiring, if necessary, a further capital buffer in addition to the one of ICAAP SREP: it’s a review of the risk measurement process carried out by the individual banks, requiring, if necessary, a further capital buffer in addition to the one of ICAAP The final goal of Pillar II is to determine an internal capital to tackle different risks. There is no regulatory requirement, but the banks are free to choose the models to adopt in order to correctly estimate risks The capital amount necessary to cover all risks is named economic capital

15. 15 Pillar II Pillar II requires the quantification of several risks not embedded in Pillar I or too much simplified. Among these: a) Concentration risk: it’s part of the credit risk. It derives from the fact that loan portfolios are not perfectly granular but some exposures are particularly heavy (therefore their defaults could result in a huge loss for the bank): The IRB formula needs to be augmented of a buffer (Granularity adjustment, GA), calculated with the Herfindahl Index (H)

16. 16 b) Interest rate risk on banking book: it’s the risk of a mismatch between asset and liabilities in a bank. Like concentration risk, it has a capital requirement Among other risks, not having a capital requirement, we find: c) Liquidity risk d) Residual risk e) Reputation risk f) Compliance risk Pillar II

17. 17 Pillar II – stress tests  A fundamental requirement of Pillar II is the stress testing of all Basel II risks (included Pillar I risks): it consists in conditioning the risk factors to particularly bad events (stress test scenarios) and working out the capital adequacy that the bank would need in those scenarios  Also for stress tests, the final goal is to determine a stressed economic capital and take actions (when needed) in order to manage those risks

18. 18 Example of stress tests Market risk: an example of a stress test could consists in a parallel shift of the yield curve of ± 200 bps For every shift, we must calculate the theoretical value of the portfolio and the eventual loss associated to each scenario

19. 19  Credit risk: considering the time series of default of Italian families (last 20 years), we could take as an extreme event the worst rate registered (source, Bank of Italy)  Conditioned on the highest default rate, we could work out the additional capital requirement basing on the IRB formula Example of stress tests

20. 20 Pillar III - market discipline  The third pillar of Basel II consists in the “transparency” of banks’ risks and its reporting to the market (included customers). Information provided include: Size and composition of capital and risky assets Size and composition of capital and risky assets Distribution of credit exposure and default rates Distribution of credit exposure and default rates Risk measurement and control systems Risk measurement and control systems Accounting practices in use Accounting practices in use Capital allocation criteria within the banks Capital allocation criteria within the banks

21. 21 Advantages and limitations of Basel II  Advantages: More flexibility of capital ratios More flexibility of capital ratios Takes into account portfolio diversification Takes into account portfolio diversification Extends the rules of the supervisors and of the market Extends the rules of the supervisors and of the market + space for risk management techniques + space for risk management techniques Internal models as source of competitive advantage Internal models as source of competitive advantage  Limitations: Procyclicality: the regulatory requirements could decrease capital in booms and increase capital in recessions the parameters should be calibrated on a long time horizon Procyclicality: the regulatory requirements could decrease capital in booms and increase capital in recessions the parameters should be calibrated on a long time horizon Excessive dependency on agency ratings Excessive dependency on agency ratings Complexity? Complexity?

22. 22 What next?  2008-09 global recession has shown many limitations of Basel II agreements Moving towards Basel III?  Anyway, capital adequacy agreements are developing also in other industries, basing on Basel II risk factors (e.g. Solvency II for insurance companies)

23. 23 References 1. 1.Resti, A. and Sironi, A., “Risk Management and Shareholders’ Value in Banking” 2. 2.Basel II: International Convergence of Capital Measurement and Capital Standards – www.bis.org 3. 3.Circolare 263/2006 Banca d’Italia – www.bancaditalia.it/vigilanza/banche/normativa/disposizioni/vigprud 4. 4.Vasicek, O. A., “Credit Valuation”, KMV Corporation 5. 5.Gordy, M. B., (2000b), “A comparative analysis of credit risk models”, Journal of Financial and Quantitative Analysis,12, 541-522