1 / 64

Market Risk Management Regulation University of Essex Expert Lecture 12 March 2010

2. Main Summary. Regulatory BackgroundBasel Accords

Leo
Download Presentation

Market Risk Management Regulation University of Essex Expert Lecture 12 March 2010

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

    1. 1 Market Risk Management & Regulation University of Essex Expert Lecture 12 March 2010 Dr Paula Haynes Financial Services Authority Traded Risk & Valuation Team

    2. 2 Main Summary Regulatory Background Basel Accords & Market Risk Pillar 1 Market Risk Capital VaR RNIV IDRC/ IRC

    3. 3 Regulatory Background Basel I and II

    4. 4 The Financial Services Authority - FSA The FSA was created, and given most of its duties and powers, by the Financial Services and Markets Act 2000 (FSMA). The FSA has the power to make rules and they are kept in the FSA’s Handbook. Regulated firms must comply with FSMA, the rules in the FSA’s Handbook and the general law. The FSA regulates banks, insurance companies, financial advisers, and general insurance intermediaries. The FSA is an independent non-governmental quasi-judicial body that regulates the financial services industry in the United Kingdom. The FSA is a company limited by guarantee and financed by the financial industry. The FSA is accountable to the Treasury, and through them to Parliament. For further information see the website: http://www.fsa.gov.uk/

    5. 5 Basel Committee on Banking Supervision The Basel Committee on Banking Supervision is an institution created by the central bank Governors of the G10 nations . It was created in 1974, after the failure of Herstatt Bank caused significant disturbances in Global Currency Markets. National representation on the committee is via Central Banks and other agencies with responsibility for Banking Supervision. The Basel Committee formulates broad supervisory standards and guidelines and recommends statements of best practice The purpose of the committee is to encourage convergence toward common approaches and standards. The committee does not have the legal authority to enforce recommendations. Recommendations are enforced through national (or EU-wide) laws and regulations. http://www.bis.org/bcbs/

    6. 6 Basel Committee & BIS Recommendations issued by the Basel Committee eventually become embedded in legal frameworks such as the European Capital Requirement Directive (CRD). The Basel Committee usually meets at the Bank for International Settlements (BIS) in Basel, Switzerland, where its Secretariat is located. The Committee is often referred to as the BIS Committee after its meeting location. However, the BIS and the Basel Committee remain two distinct entities. The BIS was created in 1930 within the framework of the Young plan to address the issue of German reparations. Its focus soon shifted to the promotion of international cooperation and monetary stability. BIS is a “Bank for Central Banks”, acting as an agent or trustee for international financial operations, prime counterparty for Central Banks in their financial transactions as well as providing/ organizing emergency financing to support the international monetary system (e.g. Mexico 1982, Brazil 1998 lead by IMF). The BIS holds approx 6% of global FX reserves invested by central Banks.

    7. 7 Basel Accords The Basel (or Basle) Accords refers to the Banking Supervision Accords i.e. Recommendations on Banking Supervision Laws and Regulations. Basel I and Basel II issued by the Basel Committee on Banking Supervision (BCBS). Basel I – 1998 Accord plus 1996 Market Risk Amendment for VaR/ CAD2 (Trading Book Regime) Basel II – 2004 Basel Rules on Capital Measurements and Capital standards implemented via the Capital Requirements Directive (CRD). CRD Replace 2 European Directives CAD2 – Capital Adequacy Directive (98/31/EEC) BCD – Bank Consolidation Directive (2000/12/EEC)

    8. 8 Basel I & II General Basle I & II define What constitutes eligible capital for regulatory purposes, & Minimum Capital amount required for an internationally active bank BI introduced the 8% Capital to RWA (Risk weighted Assets) requirement Under BI & through to BII – no. of key changes to RWA MRA under BI – VaR Option of IRB approaches for Credit Risk Inclusion of Capital requirements for Operational Risk BII did not change key concepts & standards of BI Pillar 1 of BII stipulated Reg Capital Minimum (Pillar 2 allows discretion to set higher ratios, including to address the effects of the economic cycle) Minimum level of Capital under BII was intended to be in line with BI – with incentives to encourage model based approaches In terms of eligible Reg Capital, the minimum proportion of high quality capital (Tier1) were unchanged

    9. 9 Definition of capital Capital is categorised as Tier 1 Capital or Core Capital – Common shares, plus non-cumulative perp shares, plus disclosed reserves less goodwill. Tier 2 Capital – undisclosed, asset revaluation and general provisions reserves, as well as hybrid debt capital instruments and subordinated term debt. Tier 3 Capital – Added in 1996 Amendment, but can only be used to meet a proportion of the bank’s capital requirements for market risk. Consists of short-term subordinated debt instruments Tier 1 Capital must represent at least 50% of bank’s total capital base.

    10. 10 1988 Basel (BIS) Accord - “Basel I” Landmark Financial Agreement for regulation of commercial banks – G10 countries, July 1988. Provided minimum standard for capital requirement linked to a banks credit exposures. Market Risk – VaR –added in the 1996 Amendment to Basel I (Became Mandatory in 1998). Although not statutory, implemented in G-10 countries by December 1993 Covered Credit Risks Only. Prior to Basel I, capital regulation consisted of uniform minimum capital standards that were applied to banks regardless of their risk profiles, and ignoring off-balance sheet positions. Basel I should be viewed as a first step in establishing a level playing field for banks. 2 minimum standards for meeting acceptable capital adequacy requirements: 1) Assets to capital multiple (Overall Capital Adequacy) 2) Risk based Capital Ratio = Solvency ratio = Cooke Ratio

    11. 11 “Basel I” & Amendment for Market Risk Cooke Ratio – Defined as the ratio of capital to risk weighted on-balance sheet assets plus off-balance sheet exposures, where weights are assigned on the basis of counterparty credit risk. Basel I is limited. It does not address: Portfolio Effects & Netting Capital adequacy of Trading Book securities MARKET RISK 1996 Amendment – Banks given the opportunity to develop their own Market Risk models - VaR Subject to Minimum Requirements. Strong & Independent Market Risk Management Infrastructure Sound Risk Management Policies & Practices Effective capture of relevant risks Capture of Equity and Interest Rate Specific Risk (i.e. Name related Risk)

    12. 12 Basel II In June 1999, the Basel Committee issued a first proposal to replace Basel I with a more risk sensitive agreement covering Market, Credit and Operational Risks. Following consultation etc, Basel II was released mid 2004, for implementation year end 2006, for all but the most advanced approaches. Advanced approaches were due for implementation year end 2007. Basel II was more flexible, offering a range of risk sensitive approaches and incentives for better Risk Management. The overall objective of Basel II is to increase the safety and soundness of the (international) financial system by making capital requirements for banks more risk sensitive Economic risks are better implemented than in Basel I (e.g. more sophisticated approaches for calculating credit risk requirements)

    13. 13 Basel II – 3 Pillars Basel II is structured around 3 Pillars: Pillar 1 – Relates to the minimum capital requirements that each bank must hold to cover exposure to Market, Credit & Operational Risk. Pillar 2 – Relates to supervisory Reviews ensuring that Capital is sufficient to cover overall Risk. Pillar 3 – Relates to market discipline and details minimum levels of public disclosure.

    14. 14 Basel II – Pillar 1 Market & Credit Risk Pillar 1 sets out minimum capital requirements for Market, Credit & Operational Risks. Under Basel II banks must maintain a minimum of 8% capital to risk-weighted assets. Market Risk– Min Capital Requirements unchanged under Basle II. More later! 1) Standardized Rules Approach – limited netting 2) VaR Credit Risk - 2 broad methodologies for calculating their capital requirements for credit risk: 1) Standard Approach – supported by external credit assessments – Rating Agencies. 2) Internal Ratings Based approach – Needs to be approved by Bank's Regulator

    15. 15 Basel II – Pillar 1 Operational Risk Under Basel II, 3 approaches for calculating capital requirement for Operation Risk 1) Basic Indicator Approach – sets a charge for operational risk as a fixed % (known as the “alpha factor”) of gross income – serves as proxy for bank’s risk exposure. Capital charge is fixed % of average annual income over 3 years. 2) Standardized Approach – Operations are separated into 8 standard business lines e.g. retail, corp finance etc. The capital charge for each business line is calculated by multiplying gross income for that business by a factor (denoted beta) assigned to that business line. 3) Advanced Measurement Approaches – Capital charge is the risk measure generated by the bank’s internal risk measurement system. The bank must meet quantitative & qualitative criteria set out in Basel II & must be approved by the Regulator.

    16. 16 3 Pillars of Basel II

    17. 17 Basel II – Pillars 2 and 3 Pillar 2 – Outlines the supervisory review process. Ensure a bank maintains levels of capital commensurate to its risk profile. Encourages Firm’s to develop better Risk management techniques. Importance of Stress Testing emphasized in ICAAP requirements under Pillar 2 of Basel II. Pillar 3 – Sets out disclosure requirements which will allow market participants to assess key pieces of information on the scope of the application, capital, risk exposures, risk assessment processes, and hence the capital adequacy of the institution.

    18. 18 Basel I Timeline

    19. 19 Basel II Timeline

    20. 20 Where we are Regulatory Background ü Basel Accords & Market Risk ü Pillar 1 Market Risk Capital *** VaR RNIV IDRC/ IRC

    21. 21 Pillar 1 Market Risk Capital “Pure” VaR is simply a component of Market Risk Capital

    22. 22 FSA Rules - BIPRU Full explanation of FSA rules given in “BIPRU” - FSA Handbook Prudential Source for Banks Building Societies and Investment Firms, Release 081, September 2008. Known as “BIPRU”. http://fsahandbook.info/FSA/html/handbook/BIPRU Chapter 7 covers Market Risk Chapter 7.10 covers VaR (CAD2) VaR (CAD2) is a Trading Book Regime Note that there are qualitative & quantitative aspects of VaR (see later VaR section) Systems & Controls Risk Governance Model methodology & Model Validation & testing Data & proxying FSA Notification (pre- & post-)

    23. 23 Pillar 1 – Market Risk Since 1 January 1998, banks in G10 countries were required to maintain regulatory capital to cover market risk (Market Risk amendment to the Basel Accord, 1996/ 1998). Banks' Capital Requirements for Market Risk based on 2 methods: Standardized Approach – adopts “building block” approach to interest-rate related and equity instruments which differentiates capital requirements (changes) for specific risk from those for general market risk. Internal Models Approach – VaR – Enables a bank to use its proprietary in-house method which must meet the qualitative and quantitative criteria set by the Basel Committee & is subject to the explicit approval of the bank’s Regulator. Most banks use a combination of the 2 methods depending on extent of VaR Model Approval given. VaR method has associated capital add-ons……

    24. 24 Regulatory Definition – Specific & General Market Risk Market Risk can be defined as the risk of movements in the market prices of a banks on- or off- balance sheet positions. General Market Risk – Refers to movements in market prices resulting from General market behaviour. It includes: Changes in interest rates, FX rates, commodities prices. Movements in stock indices Changes in the slope or shape of yield curves Widening/ tightening of credit spreads Specific (or residual) Market Risk refers to movements in market prices which are specific to an instrument and independent of general market movements in prices. It includes for example prices of equity securities resulting from factors specific to individual issuers.

    25. 25 Pillar 1 Market Risk Current Example

    26. 26 Revisions to Basel II Market Risk Framework Revisions to Basel II Market Risk framework (July 2009). The revisions are intended to enhance the Basel II framework & strengthen the 1996 rules governing Trading Book capital. http://www.bis.org/publ/bcbs158.htm Due to be implemented by 31 December 2010 Changes intended to reduce “Regulatory Arbitrage” VaR to be supplemented with Incremental Risk Capital Charge (IRC) - includes migration risk as well as Default Risk for unsecuritized credit products. Securitized products will not be eligible for VaR – Banking Book treatment will apply. Credit Correlation products – Regulators may allow comprehensive risk capital charge to be used – based on minimum qualitative criteria & stress tests. Additional Stressed VaR Requirement – Banks required to calculate a stressed VaR taking into account a “1 year observation period relating to significant losses” . Intended to reduce the procyclicality of the minimum capital requirements for market risk.

    27. 27 Pillar 1 Market Risk from 1 Jan 2011

    28. 28 Where we are now? Regulatory Background ü Basel Accords & Market Risk ü Pillar 1 Market Risk Capital ü VaR**** RNIV IDRC/ IRC

    29. 29 VaR Basics CAD2 is Regulatory based VaR plus add-ons Regulatory VaR vs Economic VaR An aggregated $ risk measure used to estimate the risk of a trading portfolio Takes into account correlation between (& within) asset classes VaR expresses many different types of risk as a ‘common currency’ E.g. can compare risk for equities and commodities businesses on the same basis. The idea of VAR presumes a number of concepts The “holding period” refers to the frequency with which the firm marks its books. This is usually daily. The “units” of VAR is the difference between the mark to market of the book at the beginning of the holding period, and the end (typically “close to close”, i.e. close of business one business day until close of business the next). Capital calculations are based on the value produced by the VaR model and a multiplication factor set by the FSA. I will talk more about how the multiplication factor is set later in the presentation.The idea of VAR presumes a number of concepts The “holding period” refers to the frequency with which the firm marks its books. This is usually daily. The “units” of VAR is the difference between the mark to market of the book at the beginning of the holding period, and the end (typically “close to close”, i.e. close of business one business day until close of business the next). Capital calculations are based on the value produced by the VaR model and a multiplication factor set by the FSA. I will talk more about how the multiplication factor is set later in the presentation.

    30. 30 VaR Basics One would expect to lose at least the $ VaR amount over a specific “holding period” to a certain level of “confidence” So a 1 day 99% VaR of $1m tells you that you would expect to lose $1m or more on one day in every hundred – or 2-3 times a year. 95% VaR is a ‘once a month’ measure. Typically firms use 1 day 95% or 1 day 99% for Economic Capital FSA require firms use a 99% confidence interval for a 10 day holding period for their PRR calculation Firms can scale the 1 day VaR by v10 (i.e. multiply 3.162) or use 10 day overlapping / non-overlapping periods.

    31. 31 VaR based on Normal Distribution The Normal Distribution VAR is useful because price changes in many portfolios are ‘normally distributed’. This means that very large losses relative to the average loss (known as the ‘standard deviation’) are unlikely, as the following table shows. Standard Deviation 1 Once every 6 days 2 Once every 44 days 3 Once every 2 years 4 Once every 86 years 5 Once every 9,500 years 6 Once every 3m years 7 Once every 2bn years Thus while loss in excess of the 2.3 standard deviations corresponding to a 99% confidence level will occur roughly every 100 days. A loss of 3 standard deviations, which is only 30% more, will occur only every 2 years. A 25% greater loss of 4SD will occur only every 86 years. A loss of 7 SD is not likely to occur more than once every 2bn years – about half as long as the Earth has existed! However, “fat tail” losses do in fact occur more frequently than this in single markets, and this is one of the drawbacks of VAR as a risk management tool. Stress testing is required to give an indication of the likelihood of larger-than-expected losses, although this has drawbacks too. VAR is useful because price changes in many portfolios are ‘normally distributed’. This means that very large losses relative to the average loss (known as the ‘standard deviation’) are unlikely, as the following table shows. Standard Deviation 1 Once every 6 days 2 Once every 44 days 3 Once every 2 years 4 Once every 86 years 5 Once every 9,500 years 6 Once every 3m years 7 Once every 2bn years Thus while loss in excess of the 2.3 standard deviations corresponding to a 99% confidence level will occur roughly every 100 days. A loss of 3 standard deviations, which is only 30% more, will occur only every 2 years. A 25% greater loss of 4SD will occur only every 86 years. A loss of 7 SD is not likely to occur more than once every 2bn years – about half as long as the Earth has existed! However, “fat tail” losses do in fact occur more frequently than this in single markets, and this is one of the drawbacks of VAR as a risk management tool. Stress testing is required to give an indication of the likelihood of larger-than-expected losses, although this has drawbacks too.

    32. 32 Normal distributions A loss in excess of ‘x’ standard deviations would be expected: 1 occurs every 6 days 2 every 44 days 3 every 3 years 4 every 126 years 5 every 14,000 years 6 every 4m years 7 every 3.1bn years Unfortunately real markets do not follow the normal distribution in times of stress!

    33. 33 Historical simulation most frequently used by CAD 2 firms Variance-Covariance Popular with some smaller firms with linear risk portfolios Monte Carlo Use is growing, can be very IT intensive for complex products Types of VaR Methodology These are the three main methods used to compute Value at Risk, historical simulation, variance co-variance, Monte Carlo simulation or a hybrid of these. Historical simulation is the easiest to conceptualise. It makes no statistical assumptions. You simply apply the last year or two years worth of daily price data to your current portfolio and calculate a theoretical P&L for each days worth of data. The results are then ranked and then you just pick off whichever percentile VaR you want to measure. Variance co-variance VaR also uses historical data but uses mathematical approximations to make the calculation easier and faster. This method is very quick and easy to implement and therefore popular with firms who have a largely linear risk portfolio. Thirdly there is Monte Carlo VaR which is in essence a combination of his sim and VCV VaR. It creates say 10,000 possible tomorrows by taking into account historical risk factors. Each simulation takes into account a given volatility and correlation matrix. All the simulations are then ranked and again you just pick off whichever percentile you require. Its advantages are that it can handle quite complex option portfolios and makes no assumption of normality, however its disadvantages are that it is very computationally intensive, opaque to all but the very quantitative in the firm and will not produce exactly the same result each time. We do not prescribe any one method and we will not discourage any firm from proposing an alternative method but what we do want to see is that the method chosen is appropriate for the type of trading portfolio a firm has.These are the three main methods used to compute Value at Risk, historical simulation, variance co-variance, Monte Carlo simulation or a hybrid of these. Historical simulation is the easiest to conceptualise. It makes no statistical assumptions. You simply apply the last year or two years worth of daily price data to your current portfolio and calculate a theoretical P&L for each days worth of data. The results are then ranked and then you just pick off whichever percentile VaR you want to measure. Variance co-variance VaR also uses historical data but uses mathematical approximations to make the calculation easier and faster. This method is very quick and easy to implement and therefore popular with firms who have a largely linear risk portfolio. Thirdly there is Monte Carlo VaR which is in essence a combination of his sim and VCV VaR. It creates say 10,000 possible tomorrows by taking into account historical risk factors. Each simulation takes into account a given volatility and correlation matrix. All the simulations are then ranked and again you just pick off whichever percentile you require. Its advantages are that it can handle quite complex option portfolios and makes no assumption of normality, however its disadvantages are that it is very computationally intensive, opaque to all but the very quantitative in the firm and will not produce exactly the same result each time. We do not prescribe any one method and we will not discourage any firm from proposing an alternative method but what we do want to see is that the method chosen is appropriate for the type of trading portfolio a firm has.

    34. 34 S&P500 Data- March 2007 – March 2009

    35. 35 Introduction to Reg VaR Basel market risk amendment (1996) Allowed regulators to set market risk capital requirements using a VaR model Must meet minimum standards Qualitative and quantitative standards Includes use of backtesting and stress-testing Alignment of internal and regulatory capital incentives Promotes good risk management http://www.fsa.gov.uk/pubs/cp/cp06_03_appendix2.pdf In 1996 the Basle market risk amendment was introduced which allowed firms with adequate risk management systems to benefit from a more accurate and more importantly for firm a reduced capital charge than that generated under standard rules. This encouraged firms to measure market risks more accurately and comprehensively. The capital saving when compared to standard rules charges, depending on the diversity of the trading portfolio, can be an order of magnitude in size and it is because of this large saving that a suite of comprehensive qualitative and quantitative standards were attached to the CAD2 model recognition process. All the requirements needed to achieve such recognition are detailed in chapter TV of IPRU(BANK) or appendix 11 of IPRU(INV). We will now go through these criteria highlighting those which are particularly crucial and those criteria where previous applicants have often fallen short of the standards required. In 1996 the Basle market risk amendment was introduced which allowed firms with adequate risk management systems to benefit from a more accurate and more importantly for firm a reduced capital charge than that generated under standard rules. This encouraged firms to measure market risks more accurately and comprehensively. The capital saving when compared to standard rules charges, depending on the diversity of the trading portfolio, can be an order of magnitude in size and it is because of this large saving that a suite of comprehensive qualitative and quantitative standards were attached to the CAD2 model recognition process. All the requirements needed to achieve such recognition are detailed in chapter TV of IPRU(BANK) or appendix 11 of IPRU(INV). We will now go through these criteria highlighting those which are particularly crucial and those criteria where previous applicants have often fallen short of the standards required.

    36. 36 Upgrade to Trading Book regime Revisions to Basel II Market Risk framework (July 2009) to be implemented by CAD2 firms by year end 2010. Tougher VaR-based market risk regime (but less pro-cyclical) PRR to be the sum of a current VaR-based charge and a stress VaR-based charge Also, data sets to be updated every month (currently standard is every 3 months) So we currently take the firm’s VaR measure, scaled up to 99% if necessary, and scaled up to a 10 day equivalent, and multiply by a number between 3 and 4.So we currently take the firm’s VaR measure, scaled up to 99% if necessary, and scaled up to a 10 day equivalent, and multiply by a number between 3 and 4.

    37. 37 VaR Capital Benefits CAD2 gives large capital benefit Partly from more scientific calculation of risk Standard rules are inflexible and penal Not because they are large, but because minimal netting benefit. CAD1 is a basic model approach based on scenario matrices Most of the capital saving, however, is obtained from diversification. CAD1 & CAD2 are especially beneficial for options portfolios. Diversification happens when you have exposure to more than one asset, and when the assets are not perfectly “correlated”. Correlation is the tendency of prices to move in the same direction at the same time. Intuitively, if all shares in a portfolio are perfectly correlated, then when a loss occurs in one, it will occur in all. Therefore, a value at risk is much higher for a highly correlated portfolio than one with low correlations. Describe ‘spot-vol’ matrices. When there is only a small amount of correlation or when there is negative correlation (i.e. when the tendency of one asset to go up when the other asset goes down) the risk of the portfolio falls. VAR models are able to compute the correlation benefit of any number of correlated assets. Diversification happens when you have exposure to more than one asset, and when the assets are not perfectly “correlated”. Correlation is the tendency of prices to move in the same direction at the same time. Intuitively, if all shares in a portfolio are perfectly correlated, then when a loss occurs in one, it will occur in all. Therefore, a value at risk is much higher for a highly correlated portfolio than one with low correlations. Describe ‘spot-vol’ matrices. When there is only a small amount of correlation or when there is negative correlation (i.e. when the tendency of one asset to go up when the other asset goes down) the risk of the portfolio falls. VAR models are able to compute the correlation benefit of any number of correlated assets.

    38. 38 Use of VaR VaR is used by: Investment & commercial banks with trading books Treasury operations of retail banks Prime Brokers (to set portfolio based margin requirements) Hedge Funds & Asset managers Energy firms & Utilities VaR is used for: Regulatory Capital Economic Capital/ RAROC Setting Limits (Hard and Soft) Assessing Trader Performance Front Office Risk Management (i.e not independent of Trading) Calculating Margin For example, some asset managers use VaR on a relative rather than an absolute basis, to track the risk of deviating from a benchmark e.g. how far might the equity portfolio diverge from MSCI World index.For example, some asset managers use VaR on a relative rather than an absolute basis, to track the risk of deviating from a benchmark e.g. how far might the equity portfolio diverge from MSCI World index.

    39. 39 CAD2 approval process Run by the Prudential Risk Division (PRD) accompanied by Supervision Between 4 and 10 months if no ‘showstoppers’ Firm request Pre visit questionnaire sent to firm Pre visit information supplied to FSA 1 month on site visit Follow up questions and actions for firm Further 5 day follow-up on site visit Write report and submit to CAD panel Approval granted and waiver issued This is an average! Times will vary depending on size and complexity of firm. The entire process can take between 6 and 9 months from the initial request coming from the firm depending on the complexity of the application. RRD will send out a pre-visit questionnaire for the firm to fill in, this can take some time but we expect that most of the information should be already available – we do not want to see documentation and procedures written especially for us. We normally give firm a month to submit this information. RRD will then visit 2-3 weeks after we receive the pre visit information. During the visit we would expect to see the front office traders, senior management, risk management, finance, operations, audit, IT support and development, compliance, regulatory reporting. A agenda will be agreed in the weeks before the visit along with the appropriate personnel for each meeting. After the visit if we have any further questions arising from the visit we will write to you and if we feel there are any issues that need to be addressed before we can progress with the application we will raise them at this point and agree an action plan with you. The second visit will concentrate more on details the VaR model itself and the validation of the model. This will probably involve meetings with technical staff, developers, risk managers and any front office developers involved in the model. We will write a report to the supervision team and organise a CAD panel to meet and consider the recommendation. CAD panel consists of senior management within RRD, policy and supervision departments. If model recognition is approved we will work with the firm to write the waiver which the firm must then submit to the central waivers team at the FSA. It usually takes 2-3 weeks to process. The fact that you have been given a CAD2 waiver is published on the FSA website but the details of it are not published. The entire process can take between 6 and 9 months from the initial request coming from the firm depending on the complexity of the application. RRD will send out a pre-visit questionnaire for the firm to fill in, this can take some time but we expect that most of the information should be already available – we do not want to see documentation and procedures written especially for us. We normally give firm a month to submit this information. RRD will then visit 2-3 weeks after we receive the pre visit information. During the visit we would expect to see the front office traders, senior management, risk management, finance, operations, audit, IT support and development, compliance, regulatory reporting. A agenda will be agreed in the weeks before the visit along with the appropriate personnel for each meeting. After the visit if we have any further questions arising from the visit we will write to you and if we feel there are any issues that need to be addressed before we can progress with the application we will raise them at this point and agree an action plan with you. The second visit will concentrate more on details the VaR model itself and the validation of the model. This will probably involve meetings with technical staff, developers, risk managers and any front office developers involved in the model. We will write a report to the supervision team and organise a CAD panel to meet and consider the recommendation. CAD panel consists of senior management within RRD, policy and supervision departments. If model recognition is approved we will work with the firm to write the waiver which the firm must then submit to the central waivers team at the FSA. It usually takes 2-3 weeks to process. The fact that you have been given a CAD2 waiver is published on the FSA website but the details of it are not published.

    40. 40 General and Specific Risk

    41. 41 General vs. Specific Risk Harder to get a Specific Risk recognition BIPRU 7.10.46 Model Standards for Specific Risk Specific Risk models – Name specific risk is modelled directly by full Historical Simulation or a n-factor regression model is used. Specific Risk is the residual component which cannot be explained by market factors. Specific Risk models have generally performed worse in volatile conditions that General Risk-only models Most excessive backtesting exceptions issues relate to Specific Risk models. Many firms have experienced backtesting exceptions over the period 2007 -2008 due to volatile market conditions. Banking Crisis - Rescue of AIG, collapse of Bear Stearns & Lehman Brothers, RBS etc.

    42. 42 Qualitative Considerations for CAD2 The Board & senior management must be involved Model should be closely integrated into the daily risk management process Market Risk management should be independent of the trading unit and report directly to senior management Must have skilled staff with knowledge of model in trading, risk control, operations and internal audit Risk management policies and procedures should be documented, regularly reviewed and complied with. Firstly there are some fundamental general risk management issues Those responsible for risk need to be aware of assumptions and limitations of their VaR model including executive and board level management with responsibility risk issues. They must also be actively involved in the risk control process and regard it as an essential part of the business. This requirement is one where I think it is fair to say firms have improved on quite considerably since 1996 which is a reflection of the fact that risk management in general has a much higher profile at board level than it used to. It also helps that the concept of VaR has been around for a long time now and therefore managers have become more comfortable and knowledgeable about the subject. War story – the managing director who said VAR is rubbish The models output should be an integral part of the process of planning, monitoring and controlling the firms risk It should also be used in conjunction with the firms own exposure limits. The link between VaR and other limits should be consistent over time and understood by traders and senior managers. i.e. there ids no point in having a VaR limit that will never be breached before all other exposure limits are breached. Market Risk Management/Risk Control Unit must be responsible for designing, implementing and analysing daily risk reports. The daily risk reports must be reviewed by personnel with authority to reduce positions at a trader and overall level if necessary. This is often an area where firms fail to meet our requirements. Usually there are skilled staff in front office and risk management but other control areas are found lacking. It is up to firms to ensure that VaR training is given to key personnel in all support areas. We do not want to see policies and procedure written especially for us. We would like to see evidence that they are used and read by staff and that they are regularly updated and approved. Firstly there are some fundamental general risk management issues Those responsible for risk need to be aware of assumptions and limitations of their VaR model including executive and board level management with responsibility risk issues. They must also be actively involved in the risk control process and regard it as an essential part of the business. This requirement is one where I think it is fair to say firms have improved on quite considerably since 1996 which is a reflection of the fact that risk management in general has a much higher profile at board level than it used to. It also helps that the concept of VaR has been around for a long time now and therefore managers have become more comfortable and knowledgeable about the subject. War story – the managing director who said VAR is rubbish The models output should be an integral part of the process of planning, monitoring and controlling the firms risk It should also be used in conjunction with the firms own exposure limits. The link between VaR and other limits should be consistent over time and understood by traders and senior managers. i.e. there ids no point in having a VaR limit that will never be breached before all other exposure limits are breached. Market Risk Management/Risk Control Unit must be responsible for designing, implementing and analysing daily risk reports. The daily risk reports must be reviewed by personnel with authority to reduce positions at a trader and overall level if necessary. This is often an area where firms fail to meet our requirements. Usually there are skilled staff in front office and risk management but other control areas are found lacking. It is up to firms to ensure that VaR training is given to key personnel in all support areas. We do not want to see policies and procedure written especially for us. We would like to see evidence that they are used and read by staff and that they are regularly updated and approved.

    43. 43 IT systems Data feeds to all systems downstream and upstream and inter system reconciliation Data quality and completeness System development and change control System security and audit trails Availability and contingency procedures Operational statistics for production process Qualitative Criteria for CAD2 The robustness of the IT systems used to feed data into the VaR model is a particular concern because it is often an area of weakness in a firms VaR model. It is not just the VaR model itself that needs to be robust it is the feeder systems; risk aggregation systems; time series database; stress testing system; backtesting system and any P&L cleaning system. The robustness of such systems depends on data quality, completeness of capture, inter system reconciliations along with the consistency and reliability of data sources We want to see system development procedures in place and robust change control documentation System security is looked in terms of user access rights and audit trails should be available System reliability and availability is taken into consideration and there should be contingency plans in if the live system experiences any unplanned down time. Operational statistics relating to the VaR model production process should include the timeliness of the daily VaR figures and overnight batch runs, the number of re-runs needed, reliability of the data feedsThe robustness of the IT systems used to feed data into the VaR model is a particular concern because it is often an area of weakness in a firms VaR model. It is not just the VaR model itself that needs to be robust it is the feeder systems; risk aggregation systems; time series database; stress testing system; backtesting system and any P&L cleaning system. The robustness of such systems depends on data quality, completeness of capture, inter system reconciliations along with the consistency and reliability of data sources We want to see system development procedures in place and robust change control documentation System security is looked in terms of user access rights and audit trails should be available System reliability and availability is taken into consideration and there should be contingency plans in if the live system experiences any unplanned down time. Operational statistics relating to the VaR model production process should include the timeliness of the daily VaR figures and overnight batch runs, the number of re-runs needed, reliability of the data feeds

    44. 44 Internal Audit should be assessing: Adequacy of risk management documentation Integrity of risk management information Approval process for pricing models Change control processes Scope of risks and products captured under VaR model Accuracy, completeness, consistency & timeliness of data Accuracy and appropriateness of model assumptions Reserving policies, valuation procedures and risk exposures Model validation process including backtesting Qualitative Criteria In a large bank such an independent review would be carried out by the internal audit department. The level of complexity involved in such a review can often be beyond the remit of a small internal audit department and it is often an area that firms fall short of. It should be noted that we have no objection to the use of external source to conduct such a review if sufficient expertise is not available internally. (One small firm told us they could not implement an audit function because ‘it would upset the staff’).In a large bank such an independent review would be carried out by the internal audit department. The level of complexity involved in such a review can often be beyond the remit of a small internal audit department and it is often an area that firms fall short of. It should be noted that we have no objection to the use of external source to conduct such a review if sufficient expertise is not available internally. (One small firm told us they could not implement an audit function because ‘it would upset the staff’).

    45. 45 Is the holding period appropriate (for less liquid assets)? What is the historical observation period (for CAD2 we require at least 250 days) Pros & cons of long vs. short observation period; Weighted or unweighted How frequently are data sets updated? Does the model capture non-linear risks? Risk factor granularity (e.g. yield curve buckets) Should reflect imperfect correlation where necessary Model Validation & Testing (includes Backtesting) Risks Not In VaR (RNIV) – See later Quantitative Considerations VaR can be calculated using a daily holding period and converted using the square root of time and a different confidence interval and converted assuming a normal distribution. A shorter observation period can be justified if significant price volatility is observed in a particular market. Where 250 days of data is not available then proxy data can be used provided it does not materially understate the risk. If a weighting scheme is applied then the effective observation period must still be one year. Market data sets must be updated at least quarterly For significant option positions, non-linear risks must be captured by the model The VaR model should use a separate risk factor for each portfolio or business where there is material exposure The VaR model should also capture the risk of less than perfectly correlated movements between similar but not identical products (for example between US and UK interest rates). This is crucial for desks where the whole trading strategy is to trade the spread between two types of product otherwise a VaR of zero would be produced. VaR can be calculated using a daily holding period and converted using the square root of time and a different confidence interval and converted assuming a normal distribution. A shorter observation period can be justified if significant price volatility is observed in a particular market. Where 250 days of data is not available then proxy data can be used provided it does not materially understate the risk. If a weighting scheme is applied then the effective observation period must still be one year. Market data sets must be updated at least quarterly For significant option positions, non-linear risks must be captured by the model The VaR model should use a separate risk factor for each portfolio or business where there is material exposure The VaR model should also capture the risk of less than perfectly correlated movements between similar but not identical products (for example between US and UK interest rates). This is crucial for desks where the whole trading strategy is to trade the spread between two types of product otherwise a VaR of zero would be produced.

    46. 46 Model Validation Model Validation Checking whether a model is adequate Includes Backtesting, stress testing, independent review & oversight FSA take into account l Model Validation (MV) procedures when assessing a VaR model. BIPRU 7.10.76G – 7.10.80 set out Risk Management Standards for Validation & Backtesting. BIPRU 7.10.78 “A firm must have processes in place to ensure that its VaR model has been adequately validated by suitably qualified parties independent of the development process to ensure that it is conceptually sound and adequately captures all market risk….” MV must be conducted when VaR model initially developed & when significant changes are made MV must be conducted on periodic basis & where there have been significant changes in market or portfolio Firm must follow advances in MV techniques/ best practice MV must not be limited to Backtesting. Firms should carry out their own MV tests, use hypothetical portfolios & investigate the limitations of VaR.

    47. 47 Backtesting This chart represents one of the worst backtesting exceptions from a CAD2 regulated firm. Before September 2003, the firm had an average VAR of about Ł10m. At the end of September, there was a crisis event in a pegged currency that led to a one day loss of Ł99m. The model immediately recognised the exception event, and the VAR jumped to Ł55m. However this was a measure of hindsight. The capital actually required by the firm based on the model before the exception was only about Ł100m. Thus the loss came very close to eroding the firm’s entire capital base. This also shows up a key weakness in VAR, in that it cannot easily predict ‘tail’ events such as pegged currency risk, although stress testing should have picked this risk up. Such events are picked up by quarterly monitoring. This showed up a weakness in the firm’s stress testing, and also fed into the ‘plus point’ regime which we will discuss shortly.This chart represents one of the worst backtesting exceptions from a CAD2 regulated firm. Before September 2003, the firm had an average VAR of about Ł10m. At the end of September, there was a crisis event in a pegged currency that led to a one day loss of Ł99m. The model immediately recognised the exception event, and the VAR jumped to Ł55m. However this was a measure of hindsight. The capital actually required by the firm based on the model before the exception was only about Ł100m. Thus the loss came very close to eroding the firm’s entire capital base. This also shows up a key weakness in VAR, in that it cannot easily predict ‘tail’ events such as pegged currency risk, although stress testing should have picked this risk up. Such events are picked up by quarterly monitoring. This showed up a weakness in the firm’s stress testing, and also fed into the ‘plus point’ regime which we will discuss shortly.

    48. 48 Backtesting Backtesting Exception = Daily Clean P&L shows a Loss which exceeds 1-day 99% VaR For 99% expect 2 or 3 exceptions per year One of the mechanisms for VaR model validation Backtesting should be performed overall (Legal Entity Level) and at sub portfolio level (including specific risk portfolios) FSA plus factor system increases VaR Capital via multiplier if more than 4 (Legal Entity Level) Backtesting Exceptions are observed over 1 year (=250 business days). See BIPRU 7.10.125. Specific Risk Backtesting Exceptions – If 10 or more exceptions occur in 1 year period, the firm must take immediate corrective action Firm must have the ability to analyze reasons for exceptions VaR and P&L portfolios must be materially the same to eliminate bias.

    49. 49 Backtesting - P&L Clean P&L - Actual P&L should be cleaned to exclude non-risky items e.g. fees, commissions, reserve moves & large one-off profits from new deals. However, it should include P&L due to price testing adjustments & intra-day trading. Full details in BIPRU 7.10.99 – 7.10.102 FSA also require that Firms backtest against Clean Hypothetical P&L Clean hypo P&L for a business day means the clean P&L that would have occurred for that day if the portfolio on which VaR was based remained unchanged Clean hypo P&L excludes intraday trading Purer test of VaR model Based on the days change in value on the same portfolio that was used to generate the VaR BIPRU 7.10.111 – 7.10.112 Three months of back testing data is needed before model recognition is granted. The P&L must be cleaned to exclude any material elements that are not related to market risk (for example fees or commissions, any reserves not directly related to market risk and one-off marketing profits from new deals &c) It must include any price adjustments that are market related (e.g. the month end price verification process must be included. This is to avoid “p/l smoothing”, and must for this reason be done in accordance with a firms written procedures that should include a documented method of assigning such valuation adjustments to back testing data. The FSA currently does not insist on backtesting data against theoretical P&L. However, going forward under the trading book review it is up to each regulator to decide if backtesting against hypothetical P&L should be a requirement in addition to backtesting against actual P&L. The FSA have yet to make a decision on this.Three months of back testing data is needed before model recognition is granted. The P&L must be cleaned to exclude any material elements that are not related to market risk (for example fees or commissions, any reserves not directly related to market risk and one-off marketing profits from new deals &c) It must include any price adjustments that are market related (e.g. the month end price verification process must be included. This is to avoid “p/l smoothing”, and must for this reason be done in accordance with a firms written procedures that should include a documented method of assigning such valuation adjustments to back testing data. The FSA currently does not insist on backtesting data against theoretical P&L. However, going forward under the trading book review it is up to each regulator to decide if backtesting against hypothetical P&L should be a requirement in addition to backtesting against actual P&L. The FSA have yet to make a decision on this.

    50. 50 Stress Testing VaR will not capture extreme events Relies on events within the data sets used So VaR should be complemented with a comprehensive stress testing programme Identify historical and/or possible scenarios relevant to current portfolio E.g. Tech Market Crash, Credit Crunch, 1987 Crash etc Re-run frequently & review assumptions periodically Board and senior management oversight Need Front Office ‘buy-in’ BIPRU 7.10.72 refers to Risk Management standards & Stress Testing BIPRU 7.10.84G – BIPRU 7.10.90G relate to Stress Testing of a VaR model Importance of Stress Testing emphasized in ICAAP (Internal Capital Adequacy Assessment Process) requirements under Pillar 2 of Basel II Stress testing covers the rare but still plausible ‘tail events’ that VaR by its very nature doesn't capture. The role of stress testing is to minimise the risk of the firm incurring unexpected losses through lack of understanding of P&L impact on extreme market movements. In the trading book review the results of a firms stress testing must be incorporated into the internal capital requirements under pillar 2. N.B. VaR is procyclical. We expect firms not only to have a stress testing programme in place with the results used to identify where risks need to be reduced and to ensure that the firm has the capacity to absorb such losses. Such stress tests might include known historical market crashes, what if scenarios based on large standard deviation moves and also hybrid scenarios. Such stress tests should encompass all material risk factors and be based on full revaluation for option portfolios. They should also consider joint moves in more than one risk factor simultaneously. We will consider the appropriateness of the scenarios used and that non linear effects are adequately captured and that these are reviewed regularly. The board and senior management must have oversight of the stress testing results not only to enforce a reduction in risk exposure if necessary but also to have input into the appropriateness of the parameters used in the stress tests. Senior management should also consider the appropriateness of stress testing limits for some scenarios We wouldn’t expect the whole suite of stress test to be run daily as this is often not possible due to IT constraints, however we would expect at least a limited batch of stress tests to be run on a daily basis. Stress testing covers the rare but still plausible ‘tail events’ that VaR by its very nature doesn't capture. The role of stress testing is to minimise the risk of the firm incurring unexpected losses through lack of understanding of P&L impact on extreme market movements. In the trading book review the results of a firms stress testing must be incorporated into the internal capital requirements under pillar 2. N.B. VaR is procyclical. We expect firms not only to have a stress testing programme in place with the results used to identify where risks need to be reduced and to ensure that the firm has the capacity to absorb such losses. Such stress tests might include known historical market crashes, what if scenarios based on large standard deviation moves and also hybrid scenarios. Such stress tests should encompass all material risk factors and be based on full revaluation for option portfolios. They should also consider joint moves in more than one risk factor simultaneously. We will consider the appropriateness of the scenarios used and that non linear effects are adequately captured and that these are reviewed regularly. The board and senior management must have oversight of the stress testing results not only to enforce a reduction in risk exposure if necessary but also to have input into the appropriateness of the parameters used in the stress tests. Senior management should also consider the appropriateness of stress testing limits for some scenarios We wouldn’t expect the whole suite of stress test to be run daily as this is often not possible due to IT constraints, however we would expect at least a limited batch of stress tests to be run on a daily basis.

    51. 51 VaR Summary VaR is a very useful too for monitoring day-to-day market risk with no obvious substitute takes into account asset volatilities, correlations between different assets assesses risk across different businesses on a like-for-like basis But it can’t do everything need to understand its limitations needs to be complimented with stress tests etc. Also need granular market risk measures Does not take liquidity into account Hopefully this presentation has shown that the level of detail involved in the model recognition process and that it doesn’t just cover the mechanics of the VaR model itself. The review is a complete front to back process and we will need to be assured that all business and support functions meet the necessary standards. However, we do take into account the size and complexity of the business when considering these standards. The model recognition process is not quick due to the nature of the work involved for the firm and the FSA therefore a significant amount of commitment is required usually by the risk management department in coordinating the entire process and providing us with all the necessary documentation and answers to our questions. The time scales are flexible and we do allow firms sufficient time to prepare for our visits and respond to any follow up questions. We aim to deal with application request as soon as they arrive but if every firm applies at the same time then this could be a problem. Once recognition is given it is not the end but just the beginning of a long and hopefully beautifully relationship with the traded risk department Whilst a substantial amount of effort is needed to achieve VaR recognition the capital savings are usually incentive enough to warrant such effort. Hopefully this presentation has shown that the level of detail involved in the model recognition process and that it doesn’t just cover the mechanics of the VaR model itself. The review is a complete front to back process and we will need to be assured that all business and support functions meet the necessary standards. However, we do take into account the size and complexity of the business when considering these standards. The model recognition process is not quick due to the nature of the work involved for the firm and the FSA therefore a significant amount of commitment is required usually by the risk management department in coordinating the entire process and providing us with all the necessary documentation and answers to our questions. The time scales are flexible and we do allow firms sufficient time to prepare for our visits and respond to any follow up questions. We aim to deal with application request as soon as they arrive but if every firm applies at the same time then this could be a problem. Once recognition is given it is not the end but just the beginning of a long and hopefully beautifully relationship with the traded risk department Whilst a substantial amount of effort is needed to achieve VaR recognition the capital savings are usually incentive enough to warrant such effort.

    52. 52 Where we are now? Regulatory Background ü Basel Accords & Market Risk ü Pillar 1 Market Risk Capital ü VaR ü RNIV*** IDRC/ IRC

    53. 53 RNIV Framework RNIV = Risks-not-in-VaR FSA concept, not Basel Means risks not captured or suitable for inclusion within a Firm’s VaR Model Material Risks should be Capitalised as part of Pillar I Market Risk Capital Stressed based losses – Do not go through VaR multiplier VaR based Losses - Go through VaR multiplier

    54. 54 RNIV Framework Firms should have a process and policy for identifying & quantifying RNIV Examples of RNIV Cash-Synthetic Basis for ABS Single Stock Volatility Skew Hedge Fund Gap Risk

    55. 55 Where we are now? Regulatory Background ü Basel Accords & Market Risk ü Pillar 1 Market Risk Capital ü VaR ü RNIV ü IDRC/ IRC***

    56. 56 IDRC/ IRC Charges IDRC = Incremental Default Risk Charge – based on Default Risk only. IRC = Incremental Risk Charge– based on Default & migration Risks plus other risks – Replaces IDRC from 1 January 2011. Currently banks with Interest Rate Specific Risk CAD2 Model recognition are required to measure and hold capital against default risk that is incremental to default risk captured in the VaR model. IDRC– response to the increasing amount of trading book exposure to credit-risky & often illiquid products whose risk is not accurately reflected in VaR. Significant part of Pillar 1 Market Risk Capital.

    57. 57 Recap Market Risk Capital

    58. 58 IRC – Key Supervisory Standards IRC covers equities as well as credit products. IRC expands the scope of the capital charge to capture Default risk Credit Migration Risk Credit Spread Risk Equity Price Risk Soundness Standard consistent with A-IRB IRC estimates the Trading book’s exposure to these risks over a one-year capital horizon at 99.9% confidence, taking into account the liquidity horizons of positions. Assumption of a constant level of risk over a 1 year capital horizon (not constant positions)

    59. 59 IRC – Key Supervisory Standards IRC must appropriately reflect issuer & market concentrations. IRC can include hedging but any maturity mismatch needs to be reflected. Benefit of Liquidity Liquidity horizon defined as time to sell or completely hedge an exposure in a stressed market environment Shorter liquidity horizon reduces effective PD Shorter liquidity horizon also reduces inter-period correlation

    60. 60 IDRC / IRC Models For IDRC, most banks used Gaussian Copula Model A-IRB Approach is a special case of a Gaussian Copula http://www.fsa.gov.uk/pubs/occpapers/op29.pdf http://www.fsa.gov.uk/pubs/international/gaussian_copula.pdf A few firms use Binomial approach If internal models do not map directly to the Supervisory Principles than the bank must prove the capital charge is comparable, otherwise they may be subject to a Capital Adjustment Factor.

    61. 61 IRC Challenges Double Counting Capital horizons & Confidence Levels different for VaR & IRC, but there is significant overlap. Data/ Modelling challenges 1 year Capital horizon 99.9% Confidence Assigning liquidity for each position Sourcing PDs

    62. 62 Conclusions Only a portion of Pillar 1 Market Risk Capital based on VaR VaR good average measure of risk – But not the whole story Increased Focus on RNIV / IRC –what is captured by/ not captured by VaR Model Validation & Model Standards, Policies & Controls Stress Testing (Pillar II) Stressed VaR (uses static extreme period in history) Structured Products From 1 Jan 2011 - not eligible for VaR – Stop Trading Book/ Banking Book Arb In Financial Crisis more than 70% of losses in due to Structured Products 13% of Losses in Crisis were due to Prop Trading Hedge Fund Regulation ????

    63. 63 References 1 “Value at Risk - Second Edition”, Philippe Jorion. McGraw-Hill (2001). “Risk Management and Analysis Volume 1 – Measuring and Modelling Financial Risk”, Carol Alexander, John Wiley & Sons (1998). “Banking on Basel – the Future of International Financial Regulation”, Daniel K Tarullo, Peterson Institute for International Economics (2008). BCBS Consultative Document – Principles for sound stress testing practices and supervision, January 2009, issued for comment by 13 March 2009. http://www.bis.org/publ/bcbs147.pdf?noframes=1 FSA CP 09/ 29, December 2009 – Strengthening Capital Standards. BCBS Final Document - Revisions to Basel II Market Risk framework (July 2009). http://www.bis.org/publ/bcbs158.pdf?noframes=1 FSA Handbook Prudential Source for Banks Building Societies and Investment Firms, Release 081, September 2008. Known as “BIPRU”. http://fsahandbook.info/FSA/html/handbook/BIPRU

    64. 64 References 2 BIPRU 7.10 Use of a VaR Model http://fsahandbook.info/FSA/html/handbook/BIPRU/7/10 BCBS Guidelines for Computing Capital for Incremental Risk in the Trading Book, July 2008. http://www.bis.org/publ/bcbs159.htm

    65. 65 Acknowledgements Many thanks to my colleagues in the FSA’s Traded Risk & Valuation Team especially Jon Hollis, Sikandar Hussain, Evie Vanezi, Will Mehta, Riccardo Pagnani, and Simon Arnold. Many thanks to Martin Etheridge for putting me straight on matters of FSA Trading book policy.

More Related