Advanced Concepts in Capturing Market Risk: A Supervisory Perspective

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1 Advanced Concepts in Capturing Market Risk: A Supervisory Perspective Rodanthy Tzani Federal Reserve Bank of NY The views expressed in this presentation are strictly those of the presenter and do not necessarily represent those of the Federal Reserve Bank of New York or the Federal Reserve System

2 Agenda Background Current Market Risk Rule for US bank holding companies Risk-based capital for market risk Approaches in modeling specific risk Challenges in capturing specific risk Risk factors captured and not captured in VaR models Revised Market Risk Rule Conclusions Advanced Concepts in Capturing Market Risk: A Supervisory Perspective, Chicago, IL, March 14,

3 Background Regulatory Capital: The minimum amount of capital regulators require a firm to hold. Regulatory capital is different from Economic Capital. Economic Capital: The amount of capital a firm internally determines is needed to support the risks underlying their business activities. Capital is tied to the risks of the firm s portfolio. Accurate assessment of risks of the firm needed: Correct identification of various types of risk Accurate measurement of risks Advanced Concepts in Capturing Market Risk: A Supervisory Perspective, Chicago, IL, March 14,

4 Existing Market Risk Rule as implemented for US bank holding companies: requirements for Market Risk VaR measure 4

5 Market Risk Rule (MRR) for US Bank Holding Companies MRR: based on Market Risk Amendment to Basel I Adjust risk-based capital requirements for Market Risk: - use internal models to calculate VaR market risk measure -capital requirement based on VaR measure plus an add-on for specific risk + capital charge for de minimis exposures Internal models requirements All trading account + commodity + FX positions must be in VaR ( Value-at-Risk ) model 10-day movement VaR, 99% confidence level, 1 year historical period Specific Risk ( SR ) for covered debt and equity positions Internal (VaR) model must be approved by FRB Else, conservative standard charges for SR Advanced Concepts in Capturing Market Risk: A Supervisory Perspective, Chicago, IL, March 14,

6 Requirements for SR VaR Model Approval According to MRR, SR VaR model needs to: Explain historical price variation Capture concentration Be robust to adverse environment Be validated through backtesting Capture Event and Default risk - This is a challenge to include in current VaR model - If not included, apply prudential surcharge (for partially modeled SR): If SR separated:1 x SR VaR Else: 1 x Total Risk VaR Advanced Concepts in Capturing Market Risk: A Supervisory Perspective, Chicago, IL, March 14,

7 Definitions Market Risk: risk of loss resulting from movements in market prices. Market Risk consists of general market risk & specific risk General Market Risk: changes in market value of positions resulting from broad market movements; systematic risk Specific Risk: changes in market value of a position due to factors other than broad market movements; includes event & default risk as well as idiosyncratic risk Advanced Concepts in Capturing Market Risk: A Supervisory Perspective, Chicago, IL, March 14,

8 Contribution of the work of the Quantitative Modeling Team at FRBNY in collaboration with staff from the Board of Governors to review & assess SR VaR models for US bank holding companies in accordance with the current MRR 8

9 Variations in VaR Modeling Approaches 9

10 VaR Approaches: Aggregation of GMR &SR Two ways of computing Total VaR: Do not separate specific risk from general market (systematic) risk in model: compute Total VaR, which includes both systematic and idiosyncratic risk. Separate specific risk from systematic risk component in model: compute General Market Risk ( GMR ) VaR and Specific Risk ( SR ) VaR separately. Two main ways of combining GMR & SR into Total VaR: Sum VaR components; implies maximum correlations TotalVaR = GMR + SR Use square root rule; implies zero correlations 2 TotalVaR = ( GMR + SR 2 ) Advanced Concepts in Capturing Market Risk: A Supervisory Perspective, Chicago, IL, March 14,

11 Total VaR Calculation & Capital Implication Firm s Total VaR methodology leads to different capital implication Capital add-on required for partially modeled specific risk Capital add-on 1xSR-VaR, if SR and GMR are separated 1xTR-VaR, otherwise What have we seen? Capital Impact Total VaR Calculated without separating GMR and SR, TR-VaR Calculated by separating GMR and SR, GMR + SR Calculated by separating GMR and SR, 2 2 ( GMR + SR ) Capital Add-on TR-VaR SR-VaR SR-VaR Capital- Market Risk Measure {m* TR} +TR {m* (GMR+SR)} + SR 2 2 { m * ( GMR + SR )} + SR m is a multiplier, which depends on the number of exceptions 11

12 VaR Modeling: Historical vs Monte-Carlo Advanced Concepts in Capturing Market Risk: A Supervisory Perspective, Chicago, IL, March 14,

13 Length of Time Series & Frequency of Update Length of historical data, weighting scheme and data update frequency lead to differences in: Responsiveness of VaR to market volatility Capturing long-term vs current market conditions What have we seen? Length of historical data varies between 1 and 5 years - Heavy weight on recent data reacts quickly to changing market conditions, but forgets history - Longer historical period slow to react to market volatility, but remembers history better Frequency of data update - Daily data update - Less frequent (1 to 2 weeks) Advanced Concepts in Capturing Market Risk: A Supervisory Perspective, Chicago, IL, March 14,

14 Full Revaluation vs Risk Sensitivities Full revaluation: The firm s whole portfolio is fully revaluated at each historical shock w/o approximations - robust in capturing risk - requires increased computational resources Approximation: - Risk Sensitivities (Greeks), based on first or secondorder partial derivatives of Taylor expansion - effectiveness depends on the order considered - Grids, full revaluation at specific discrete points and interpolation between especially for non-linear products What have we seen? Full Revaluation Risk Sensitivities Use of full revaluation for majority of portfolios & products resulting in adequate VaR measure, VaR follows P&L Use of approximations (Taylor expansion & grids) resulting in VaR not always following P&L Advanced Concepts in Capturing Market Risk: A Supervisory Perspective, Chicago, IL, March 14,

15 Modeling of Risk Factors & Efficiency in Capturing Risk 15

16 Methods in Modeling Risk Factors What have we seen? Historical Simulations: risk factors defined per name proxies or benchmarks used for names for which data do not exist risk factors use their own time series- not decomposed into systematic & idiosyncratic components risk factors defined per cohort or basket of names risk factors decomposed into systematic & idiosyncratic components systematic component mapped into various market factors historical information provided for market factors Monte Carlo simulations used for specific risk: draws from empirical idiosyncratic distributions parametric modeling of specific risk, model parameters & inputs calibrated to market or to historical data Advanced Concepts in Capturing Market Risk: A Supervisory Perspective, Chicago, IL, March 14,

17 Completeness of Risk Capture Risk factors missing from VaR generally lack observability Common missing risk factors: Dividends*, implied volatility skew, implied correlation for equities** Recovery rate for correlation and structured products Index/tranche basis for index tranche products Index/bespoke basis for bespoke tranche products Less observable risk factors typically rely on proxies Examiners assess: Relevance of proxies Adequacy of proxy mapping Proper capture of basis risks * Some banks now incorporate dividend risk in VAR ** Some banks capture implied correlation for equities, but still industry-wide challenge Advanced Concepts in Capturing Market Risk: A Supervisory Perspective, Chicago, IL, March 14,

18 Examples of Products Reviewed for SR Equities: Linear, Non-Linear, Exotics, Baskets Credit Products: Bonds, CDSs, Indices, Options Correlation Products: Index Tranches, Bespoke CDO tranches, Index tranches of LCDS Structured Products: CDOs, CDO collateralized, 1 st & Nth to default, CDO^2, exotic CDO structures Resecuritization Products: Sub-prime single name CDSs, ABX &CMBX indices, single name CDSs of CMBS Loans: Loans, Loan CDSs, Loan indices Agencies: Agencies of MBSs, Agencies Pass-through Emerging Markets: Emerging market hard currency sovereigns, emerging market hard currency corporates, sovereign CDXs Advanced Concepts in Capturing Market Risk: A Supervisory Perspective, Chicago, IL, March 14,

19 What have we seen? Key Risk Factors in VaR Products Risk Factors Equities Price Implied Volatility Implied Correlation Key Risk Factors Captured in VaR Credit Products Default Intensities of single names & indices Credit Spreads of single names CDS/Bond basis Single Name/Index basis Correlation Products Default intensities of single names & indices Spreads of single names Correlations Advanced Concepts in Capturing Market Risk: A Supervisory Perspective, Chicago, IL, March 14,

20 What have we seen? Risk Factors not in VaR Products Missing Risk Factors Key Risk Factors not in VaR Equities Credit Products Dividend risk Implied volatility skew Implied volatility term structure Cross gamma risk Implied correlation Recovery risk Correlation Products Recovery risk Index/Tranche & Index/Bespoke basis for correlation products Advanced Concepts in Capturing Market Risk: A Supervisory Perspective, Chicago, IL, March 14,

21 Backtesting & Capital Implication 21

22 Backtesting Challenges VaR backtesting: comparison of daily VaR to actual daily trading P&L to measure number of exceptions (i.e., when P&L exceeds VaR). What have we seen? Length of historical data: varies from months to years. Holding period: 1-day across firms Trading P&L: Dirty P&L that includes fee income and commissions Clean P&L without fee income and commissions Hypothetical P&L with fixed portfolio with no intra-day trading Percentile: 95% & 99% Level of Aggregation Firm-wide level Portfolio level / Product level Advanced Concepts in Capturing Market Risk: A Supervisory Perspective, Chicago, IL, March 14,

23 Specific Risk Model Approval & Capital Implication Products not approved typically: - lack price observability - lack transparency in backtesting analysis - inefficient modeling due to use of approximations What have we seen? Examples of Internal Model vs Standardized Charge Internal Model Charge over Standardized Charge Varies form 6% to 64% Standardized Charge over Exposure (Fair Value or Gross Notional) Internal Model Charge over Exposure (Fair Value or Gross Notional) Varies from 3% to 22% Varies from.6% to 2.3% Advanced Concepts in Capturing Market Risk: A Supervisory Perspective, Chicago, IL, March 14,

24 Looking Forward to Revised Market Risk Rule 24

25 Stressed VaR Revised Market Risk Rule According to current MRR, stress tests are required to assess impact of adverse market conditions No specific stress scenarios are prescribed Revised Market Risk Rule include: Required additional new models for Stressed VaR (S-VaR) Optional models for Incremental Risk Charge (IRC) Comprehensive Risk Measure (CRM) Firms are working towards implementing revised requirements FRB will need to review bank holding companies for model compliance with revised MRR requirements Advanced Concepts in Capturing Market Risk: A Supervisory Perspective, Chicago, IL, March 14,

26 Revised Market Risk Measure for Capital Calculation Revised MRR: risk-based capital requirements for Market Risk is defined as the sum of: - VaR-based capital requirement - Stressed VaR-based capital requirement - Specific risk add-ons - Incremental risk capital requirement - Comprehensive risk capital requirement - Capital requirements for de minimis exposures Stressed VaR: 10-day, 99% percentile, use historical data from a continuous 12 month stress period Stronger Backtesting: P&L, emphasis on sub-portfolios Advanced Concepts in Capturing Market Risk: A Supervisory Perspective, Chicago, IL, March 14,

27 Conclusions Current MRR uses VaR-based market risk measure for capital requirements for US bank holding companies Techniques and approaches used by firms to calculate market risk vary Challenges in capturing all risk factors remain Revised MRR enhances market risk measure New challenges ahead Advanced Concepts in Capturing Market Risk: A Supervisory Perspective, Chicago, IL, March 14,

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