Advanced Concerts in Capturing Market Risk: A ... - ERM Symposium

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

Background 

Agenda 

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, 2011 

2

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 


3

Existing Market Risk Rule as implemented for US bank holding 

companies: requirements for Market Risk VaR measure 

4

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, 2011 5

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 


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 


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

Variations in VaR Modeling Approaches 

9

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 

) 


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 

What have we seen? 

Total VaR 

1xSR-VaR, if SR and GMR are separated 

1xTR-VaR, otherwise 

Calculated without 

separating GMR and SR, 

TR-VaR 

Capital Impact 

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 

m is a multiplier, which depends on the number of exceptions 

2 2 

{ m * ( GMR + SR ) } + SR 

11

VaR Modeling: Historical vs Monte-Carlo 


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 


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) 


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 


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 


14

Modeling of Risk Factors & Efficiency in 

Capturing Risk 

15

Methods in Modeling Risk Factors 


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 


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 


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 



Key Risk 

Factors 

Captured in 

VaR 

Key Risk Factors in VaR 

Products Risk Factors 

Equities 

Credit Products 

Correlation Products 

•Price 

• Implied Volatility 

• Implied Correlation 

• Default Intensities of single names & indices 

• Credit Spreads of single names 

• CDS/Bond basis 

• Single Name/Index basis 

• Default intensities of single names & indices 

• Spreads of single names 

• Correlations 



Key Risk 

Factors not in 

VaR 

Risk Factors not in VaR 

Products Missing Risk Factors 

Equities 

Credit Products 

Correlation Products 

• Dividend risk 

• Implied volatility skew 

• Implied volatility term structure 

• Cross gamma risk 

• Implied correlation 

• Recovery risk 

• Recovery risk 

• Index/Tranche & Index/Bespoke basis for 

correlation products 


Backtesting & Capital Implication 

21

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). 


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 


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 


Examples of Internal Model vs Standardized Charge 

Internal Model Charge over 

Standardized Charge 

Standardized Charge over Exposure 

(Fair Value or Gross Notional) 

Internal Model Charge over Exposure 

(Fair Value or Gross Notional) 

Varies form 6% to 64% 

Varies from 3% to 22% 

Varies from .6% to 2.3% 


Looking Forward to Revised Market Risk Rule 

24

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 


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 


26

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 Concerts in Capturing Market Risk: A ... - ERM Symposium

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?