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Laurent MORTREUIL - Financial divisionJérôme BRUN - Market risk modelling

14 October 2011, Ljubljana, Fakulteta za matematiko in fiziko

Basel II.5 :The regulators' reply to the limits of

Value-at-Risk during the crisis

C2 | Basel II.5 - the reply to VaR weaknesses

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A bank is a financial institution that serves as a financial intermediary. As such, it is an organized community of persons, serving financial needs of people, communities and organisations.

Banks face a number of risks in order to conduct their business, and how well these risks are managed and understood is a key driver behind profitability, and how much capital a bank is required to hold. Some of the main risks faced by banks include:

Counterpartry risk: risk of loss arising from a borrower who does not make payments as promised.

Liquidity risk: risk that a given security or asset cannot be traded quickly enough in the market to prevent a loss (or make the required profit).

Market risk: risk that the value of a portfolio, either an investment portfolio or a trading portfolio, will decrease due to the change in value of the market risk factors.

Operational risk: risk arising from execution of a company's business functions.

Reputational risk: a type of risk related to the trustworthiness of business.

The capital requirement is a bank regulation, which sets a framework on how banks and depository institutions must handle their capital. The categorization of assets and capital is highly standardized so that it can be risk weighted

Introduction – What is a bank ?

C2 | Basel II.5 - the reply to VaR weaknesses

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Introduction – Relationship v/s transactionship

C2 | Basel II.5 - the reply to VaR weaknesses

Credit is the trust which allows one party to provide resources to another party where that second party does not reimburse the first party immediately (thereby generating a debt), but instead arranges either to repay or return those resources (or other materials of equal value) at a later date.

Movements of financial capital are normally dependent on either credit or equity transfers. Credit is in turn dependent on the reputation or creditworthiness of the entity which takes responsibility for the funds. Credit is also traded in financial markets.

Banking is at the crossroad of Time and Numbers

It is based on Human Behaviors, therefore depending on Expectations, Uncertainties, Statistics.

In order to make decisions, bankers rely on calculus, made possible by the development of Information Technologies, but based on strong mathematical assumptions which are often taken for granted.

This is only sustainable if it is secured by regulation, and pedagogy, and if the purpose of the Institution is well preserved : serving the financial needs for the common good and the full development of the persons.

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Since the 1990s, large flow of mathematicians to the trading floors

• Roughly 100 students per year are trained specifically for mathematical finance in Paris

Trigger : development of option market

• With their 1973 paper on the pricing of simple call/put options, Black & Scholes launched option pricing theory

• Option pricing is used for complex products with no observable price in the market

• Expectations are taken under the risk-neutral probability, which differs from the historical/physical probability: model parameters implied from today prices of observable products

Here we look at internal models

• developped by banks to compute risk-indicators reflecting a global risk for the bank portfolio

• Work under historical/physical probability: model parameters implied from historical series of prices of observable products

Not be confused with other models

• Forecasts

• Trading Strategies (automats)

• Etc.

Introduction – what models for capital markets ?

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Basel II.5 only deals with market risk, with an emphasis on issuer risk

Issuer risk is the credit risk of

• … the issuers of the bonds we hold

• … the underlying issuer of the CDSs where we buy/sell protection

Counterparty risk (RDC) is the credit risk of our counterparts for OTC derivatives

• RDC is addressed by Basel III: CVA, VaR on EEPE, etc.

Example:

• hold a bond issued by XYZ, or buy CDS protection on XYZ: issuer risk

• IR swap facing XYZ: counterparty risk

A reminder on credit risk : issuer risk vs. counterparty risk

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Up to now, RWA for market risk is based on VaR only

The 2007-2009 crisis highlighted weaknesses of VaR

July 2009: Basel Committee recommends new package capital charges = Basel II.5

• 3 new internal models added to VaR: Stressed VaR, IRC, CRM

July 2010: European Parliament votes the 3rd Capital Requirements Directive = CRD3

• CRD 3 = “traders” compensation + transcription of Basel requirements

• To be implemented before Q4 2011

Regulatory context

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Perimeter = Trading Book

Computation of the 1-day 99% VaR

• Definition :1-day loss that is exceeded only in 1% of the days, i.e. « 2.5 » times per year (250 days)

• SG uses historical approach:

▫ Apply to market parameters the 250 1-day shocks observed over the past year

▫ Compute the 250 P&L generated by these shocks VaR is the average between 2nd and 3rd worst

• Other banks use parametric approach (« Monte-Carlo VaR »)

▫ Shocks on market parameters are generated from a model

Link between VaR, Capital and RWA

• Regulator requires 10-day VaR ~ (square root of 10) x (1-day VaR)

• capital requirement = 10-day VaR x multiplier (>3, bank-specific, fixed by regulator)

• RWA « RDM » = capital requirement x 12.5

Bottom line matters:

• Realised P&L should be worse than VaR only 2-3 times per year

• Multiplier directly impacted by number of breaches

A reminder on VaR

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HHard facts: too many VaR breaches

• >20 for many banks in 2008

WWeakness #1: Pro-cyclicality

• VaR is small after a quiet year, high after a volatile year

Stressed VaR (Shocks taken on a fixed, stressed period)

WWeakness #2: Impact of sudden defaults is not captured

IRC (Incremental Risk Charge) + CRM (Comprehensive Risks Measure, specifically for exotic credit)

W

VaR weaknesses and Basel reply

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Perimeters impacted

Before Q4 2011 From Q4 2011

VaR x [3+]

Book with specific risk (credit and equity)

VaR x [3+]

Book withoutspecific risk

Stressed VaR x [4]

CRM

Equity book

Correlation trading portfolio

(CDO + CDS)

Other credit(bonds and CDSs

on corpo / fin / sov issuers)

IRC

Credit book

“Securitisation” (= all tranches except correl)

Standardised approach

14 Oct 2011C2 | Basel II.5 - the reply to VaR weaknesses

Book withoutspecific risk

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Stressed VaR

Stressed VaR = VaR “calibrated to historical data from a period of significant financial stress”

• Stress period must be “relevant to the firm’s portfolio”

• Fixed period (to be updated yearly)

• Typically : 2009

Very similar to VaR

• Same risk horizon (10 days), severity (99%), perimeter, multiplier (x5)

• Same computation, only the period for shock changes:

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01/10/2011 Portfolio / Market250 VaR shocksChosen 250 SVaR shocks

2007 2008 2009 2010 2011

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IRC & CRM – general principles

Capture P&L impact of rating migration and default

• Longer horizon : 1-year risk horizon

• High severity: 99,9% confidence level

• 1 day VaR to be breached 2-3 times per year, IRC to be breached every millenium

Perimeter

• CRM Correlation trading portfolio:

▫ CDOs on corporate portfolios

▫ CDSs used as hedge

• IRC All vanilla credit

▫ Bonds and CDS on corporates, financial and Sovereigns

▫ except CDSs used to hedge CDOs !

Risks covered

• IRC & CRM: migration and default

• CRM: also captures volatility of spreads, recovery rates, and credit correlations

CRM impact subject to floor = 8% of standardized approach

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IRC & CRM – focus on methodology

Start with scenarios of correlated migrations on the 2000+ issuers in book

• 99.9% = severity (every 1000 scenarios) need large number of scenarios ~1 million(vs. 250 for VaR)

• Transition matrix gives probabilities of migrating or defaulting over 1y, as a function of current rating

• Model ensures that migrations (and defaults) are correlated

In each scenario, get migration or default for each issuer

• E.g. : Peugeot: AAA, Renault: AAAA, Ford: BBDefault, etc.

• Migrations are translated into spread moves, generating P&L

• Names defaulting have a P&L equal to their Jump-to-Default

• Need to reprice full credit perimeter for each of the 1 million scenarios !

▫ In practice, we avoid full repricing via the use of sensitivities

CRM specificities (for CDOs and their hedge)

• Market moves are added to spread moves resulting from migrations.

• These market moves must account for correlation between “credit” and market

▫ Expect spread widening in scenarios with many downgrades/defaults

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IRC & CRM – illustration

Focus on scenario 1 (red, downgrade)

Final spread move in IRC results only from the migration from AA to BBB over the year

Higher spread move in CRM, as the move coming migration is combined with the move of the BBB spreads

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Summary of all internal models for market risk

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  Perimeter Captured risk Model Risk horizo

n

Severity Multiplier Pro-cyclical ?

VaR Trading book All market risks Historical VaR(shocks over past year)

10 days 99% [3+] Yes

SVaR Trading book All market risks Historical VaR (shocks over “worst” year)

10 days 99% [3+] No

IRC Vanilla credit book Rating migration& Default

Correlated migrations& defaults

1 year 99.9% 1 No

CRM Exotic credit books Rating migration& Default

& all market risks

Correlated migrations& Dynamics for credit market parameters

1 year 99.9% 1 No

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A revolution for the industry

• RWA “market risk” x4

• Total RWA (incl. “operational risk” & “counterparty risk”) x1.5

Competitive distortion

• US banks benefit from a 6-month delay on the implementation

• Asian banks not concerned ?

• Hedge funds (and brokers) will not be impacted

Incentive at industry level to reshape their business model• Shift towards equity, IRD, FX, commos (but beware of liquidity ratio)

• Alternatively, focus on activities eligible to regulatory banking book (govies…) ?

Conclusion

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Regulations tend to make our environment safer

It also puts a burden on the service that society expects from financial institutions.

But it will not ensure security without a dual change of perspective :

• Humility versus figures and numbers (by understanding the limits of their relevance)

• Personal commitment of all the actors (from providers to consummers) to use finance as a tool and not a goal ...

Conclusion

14 Oct 2011C2 | Basel II.5 - the reply to VaR weaknesses