Mark Staley Risk & Capital Modeling Group, Quantitative Analytics – Trading Risk April 2010 The Incremental Risk Charge in Basel II

1.Sticker Shock: The impact of the new rules 2.Summary of the new rules and their motivation: - Injecting capital into the system - removing capital arbitrage 3.IRC: challenges in measuring credit risk in the trading book 4.The future Agenda

Sticker Shock In October 2009, BIS published “Analysis of the Trading Book Quantitative Impact Study”.* The main findings, based on a survey of 43 banks across 10 countries (including TD Bank), were as follows:  Average (median) overall capital under the new rules increases by 11% (3%).  Average (median) trading book capital increases 223% (102%).  The biggest contributors are:  - Stress-VaR: Average (median) trading book increases 110% (63%)  - Incremental Risk Charge (IRC): average (median) trading book increases 103% (60.4%). This represents an increase in capital for “specific risk” by a factor of nine! *

Sticker Shock Note the wide variation: banks that previously developed debt- specific risk models are now seeing the biggest increases in IRC- capital.

Summary of the new rules Current Rules: Capital = max { GMR VaR, 3 X (average GMR VaR over 60 days) } + max { SR VaR, 4 X (average SR VaR over 60 days) } where GMR is “General market Risk” and SR is “Specific Risk”, both over 10 days, measured at the 99% confidence level. Note that GMR and SR is pro-rated based on correlated total. New Rules:* Capital = max {VaR, 3 X (average VaR over 60 days) } + max {Stress VaR, 3 X (average Stress VaR over 60 days) } + IRC where VaR is the combined GMR and SR (10-days, 99% VaR), Stress VaR is computed using data from a stressful period ( ), IRC is Credit VaR over one year at the 99.9% confidence level * Revisions to the Basel II market risk framework: Guidelines for computing capital for incremental risk:

Motivation for the new rules  Inject capital into the system: prevent a repeat of credit crisis, when banks did not have enough capital to prevent insolvency. As of Dec , the loss was $732 billion.* Hence the introduction of “Stress VaR”. *Source: Bloomberg

Motivation for the new rules  Prevent capital arbitrage: bank loans attract capital based on a one- year 99.9% VaR measure. This VaR model captures default risk and migration risk (through a “maturity adjustment factor”), and is calibrated to bank’s own “Through-the-Cycle” historical loss experience. This is much more punitive than capital requirements for credit exposures in the trading book (10-day VaR at 99% X 4). Up until now there has been an incentive to move assets off the balance sheet in order to save capital (witness the growth of securitization vehicles). Hence the introduction of “IRC”. The new rules are provisional and somewhat piecemeal; a more comprehensive set of guidelines (Basel 3) will undoubtedly appear in the future…

IRC Chronology of IRC  October 2007: BIS Proposal to model default risk in the trading book (IDR).  March 2008: Expansion to include migration, spread risk (IRC).  July 2009: Final BIS document on IRC covering default and migration risk, but not spread risk. Securitization removed from IRC  now covered under standardized approach, which is more conservative.  January 2010: BIS issues “FAQ on IRC”. One question was “Are sovereign exposures to be included in IRC?” Answer: “Yes.”  National regulators continue to press for other enhancements.  …..  Deadline for implementation: December 31, 2010.

IRC Credit portfolio modeling Portfolio Value at 1 year horizon Frequency Expected Loss (already captured in pricing – on balance sheet) Unexpected Loss Regulatory Capital 0.1% of samples Portfolio value at time 0

IRC CreditMetrics (1997)* The following risks are captured: Default risk Downgrade risk (rising spreads) Recovery risk Concentration risk (portfolio diversification and correlation risk) Note: The Basel II formula** for capital is based on the CreditMetrics model (in the limit of an infinitely granular portfolio) * ** Vasicek (2002), Risk. Gordy, M. B. (2003) A risk-factor model foundation for ratings-based bank capital rules. Journal of Financial Intermediation 12,

IRC CreditMetrics: Migration and Default Initial State: * Fixed rate loan, 5-year term * CAD * Subordinated * Obligor rating = AA --> spreads Value = discounted cash-flows Rating = AA (unchanged) --> no change in spreads --> no change in value Rating = A (downgrade) --> spreads go up --> value goes down Rating = AAA (upgrade) --> spreads go down --> value goes up Default --> subordinated: LGD=80% --> stdev of loss = 19% P=90% P=8% P=0.7% P=1 bps

IRC CreditMetrics: Default correlation Assets Value Probability of default Face-Value of Debt Threshold is

IRC Challenges Constant Level of Risk:  In the banking book, the minimum maturity is one year (e.g. revolving LOC).  We treat credit exposures in the banking book as “buy and hold”.  Trading exposures are not “buy and hold”. They are traded frequently.  BIS says that credit exposures should be modeled assuming a “constant level of risk”.  But a constant level of risk means no migrations and no defaults. How do we square this circle?

IRC Challenges Constant Level of Risk: In simulation we must take turns: 1. Allow for migrations and defaults during one interval of time. 2. Then reset all ratings to their original ratings. 3. Repeat. The first interval is called the “Liquidity Horizon”. The minimum liquidity horizon is three months.

IRC Challenges Constant Level of Risk: Challenges  What if an instrument matures before the liquidity horizon?  What if a credit default swap is more liquid than the underlying bond? How can one maintain different liquidity horizons while maintaining hedging properties on basis trades?  What is the sound of one hand clapping?

IRC Challenges Other Challenges: Migration and Default  How to treat Sovereign obligors differently from corporate obligors?  Should the probabilities of migration and default be based on “Through-the-Cycle” data or “Point-in-Time” data? Through-the-Cycle data would make IRC consistent with models in the banking book, but trading risk models are typically supposed to be more reactive to changing market conditions.

The Future Predictions for Basel 3  We will need to address “downturn LGD” and “PD/LGD correlation” in the trading book.  We will need to capture “Downturn PD”.  Correlation modeling will be emphasized.  All risks will need to be modeled over a one-year horizon: historical simulation will no longer be an option.  The diversification benefits between trading and banking will need to be modeled explicitly: this will necessitate the development of the “Mother of all Models”.